The document discusses objectives and concepts related to statistical analysis in biology, including:
- Types of data, graphs, and statistical analyses such as mean, standard deviation, and chi square analysis.
- Calculating and interpreting the mean and standard deviation of a data set to describe variability.
- Using standard deviation to compare the spread of data between samples and determine significance.
- Performing hypothesis testing using calculated t values, t tables, and p values to determine if differences between data sets are statistically significant.
This document discusses a study that compared bill length in two species of hummingbirds: Archilochus colubris and Cynanthus latirostris. Researchers took measurements of 10 individuals of each species and calculated the mean and standard deviation. The mean bill length was 15.9mm for A. colubris and 18.8mm for C. latirostris. A. colubris had greater variability in its data (standard deviation of 1.91) compared to C. latirostris (1.03). A t-test showed a statistically significant difference between the means, allowing the researchers to reject the null hypothesis that there is no difference in bill length between the species.
1) The document discusses how surface area to volume ratio limits cell size. As cells increase in size, their volume increases much faster than their surface area.
2) A smaller surface area to volume ratio makes it more difficult for cells to exchange materials by diffusion with their surroundings.
3) Organisms with smaller sizes, such as microbes, have much higher surface area to volume ratios that allow for more efficient exchange of materials compared to larger organisms.
This slide explains term biostatistics, important terms used in the field of bio statistics and important applications of biostatistics in the field of agriculture, physiology, ecology, genetics, molecular biology, taxonomy, etc.
This document provides an overview of the key concepts around the chemistry of life that will be covered in AP Biology. It discusses how chemistry is the foundation of biology and explores some of the main topics including the elements that make up living things, bonding properties, macromolecules like carbohydrates and proteins, and polymers. It emphasizes that life requires around 25 essential chemical elements and that four elements - carbon, hydrogen, oxygen, and nitrogen - make up 96% of living matter. It also examines water's special properties including its role as the solvent of life and how hydrogen bonding allows it to moderate temperatures and transport nutrients in organisms.
The document discusses converting between moles, number of particles, and mass for various substances. It provides examples of calculating the mass of substances like magnesium and arsenic given a number of moles. The key steps shown are using the molar mass from the periodic table to convert between moles and mass, and using Avogadro's number to convert between number of particles and moles.
Introduction to Foundation of Chemistry 1M.T.H Group
This document provides an introduction to foundational concepts in organic chemistry. It begins with learning outcomes focusing on orbitals, bonding structures, and the periodic table. It then reviews electron configuration, atomic structure including shells and subshells. The document discusses hybridization and molecular shapes for sp, sp2, and sp3 including examples. It introduces ionic and covalent bonding, and how atoms bond to attain stable electron configurations. Key concepts are defined such as line angle formulas, Hund's rule, and octet rule. Exercises are provided to identify bonding types and draw Lewis structures.
IB Biology 4.1-4.2 Slides: Ecosystems & Energy FlowJacob Cedarbaum
This document discusses several ecological sampling and analysis techniques:
1) Quadrats are used to sample populations by placing frames randomly and counting organisms, providing estimates of population sizes.
2) Chi-squared testing analyzes associations between variables by calculating expected and observed frequencies in contingency tables and comparing a chi-squared value to a critical value.
3) Ecosystems cycle nutrients which flow through food chains and are recycled by decomposers to maintain sustainability.
Carbohydrates and lipids are both organic macromolecules composed of carbon, hydrogen and oxygen. Carbohydrates, such as starch and glycogen, are used for energy storage and structure in plants and animals. Lipids, including fats and oils, provide dense energy storage and make up cell membranes. Both molecule types are insoluble in water and made of long chains of monomers like glucose or fatty acids.
This document discusses a study that compared bill length in two species of hummingbirds: Archilochus colubris and Cynanthus latirostris. Researchers took measurements of 10 individuals of each species and calculated the mean and standard deviation. The mean bill length was 15.9mm for A. colubris and 18.8mm for C. latirostris. A. colubris had greater variability in its data (standard deviation of 1.91) compared to C. latirostris (1.03). A t-test showed a statistically significant difference between the means, allowing the researchers to reject the null hypothesis that there is no difference in bill length between the species.
1) The document discusses how surface area to volume ratio limits cell size. As cells increase in size, their volume increases much faster than their surface area.
2) A smaller surface area to volume ratio makes it more difficult for cells to exchange materials by diffusion with their surroundings.
3) Organisms with smaller sizes, such as microbes, have much higher surface area to volume ratios that allow for more efficient exchange of materials compared to larger organisms.
This slide explains term biostatistics, important terms used in the field of bio statistics and important applications of biostatistics in the field of agriculture, physiology, ecology, genetics, molecular biology, taxonomy, etc.
This document provides an overview of the key concepts around the chemistry of life that will be covered in AP Biology. It discusses how chemistry is the foundation of biology and explores some of the main topics including the elements that make up living things, bonding properties, macromolecules like carbohydrates and proteins, and polymers. It emphasizes that life requires around 25 essential chemical elements and that four elements - carbon, hydrogen, oxygen, and nitrogen - make up 96% of living matter. It also examines water's special properties including its role as the solvent of life and how hydrogen bonding allows it to moderate temperatures and transport nutrients in organisms.
The document discusses converting between moles, number of particles, and mass for various substances. It provides examples of calculating the mass of substances like magnesium and arsenic given a number of moles. The key steps shown are using the molar mass from the periodic table to convert between moles and mass, and using Avogadro's number to convert between number of particles and moles.
Introduction to Foundation of Chemistry 1M.T.H Group
This document provides an introduction to foundational concepts in organic chemistry. It begins with learning outcomes focusing on orbitals, bonding structures, and the periodic table. It then reviews electron configuration, atomic structure including shells and subshells. The document discusses hybridization and molecular shapes for sp, sp2, and sp3 including examples. It introduces ionic and covalent bonding, and how atoms bond to attain stable electron configurations. Key concepts are defined such as line angle formulas, Hund's rule, and octet rule. Exercises are provided to identify bonding types and draw Lewis structures.
IB Biology 4.1-4.2 Slides: Ecosystems & Energy FlowJacob Cedarbaum
This document discusses several ecological sampling and analysis techniques:
1) Quadrats are used to sample populations by placing frames randomly and counting organisms, providing estimates of population sizes.
2) Chi-squared testing analyzes associations between variables by calculating expected and observed frequencies in contingency tables and comparing a chi-squared value to a critical value.
3) Ecosystems cycle nutrients which flow through food chains and are recycled by decomposers to maintain sustainability.
Carbohydrates and lipids are both organic macromolecules composed of carbon, hydrogen and oxygen. Carbohydrates, such as starch and glycogen, are used for energy storage and structure in plants and animals. Lipids, including fats and oils, provide dense energy storage and make up cell membranes. Both molecule types are insoluble in water and made of long chains of monomers like glucose or fatty acids.
Okay, here are the steps:
1) Convert the mass percentages to grams of each element in 100 g of the compound:
K: 24.75% = 24.75 g
Mn: 34.77% = 34.77 g
O: 40.51% = 40.51 g
2) Calculate the moles of each element:
K: 24.75 g / 39.10 g/mol (molar mass of K) = 0.634 mol
Mn: 34.77 g / 54.94 g/mol (molar mass of Mn) = 0.634 mol
O: 40.51 g / 16.00 g/mol (molar mass of O)
This document discusses the key branches and importance of chemistry. The main branches covered are organic chemistry, inorganic chemistry, physical chemistry, biochemistry, and analytical chemistry. It emphasizes that chemistry is important to society and industry, with applications in areas like materials development, medicine, and consumer products. A variety of career paths are available to chemists across sectors like industry, teaching, healthcare, law and more.
This document discusses various types of macromolecules including carbohydrates, lipids, proteins, and nucleic acids. It begins by defining biochemistry and explaining that it studies the chemical reactions that occur in living organisms, focusing on substances like enzymes, hormones, carbohydrates, proteins, lipids, DNA and RNA. It then discusses the importance of biochemistry in pharmacy and nursing, explaining how it helps understand drug constitution, metabolism, storage and biochemical tests. The document proceeds to discuss carbohydrates in depth, explaining their classification into mono-, di-, oligo- and polysaccharides. It provides examples and functions of important carbohydrates like glucose, fructose, starch and cellulose. Finally, it briefly introduces lipids and
Within species, there is usually a great deal of variation between individuals. Variations can be inherited through genes or acquired through environmental factors and experiences over a lifetime. Inherited variations are genetically controlled and cannot be changed, while acquired variations are influenced by activities, nutrition, and environment during one's life. Examples of inherited variations include hair and eye color, while acquired variations include skills, behaviors, and physical characteristics developed over time like tanning or obesity. Both genetic and environmental factors influence many traits exhibiting continuous variation, where there is a range of possible expressions between extremes. Height is an example that depends on both inherited genes and acquired nutrition.
The document is a daily lesson log for a 9th grade science class. Over the course of a week, the class will cover topics related to biodiversity and species extinction. They will learn about population density, endangered species, and environmental issues that contribute to species extinction. The class will make a multimedia timeline presentation on the extinction of organisms and take a summative test on biodiversity and evolution.
Covalent bonds form when atoms share valence electrons in order to achieve stable electron configurations like the noble gases. Atoms form single, double or triple covalent bonds by sharing one, two or three pairs of electrons. Molecular compounds are held together by covalent bonds and have lower melting and boiling points than ionic compounds. Molecular formulas show the types and numbers of atoms in a molecule but not their arrangement, which can be represented using structural formulas.
IB Biology 3.5 genetic modifcation and biotechnologyBob Smullen
Here is a possible design for an experiment to assess one factor affecting the rooting of stem cuttings:
- Plant species chosen: Coleus canina (common name cut-leaf coleus), which is known to form roots readily from stem cuttings.
- Factor to be tested: Effect of auxin treatment on root formation.
- Materials: Coleus canina stem cuttings, water, rooting hormone powder containing auxin (IBA).
- Methods: Take stem cuttings of uniform size and remove lower leaves. Dip half the cuttings in auxin powder solution and half in water only. Insert all cuttings in potting soil. Maintain soil moisture and observe over 4 weeks.
The document defines key terms related to chemical equations:
- Chemical reactions represent changes where reactants are converted to products through chemical changes.
- Chemical equations express reactions using formulas, numbers, and symbols to represent reactants and products.
- Coefficients indicate the number of atoms or molecular units of each substance involved in the reaction.
The document summarizes key aspects of human digestion and nutrition. It describes the five stages of food processing: ingestion, digestion, absorption, assimilation, and egestion. It details the organs and structures involved in digestion, including the oral cavity, esophagus, stomach, small intestine, large intestine, liver, and pancreas. It explains the roles of enzymes and hormones in breaking down food and regulating digestion. The document also covers nutrient absorption in the small intestine and discusses nutrition, including energy sources, vitamins, minerals, and essential nutrients required in the diet.
Atomic Models: Everything You Need to Knowjane1015
The document traces the development of atomic models from ancient Greek philosophers to modern quantum mechanics. It describes early ideas that atoms were indivisible spheres (Democritus), John Dalton's model of atoms as hard spheres, J.J. Thomson's "plum pudding" model with electrons in a positively charged substance, Ernest Rutherford's discovery of the nucleus from his gold foil experiment, Niels Bohr's model with electrons in specific energy levels around the nucleus, and the modern wave model where electrons exist as probability clouds.
Statistics can be misused in several ways: by using small, non-random samples; reporting averages that don't accurately represent the data; changing values to misrepresent facts; making claims without proper context or comparison; implying connections that aren't supported; or using misleading visuals. Common statistical misuses include using small samples to draw broad conclusions, citing a mean when the median is more relevant, changing a percentage to an absolute value to distort perceptions, making claims without a baseline for comparison, implying causal relationships not supported by evidence, and graphs that mislead viewers.
There are four main classes of biological macromolecules: proteins, lipids, carbohydrates, and nucleic acids. The document provides information about each macromolecule including what they are made of, where they are found, and their functions. It also discusses that carbohydrates, lipids, and proteins can be used by the body for energy, while nucleic acids do not provide energy.
This document provides an overview of the key topics in genetics. It discusses the history and founders of genetics from Darwin's theory of evolution to modern discoveries like the structure of DNA. It outlines the major fields in genetics including transmission genetics, molecular and biochemical genetics, and population genetics. It also provides examples of applications of genetics in agriculture, medicine, forensics, industries, humans, and the environment.
This document discusses Mendelian genetics and inheritance patterns. It covers Mendel's experiments with pea plants and his principles of inheritance, including dominance, segregation, independent assortment, and probability. It introduces modern genetic terminology and genetic crosses such as monohybrid, dihybrid, and test crosses. It also discusses how Mendel's principles apply to human pedigrees and inheritance of traits, including examples of autosomal recessive and dominant traits like familial hypercholesterolemia.
This document contains a chemistry lesson on molar mass. It defines molar mass as the sum of the atomic masses in a molecule. It provides examples of calculating the molar mass of different compounds by adding up the atomic masses of each element. The lesson concludes by having students practice calculating molar masses in groups and answering an exit slip with questions.
1) Miller and Urey conducted experiments in 1953 that simulated early Earth conditions and found that organic molecules like amino acids could form spontaneously from inorganic precursors.
2) RNA may have played an early role in the origin of life on Earth as it can both store genetic information and catalyze chemical reactions through ribozymes.
3) The endosymbiotic theory proposes that mitochondria and chloroplasts were once free-living prokaryotes that were engulfed by larger cells and evolved to become cellular organelles.
This document outlines a lesson plan on genetic engineering that includes activities and videos. It will begin with having students pretend they have the "warrior gene" and watching a video on it. They will then learn about how cloning is used to purify DNA and isolate genes. The process of cloning a gene will be illustrated by cutting DNA with enzymes, inserting it into a vector, and transforming bacteria. Later, the class will watch several videos on topics like DNA sequencing, gene chips, using sequencing to diagnose rare diseases, and genetically modifying T-cells to cure leukemia. If time allows, the lesson will cover using biotechnology in plants through techniques like PCR and DNA markers to select for traits in plant breeding.
Diffusion will occur from areas of higher concentration to lower concentration. Molecules will diffuse into and out of cells down their concentration gradients, without requiring energy expenditure by the cell. The cell membrane is selectively permeable, allowing some molecules like sugars to pass through, driving diffusion across the membrane.
Water is essential for life and makes up about two-thirds of the human body. It has no taste or smell and exists in solid, liquid, and gas forms. Water regulates body temperature, transports nutrients and waste, cushions joints, and maintains pH levels. The pH scale measures hydrogen ion concentration from 0-14, with 7 being neutral. Acids donate protons and have a pH below 7, while bases accept protons and have a pH above 7. Buffers resist pH changes and are important for biological processes.
This document outlines objectives and concepts for a unit on statistical analysis in IB Diploma Biology. It discusses types of data, graphs, and statistics including mean, standard deviation, correlation, and significance testing. Key concepts covered are descriptive statistics like mean and standard deviation to summarize data, the importance of variability, and inferential statistics like hypothesis testing and p-values to draw conclusions about populations from samples. The goals are to calculate basic statistics, choose appropriate graphs, understand significance, and apply proper lab techniques and formats.
This document provides an introduction to biostatistics. It outlines several key objectives of a biostatistics course including understanding descriptive statistics, statistical inference, common tests and their assumptions. It defines important statistical concepts like population, sample, parameters, statistics, variables, and types of statistical analysis. Descriptive statistics are used to summarize data, while inferential statistics allow generalizing from samples to populations. Examples of potential statistical abuses are also provided.
Okay, here are the steps:
1) Convert the mass percentages to grams of each element in 100 g of the compound:
K: 24.75% = 24.75 g
Mn: 34.77% = 34.77 g
O: 40.51% = 40.51 g
2) Calculate the moles of each element:
K: 24.75 g / 39.10 g/mol (molar mass of K) = 0.634 mol
Mn: 34.77 g / 54.94 g/mol (molar mass of Mn) = 0.634 mol
O: 40.51 g / 16.00 g/mol (molar mass of O)
This document discusses the key branches and importance of chemistry. The main branches covered are organic chemistry, inorganic chemistry, physical chemistry, biochemistry, and analytical chemistry. It emphasizes that chemistry is important to society and industry, with applications in areas like materials development, medicine, and consumer products. A variety of career paths are available to chemists across sectors like industry, teaching, healthcare, law and more.
This document discusses various types of macromolecules including carbohydrates, lipids, proteins, and nucleic acids. It begins by defining biochemistry and explaining that it studies the chemical reactions that occur in living organisms, focusing on substances like enzymes, hormones, carbohydrates, proteins, lipids, DNA and RNA. It then discusses the importance of biochemistry in pharmacy and nursing, explaining how it helps understand drug constitution, metabolism, storage and biochemical tests. The document proceeds to discuss carbohydrates in depth, explaining their classification into mono-, di-, oligo- and polysaccharides. It provides examples and functions of important carbohydrates like glucose, fructose, starch and cellulose. Finally, it briefly introduces lipids and
Within species, there is usually a great deal of variation between individuals. Variations can be inherited through genes or acquired through environmental factors and experiences over a lifetime. Inherited variations are genetically controlled and cannot be changed, while acquired variations are influenced by activities, nutrition, and environment during one's life. Examples of inherited variations include hair and eye color, while acquired variations include skills, behaviors, and physical characteristics developed over time like tanning or obesity. Both genetic and environmental factors influence many traits exhibiting continuous variation, where there is a range of possible expressions between extremes. Height is an example that depends on both inherited genes and acquired nutrition.
The document is a daily lesson log for a 9th grade science class. Over the course of a week, the class will cover topics related to biodiversity and species extinction. They will learn about population density, endangered species, and environmental issues that contribute to species extinction. The class will make a multimedia timeline presentation on the extinction of organisms and take a summative test on biodiversity and evolution.
Covalent bonds form when atoms share valence electrons in order to achieve stable electron configurations like the noble gases. Atoms form single, double or triple covalent bonds by sharing one, two or three pairs of electrons. Molecular compounds are held together by covalent bonds and have lower melting and boiling points than ionic compounds. Molecular formulas show the types and numbers of atoms in a molecule but not their arrangement, which can be represented using structural formulas.
IB Biology 3.5 genetic modifcation and biotechnologyBob Smullen
Here is a possible design for an experiment to assess one factor affecting the rooting of stem cuttings:
- Plant species chosen: Coleus canina (common name cut-leaf coleus), which is known to form roots readily from stem cuttings.
- Factor to be tested: Effect of auxin treatment on root formation.
- Materials: Coleus canina stem cuttings, water, rooting hormone powder containing auxin (IBA).
- Methods: Take stem cuttings of uniform size and remove lower leaves. Dip half the cuttings in auxin powder solution and half in water only. Insert all cuttings in potting soil. Maintain soil moisture and observe over 4 weeks.
The document defines key terms related to chemical equations:
- Chemical reactions represent changes where reactants are converted to products through chemical changes.
- Chemical equations express reactions using formulas, numbers, and symbols to represent reactants and products.
- Coefficients indicate the number of atoms or molecular units of each substance involved in the reaction.
The document summarizes key aspects of human digestion and nutrition. It describes the five stages of food processing: ingestion, digestion, absorption, assimilation, and egestion. It details the organs and structures involved in digestion, including the oral cavity, esophagus, stomach, small intestine, large intestine, liver, and pancreas. It explains the roles of enzymes and hormones in breaking down food and regulating digestion. The document also covers nutrient absorption in the small intestine and discusses nutrition, including energy sources, vitamins, minerals, and essential nutrients required in the diet.
Atomic Models: Everything You Need to Knowjane1015
The document traces the development of atomic models from ancient Greek philosophers to modern quantum mechanics. It describes early ideas that atoms were indivisible spheres (Democritus), John Dalton's model of atoms as hard spheres, J.J. Thomson's "plum pudding" model with electrons in a positively charged substance, Ernest Rutherford's discovery of the nucleus from his gold foil experiment, Niels Bohr's model with electrons in specific energy levels around the nucleus, and the modern wave model where electrons exist as probability clouds.
Statistics can be misused in several ways: by using small, non-random samples; reporting averages that don't accurately represent the data; changing values to misrepresent facts; making claims without proper context or comparison; implying connections that aren't supported; or using misleading visuals. Common statistical misuses include using small samples to draw broad conclusions, citing a mean when the median is more relevant, changing a percentage to an absolute value to distort perceptions, making claims without a baseline for comparison, implying causal relationships not supported by evidence, and graphs that mislead viewers.
There are four main classes of biological macromolecules: proteins, lipids, carbohydrates, and nucleic acids. The document provides information about each macromolecule including what they are made of, where they are found, and their functions. It also discusses that carbohydrates, lipids, and proteins can be used by the body for energy, while nucleic acids do not provide energy.
This document provides an overview of the key topics in genetics. It discusses the history and founders of genetics from Darwin's theory of evolution to modern discoveries like the structure of DNA. It outlines the major fields in genetics including transmission genetics, molecular and biochemical genetics, and population genetics. It also provides examples of applications of genetics in agriculture, medicine, forensics, industries, humans, and the environment.
This document discusses Mendelian genetics and inheritance patterns. It covers Mendel's experiments with pea plants and his principles of inheritance, including dominance, segregation, independent assortment, and probability. It introduces modern genetic terminology and genetic crosses such as monohybrid, dihybrid, and test crosses. It also discusses how Mendel's principles apply to human pedigrees and inheritance of traits, including examples of autosomal recessive and dominant traits like familial hypercholesterolemia.
This document contains a chemistry lesson on molar mass. It defines molar mass as the sum of the atomic masses in a molecule. It provides examples of calculating the molar mass of different compounds by adding up the atomic masses of each element. The lesson concludes by having students practice calculating molar masses in groups and answering an exit slip with questions.
1) Miller and Urey conducted experiments in 1953 that simulated early Earth conditions and found that organic molecules like amino acids could form spontaneously from inorganic precursors.
2) RNA may have played an early role in the origin of life on Earth as it can both store genetic information and catalyze chemical reactions through ribozymes.
3) The endosymbiotic theory proposes that mitochondria and chloroplasts were once free-living prokaryotes that were engulfed by larger cells and evolved to become cellular organelles.
This document outlines a lesson plan on genetic engineering that includes activities and videos. It will begin with having students pretend they have the "warrior gene" and watching a video on it. They will then learn about how cloning is used to purify DNA and isolate genes. The process of cloning a gene will be illustrated by cutting DNA with enzymes, inserting it into a vector, and transforming bacteria. Later, the class will watch several videos on topics like DNA sequencing, gene chips, using sequencing to diagnose rare diseases, and genetically modifying T-cells to cure leukemia. If time allows, the lesson will cover using biotechnology in plants through techniques like PCR and DNA markers to select for traits in plant breeding.
Diffusion will occur from areas of higher concentration to lower concentration. Molecules will diffuse into and out of cells down their concentration gradients, without requiring energy expenditure by the cell. The cell membrane is selectively permeable, allowing some molecules like sugars to pass through, driving diffusion across the membrane.
Water is essential for life and makes up about two-thirds of the human body. It has no taste or smell and exists in solid, liquid, and gas forms. Water regulates body temperature, transports nutrients and waste, cushions joints, and maintains pH levels. The pH scale measures hydrogen ion concentration from 0-14, with 7 being neutral. Acids donate protons and have a pH below 7, while bases accept protons and have a pH above 7. Buffers resist pH changes and are important for biological processes.
This document outlines objectives and concepts for a unit on statistical analysis in IB Diploma Biology. It discusses types of data, graphs, and statistics including mean, standard deviation, correlation, and significance testing. Key concepts covered are descriptive statistics like mean and standard deviation to summarize data, the importance of variability, and inferential statistics like hypothesis testing and p-values to draw conclusions about populations from samples. The goals are to calculate basic statistics, choose appropriate graphs, understand significance, and apply proper lab techniques and formats.
This document provides an introduction to biostatistics. It outlines several key objectives of a biostatistics course including understanding descriptive statistics, statistical inference, common tests and their assumptions. It defines important statistical concepts like population, sample, parameters, statistics, variables, and types of statistical analysis. Descriptive statistics are used to summarize data, while inferential statistics allow generalizing from samples to populations. Examples of potential statistical abuses are also provided.
This document discusses various statistical concepts including outliers, transforming data, normalizing data, weighting data, robustness, and homoscedasticity and heteroscedasticity. Outliers are values far from other data points and should be carefully examined before removing. Data can be transformed using logarithms, square roots, or other functions to better fit a normal distribution or equalize variances between groups. Normalizing data puts variables on comparable scales. Weighting data adjusts for under- or over-representation in samples. Robust tests are resistant to violations of assumptions. Homoscedasticity refers to equal variances between groups while heteroscedasticity refers to unequal variances.
Descriptive analysis and descriptive analytics involve examining and summarizing data using techniques like charts, graphs, and narratives to identify patterns. Common visualization tools include pie charts, bar charts, histograms, and more. Tableau, Excel, and Datawrapper are popular tools that allow users to import data and generate various visualizations. Queries allow users to sort, filter, and extract specific information from large datasets using clauses like ORDER BY and WHERE. Hypothesis testing uses the null and alternative hypotheses to determine if experimental results are statistically significant or due to chance. Analysis of variance (ANOVA) specifically tests hypotheses by comparing means across independent groups.
The use of data and its modelling in science provides meaningful interpretation of real world problems. This presentation provides an easy to understand overview of data visualization and analytics , and snippets of data science applications using R - programming.
This document discusses descriptive and inferential statistics. Descriptive statistics summarize and organize data through frequency distributions, graphs, and summary statistics like the mean, median, mode, variance, and standard deviation. Inferential statistics allow generalization from samples to populations through hypothesis testing, where the null hypothesis is tested against the alternative hypothesis. Type I and type II errors are possible, and significance tests control the probability of type I errors through the alpha level while power analysis aims to reduce type II errors. Common inferential tests mentioned include t-tests, ANOVA, and meta-analysis.
The document discusses hypothesis testing and the scientific research process. It begins by defining a hypothesis as a tentative statement about the relationship between two or more variables that can be tested. It then outlines the typical steps in the scientific research process, which includes forming a question, background research, creating a hypothesis, experiment design, data collection, analysis, conclusions, and communicating results. Finally, it provides details on characteristics of a strong hypothesis, the process of hypothesis testing through statistical analysis, and setting up an experiment for hypothesis testing, including defining hypotheses, significance levels, sample size determination, and calculating standard deviation.
This document provides an overview and summary of key concepts from chapters 10 and 11 of the book "How to Design and Evaluate Research in Education". It discusses both descriptive and inferential statistics. For descriptive statistics, it defines common measures like mean, median, standard deviation, and explains how they are used to summarize sample data. For inferential statistics, it outlines statistical techniques like hypothesis testing, confidence intervals, and parametric and nonparametric tests that allow researchers to generalize from samples to populations. It provides examples of how these statistical concepts are applied in educational research.
Descriptive And Inferential Statistics for Nursing Researchenamprofessor
This document provides an overview of descriptive and inferential statistics. Descriptive statistics summarize and organize data through frequency distributions, graphs, measures of central tendency, and measures of variability. Inferential statistics allow generalization from samples to populations through hypothesis testing, which involves specifying a null hypothesis and alternative hypothesis. Statistical significance is determined by calculating a p-value and rejecting the null hypothesis if the p-value is less than a predetermined alpha level, typically 0.05. Type I and type II errors can occur in hypothesis testing.
This document provides an overview of descriptive and inferential statistics. Descriptive statistics summarize and organize data through frequency distributions, graphs, measures of central tendency, and measures of variability. Inferential statistics allow generalization from samples to populations through hypothesis testing, which involves specifying a null hypothesis and alternative hypothesis. Statistical significance is determined by calculating a p-value and comparing it to the significance level alpha to either reject or fail to reject the null hypothesis, with Type I and Type II errors a possibility. Common inferential tests include t-tests, ANOVAs, and meta-analyses.
The document discusses various steps involved in analyzing and interpreting data, including developing an analysis plan, collecting and cleaning data, analyzing the data using appropriate techniques, interpreting the results by drawing conclusions and recommendations while also considering limitations. It provides examples of different analysis techniques like descriptive statistics, inferential statistics, and qualitative data analysis and emphasizes the importance of interpreting data in the context of the research questions.
1) Statistics is the science of collecting, analyzing, and drawing conclusions from data. It is used to understand populations based on samples since directly measuring entire populations is often impossible.
2) There are two main types of data: qualitative data which relates to descriptive characteristics, and quantitative data which can be expressed numerically. Common statistical analyses include calculating the mean, standard deviation, and using t-tests, ANOVA, correlation, and chi-squared tests.
3) Statistical analyses allow researchers to determine uncertainties in measurements, compare groups, identify relationships between variables, and assess whether observed differences are likely due to chance or a factor being studied. Key concepts include null and alternative hypotheses, p-values, and effect size.
This document provides an overview of quantitative data analysis methods for medical education research. It discusses summary measures, hypothesis testing, statistical methodologies, sample size determination, and additional resources for statistical support. Key points covered include choosing appropriate statistical tests based on study design, translating research questions into testable hypotheses, interpreting p-values and making conclusions, and factors that influence required sample size such as effect size and variability.
Introduction to Statistics53004300.pptTripthiDubey
This document provides an introduction to descriptive statistics and measures of central tendency. It discusses the difference between descriptive statistics of a population versus inferential statistics of samples. It then describes three common measures of central tendency: the mean, median, and mode. It explains how to calculate each measure and the advantages and disadvantages of each. The document concludes by discussing different types of graphs that can be used to organize and present descriptive statistics, including histograms, pie charts, line graphs, and scatter plots.
This document provides an introduction to statistics and biostatistics in healthcare. It defines statistics and biostatistics, outlines the basic steps of statistical work, and describes different types of variables and methods for collecting data. The document also discusses different types of descriptive and inferential statistics, including measures of central tendency, dispersion, frequency, t-tests, ANOVA, regression, and different types of plots/graphs. It explains how statistics is used in healthcare for areas like disease burden assessment, intervention effectiveness, cost considerations, evaluation frameworks, health care utilization, resource allocation, needs assessment, quality improvement, and product development.
This document summarizes an R boot camp focusing on statistics. It includes an agenda that covers introducing the lab component, R basics, descriptive statistics in R, revisiting installation instructions, and measures of variability in R. Descriptive statistics are presented as ways to characterize data through measures of central tendency, shape, and variability. Examples are provided in R for calculating the mean, median, mode, range, percentiles, variance, standard deviation, and coefficient of variation. The central limit theorem and standardizing scores are also discussed. Real-world applications of R for clean and messy data are mentioned.
This document provides an introduction to statistics for data science. It discusses why statistics are important for processing and analyzing data to find meaningful trends and insights. Descriptive statistics are used to summarize data through measures like mean, median, and mode for central tendency, and range, variance, and standard deviation for variability. Inferential statistics make inferences about populations based on samples through hypothesis testing and other techniques like t-tests and regression. The document outlines the basic terminology, types, and steps of statistical analysis for data science.
Statistical concepts and their applications in various fields:
- Statistics involves collecting and analyzing numerical data to draw valid conclusions. It requires careful research planning and design.
- Descriptive statistics summarize data through measures of central tendency (mean, median, mode) and variability (range, standard deviation).
- Inferential statistics test hypotheses and make estimates about populations based on samples.
- Biostatistics is applied in community medicine, public health, cancer research, pharmacology, and demography to study disease trends, treatment effectiveness, and population attributes. It is also used in advanced biomedical technologies and ecology.
Get ready to face Data Science interviews with this set of Statistics questions. This will help you have insight upon the important statistics concepts that are frequently asked in interviews.
The document discusses the origin of the first cells on Earth. It states that cells can only be formed through the division of pre-existing cells, so the first cells must have arisen from non-living material through a process known as abiogenesis. Abiogenesis likely occurred in four stages: 1) the non-living synthesis of simple organic molecules, 2) the assembly of these molecules into complex polymers, 3) the development of polymers that could self-replicate, and 4) the encapsulation of these molecules within membranes. Early Earth had a reducing atmosphere containing gases like hydrogen, nitrogen, and methane that could have contributed to the non-living synthesis of organic compounds from which the first cells developed.
Membranes control the composition of cells through active and passive transport. Materials move across membranes via simple diffusion, facilitated diffusion, osmosis, and active transport. The sodium-potassium pump uses active transport to move ions against their gradients in axons. Vesicles transport materials within cells from the ER to the Golgi and plasma membrane by budding off and fusing. Endocytosis transports materials into cells while exocytosis releases them out of cells.
Membranes control the composition of cells through active and passive transport. Passive transport involves diffusion of substances down a concentration gradient and does not require energy. There are three main types of passive transport: simple diffusion of small molecules, osmosis of water molecules, and facilitated diffusion of larger molecules via membrane proteins. Active transport moves substances against a concentration gradient and requires energy. Membranes play a key role in cellular function by regulating what passes in and out of cells.
The structure of biological membranes allows them to be fluid and dynamic. Membranes are made of a phospholipid bilayer with proteins and cholesterol embedded within. Phospholipids form bilayers due to their amphipathic properties - their hydrophobic tails orient inward while hydrophilic heads remain on the outer surfaces. Membrane proteins perform diverse functions and can be integral or peripheral. Cholesterol increases membrane stability while reducing fluidity. Early models of membrane structure proposed protein layers sandwiching the bilayer, but evidence demonstrated proteins are mobile within the bilayer, leading to the current fluid mosaic model.
The document discusses membrane transport mechanisms, including passive transport processes like simple diffusion, facilitated diffusion, and osmosis as well as active transport. It provides examples of sodium-potassium pumps, potassium channels, and vesicles. The importance of osmotic control in medical procedures is highlighted. Summaries of laboratory techniques for estimating osmolarity in tissues are also included.
The structure of biological membranes allows them to be fluid and dynamic. Phospholipid molecules spontaneously arrange into a bilayer structure in water due to their amphipathic properties. This structure orients the hydrophobic tails of the phospholipids inward, shielded from water, while the hydrophilic heads remain in contact with water. Additional components such as membrane proteins and cholesterol are embedded within the phospholipid bilayer and influence membrane properties such as fluidity. Cholesterol increases the packing of phospholipids and regulates membrane fluidity and permeability.
Eukaryotic cells have a more complex structure than prokaryotic cells due to compartmentalization by membrane-bound organelles. An electron micrograph of pancreatic exocrine cells clearly shows organelles such as the nucleus, mitochondria, rough endoplasmic reticulum, Golgi apparatus, and vesicles. These organelles have specialized functions, for example the nucleus contains genetic material, mitochondria produce ATP through respiration, and the endoplasmic reticulum and Golgi apparatus are involved in protein transport and modification.
1. The cell theory states that all living things are composed of cells, cells are the basic unit of structure and function in living things, and new cells are produced from existing cells.
2. Unicellular organisms carry out all the functions of life within a single cell, including metabolism, reproduction, response to stimuli, homeostasis, excretion, nutrition, and growth. These functions can be observed in organisms like Paramecium and Chlorella through processes like contracting vacuoles and photosynthesis.
3. As cells increase in size, their surface area to volume ratio decreases, limiting their ability to exchange materials and wastes. This limitation on cell size is an important factor in the cell theory.
हिंदी वर्णमाला पीपीटी, hindi alphabet PPT presentation, hindi varnamala PPT, Hindi Varnamala pdf, हिंदी स्वर, हिंदी व्यंजन, sikhiye hindi varnmala, dr. mulla adam ali, hindi language and literature, hindi alphabet with drawing, hindi alphabet pdf, hindi varnamala for childrens, hindi language, hindi varnamala practice for kids, https://www.drmullaadamali.com
Thinking of getting a dog? Be aware that breeds like Pit Bulls, Rottweilers, and German Shepherds can be loyal and dangerous. Proper training and socialization are crucial to preventing aggressive behaviors. Ensure safety by understanding their needs and always supervising interactions. Stay safe, and enjoy your furry friends!
How to Manage Your Lost Opportunities in Odoo 17 CRMCeline George
Odoo 17 CRM allows us to track why we lose sales opportunities with "Lost Reasons." This helps analyze our sales process and identify areas for improvement. Here's how to configure lost reasons in Odoo 17 CRM
Physiology and chemistry of skin and pigmentation, hairs, scalp, lips and nail, Cleansing cream, Lotions, Face powders, Face packs, Lipsticks, Bath products, soaps and baby product,
Preparation and standardization of the following : Tonic, Bleaches, Dentifrices and Mouth washes & Tooth Pastes, Cosmetics for Nails.
Executive Directors Chat Leveraging AI for Diversity, Equity, and InclusionTechSoup
Let’s explore the intersection of technology and equity in the final session of our DEI series. Discover how AI tools, like ChatGPT, can be used to support and enhance your nonprofit's DEI initiatives. Participants will gain insights into practical AI applications and get tips for leveraging technology to advance their DEI goals.
How to Build a Module in Odoo 17 Using the Scaffold MethodCeline George
Odoo provides an option for creating a module by using a single line command. By using this command the user can make a whole structure of a module. It is very easy for a beginner to make a module. There is no need to make each file manually. This slide will show how to create a module using the scaffold method.
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.
How to Fix the Import Error in the Odoo 17Celine George
An import error occurs when a program fails to import a module or library, disrupting its execution. In languages like Python, this issue arises when the specified module cannot be found or accessed, hindering the program's functionality. Resolving import errors is crucial for maintaining smooth software operation and uninterrupted development processes.
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar Kanvaria
2. Objectives of this Unit:
Types of Data, Types of Graphs, Applications and Statistics to match your data
o Bar Graphs, Line Graph, Scatter Plot, Histogram, Pie Chart
o Mean, S.D., Regression, Chi Square Analysis
State that error bars are a graphical representation of the variability of data
o Range and standard deviation show the variability/spread in the data
Calculate the mean and standard deviation of a set of values
Using Excel formulas
o Given a mean and S.D. state the range for different parameters
State the term standard deviation is used to summarize the spread of values around the mean
o 68% of all data +/- 1 standard deviation, 95% within 2 SD
Explain how S.D. is useful for comparing the means and spread of data between two or more
samples
o Greater S.D. shows greater variability of data
o This can be used to inter reliability in methods or results BUT in Biology we also expect
variability
Deduce the significance of the difference between two sets of data using calculated values for t and
tables
o Using t value and t table and critical values
o Directly calculating P values using excel in lab reports
o Difference between P and T
Explain that correlation does not establish that there is a causal relationship between two variables
Proper Lab Format
Designing Lab Process
3. What are statistics?
• Statistics are numbers used to:
Describe and draw conclusions about DATA
• These are called descriptive (or “univariate”) and
inferential (or “analytical”) statistics, respectively.
4. Variables
• A variable is anything we can measure/observe
• Three types:
– Continuous: values span an uninterrupted range (e.g. height)
– Discrete: only certain fixed values are possible (e.g. counts)
– Categorical: values are qualitatively assigned (e.g. low/med/hi)
• Dependence in variables:
“Dependent variables depend on independent ones”
– Independent variable – variable you are changing
– Dependent variable – variable you measure to see result
– Controlled variables – variables that can also impact the
dependent variable that you identify as needed to not vary
*** Experimental Control – NOT the same as controlled variables
5. Descriptive statistics
Numerical
– Mean
– Variance
• Standard deviation
• Standard error
– Median
– Mode
– Skew
– etc.
Graphical
– Histogram
– Boxplot
– Scatterplot
– etc.
Techniques to summarize data
7. What graph to use ?
Line Scatter Histogram Bar
Appropriat
e for data
when:
Important
Features
Include
Sample and
other notes
Outlier - An outlier is an observation that lies an abnormal distance from other values in
a random sample from a population. In a sense, this definition leaves it up to the analyst
(or a consensus process) to decide what will be considered abnormal. Before abnormal
observations can be singled out, it is necessary to characterize normal observations.
11. Additional central tendency measures
M = X(n+1)/2 (n is odd)
Median: the 50th percentile
(n is even)
Xn/2 + X(n/2)+1
2
M =
Mode: the most common value
1, 1, 2, 4, 6, 6, 6, 7, 7, 7, 7, 8, 8, 9, 9, 10, 12, 15
Which to use: mean, median or mode?
13. Variance:
Most important measure of “dispersion”
s2 = S
n - 1
Sample Variance
(Xi - X)2
From now on, we’ll ignore sample vs. population. But remember:
We are almost always interested in the population, but can measure only a sample.
15. The Friendly Histogram
• Histograms represent the distribution of data
• They allow you to visualize the mean, median,
mode, variance, and skew at once!
16. Constructing a Histogram is Easy
X (data)
7.4
7.6
8.4
8.9
10.0
10.3
11.5
11.5
12.0
12.3
Histogram of X
Value
6 8 10 12 14
0
1
2
3
Frequency
(count)
17. The Normal Distribution
aka “Gaussian” distribution
• Occurs frequently in nature
• Especially for measures that
are based on sums, such as:
– sample means
– body weight
– “error”
• Many statistics are based on
the assumption of normality
– You must make sure your data
are normal, or try something
else!
Sample normal data:
Histogram + theoretical distribution
(i.e. sample vs. population)
18. Properties of the Normal Distribution
• Symmetric
Mean = Median = Mode
• Theoretical percentiles can be computed exactly
~68% of data are within 1 standard deviation of the mean
>99% within 3 s.d.
“skinny tails”
24. What if my data aren’t Normal?
• It’s OK!
• Although lots of data are Gaussian (because of the CLT),
many simply aren’t.
– Example: Fire return intervals
Time between fires (yr)
• Solutions:
– Transform data to make it
normal (e.g. take logs)
– Use a test that doesn’t
assume normal data
• Don’t worry, there are plenty
• Especially these days...
• Many stats work OK as long as data are “reasonably” normal
25. That is enough for today
Please complete the flipped notes while watching the
video before next class
IMPORTANT: Bring a Device Next classs with
either excel or google sheets
27. Inference: the process by which we draw
conclusions about an unknown based on
evidence or prior experience.
In statistics: make conclusions about a
population based on samples taken from
that population.
Important: Your sample must reflect the
population you’re interested in, otherwise
your conclusions will be misleading!
28. Statistical Hypotheses
• Should be related to a scientific hypothesis!
• Very often presented in pairs:
– Null Hypothesis (H0):
the “boring” hypothesis of “no difference”
– Alternative Hypothesis (HA)
the interesting hypothesis of “there is an effect”
• Statistical tests attempt to (mathematically)
reject the null hypothesis
29. Significance
• Your sample will never match H0 perfectly,
even when H0 is in fact true
• The question is whether your sample is
different enough from the expectation under
H0 to be considered significant
• If your test finds a significant difference, then
you reject H0.
30. p-Values Measure Significance
The p-value of a test is the probability of observing data
at least as extreme as your sample, assuming H0 is true
• If p is very small, it is unlikely that H0 is true
(in other words, if H0 were true, your observed sample would be unlikely)
• How small does p have to be?
– 0.05 is a common cutoff
• If p<0.05, then there is less than 5% chance that you would observe
your sample if the null hypothesis was true.
31. ‘Proof’ in statistics
• Failing to reject (i.e. “accepting”) H0 does not
prove that H0 is true!
• And accepting HA doesn’t prove that HA is true
either!
Why?
• Statistical inference tries to draw conclusions
about the population from a small sample
– By chance, the samples may be misleading
– Example: if you always accept H0 at p=0.05, then
1 in 20 times you will be wrong!
32. Play it Safe
Avoid using the term Prove in your labs
Instead say “the data accepts or supports” the
hypothesis
Watch out for reaching – classic student error,
stick to the scope of your lab data in your
conclusions, this is not your life work.
33. “Why is this Biology?”
Variation in populations.
Variability in results.
affects
Confidence
in conclusions.
The key methodology in Biology is hypothesis
testing through experimentation.
Carefully-designed and controlled
experiments and surveys give us quantitative
(numeric) data that can be compared.
We can use the data collected to test our
hypothesis and form explanations of the
processes involved… but only if we can be
confident in our results.
We therefore need to be able to evaluate the
reliability of a set of data and the significance
of any differences we have found in the data.
Image: 'Transverse section of part of a stem of a Dead-nettle (Lamium sp.) showing+a+vascular+bundle+and+part+of+the+cortex'
http://www.flickr.com/photos/71183136@N08/6959590092 Found on flickrcc.net
34. “Which medicine should I prescribe?”
Image from: http://www.msf.org/international-activity-report-2010-sierra-leone
Donate to Medecins Sans Friontiers through Biology4Good: http://i-biology.net/about/biology4good/
35. “Which medicine should I prescribe?”
Image from: http://www.msf.org/international-activity-report-2010-sierra-leone
Donate to Medecins Sans Friontiers through Biology4Good: http://i-biology.net/about/biology4good/
Generic drugs are out-of-patent, and are
much cheaper than the proprietary
(brand-name) equivalents. Doctors need to
balance needs with available resources.
Which would you choose?
36. “Which medicine should I prescribe?”
Image from: http://www.msf.org/international-activity-report-2010-sierra-leone
Donate to Medecins Sans Friontiers through Biology4Good: http://i-biology.net/about/biology4good/
Means (averages) in Biology are almost
never good enough. Biological systems
(and our results) show variability.
Which would you choose now?
37.
38. Hummingbirds are nectarivores (herbivores
that feed on the nectar of some species of
flower).
In return for food, they pollinate the flower.
This is an example of mutualism –
benefit for all.
As a result of natural selection,
hummingbird bills have evolved.
Birds with a bill best suited to
their preferred food source have
the greater chance of survival.
Photo: Archilochus colubris, from wikimedia commons, by Dick Daniels.
39. Researchers studying comparative anatomy collect
data on bill-length in two species of hummingbirds:
Archilochus colubris
(red-throated hummingbird) and
Cynanthus latirostris (broadbilled hummingbird).
To do this, they need to collect sufficient
relevant, reliable data so they can test
the Null hypothesis (H0) that:
“there is no significant difference
in bill length between the two species.”
Photo: Archilochus colubris (male), wikimedia commons, by Joe Schneid
40. The sample size must
be large enough to provide
sufficient reliable data and for us
to carry out relevant statistical
tests for significance.
We must also be mindful of
uncertainty in our measuring tools
and error in our results.
Photo: Broadbilled hummingbird (wikimedia commons).
41. The mean is a measure of the central tendency
of a set of data.
Table 1: Raw measurements of bill length in
A. colubris and C. latirostris.
Bill length (±0.1mm)
n A. colubris C. latirostris
1 13.0 17.0
2 14.0 18.0
3 15.0 18.0
4 15.0 18.0
5 15.0 19.0
6 16.0 19.0
7 16.0 19.0
8 18.0 20.0
9 18.0 20.0
10 19.0 20.0
Mean
s
Calculate the mean using:
• Your calculator
(sum of values / n)
• Excel
=AVERAGE(highlight raw data)
n = sample size. The bigger the better.
In this case n=10 for each group.
All values should be centred in the cell, with
decimal places consistent with the measuring
tool uncertainty.
42. The mean is a measure of the central tendency
of a set of data.
Table 1: Raw measurements of bill length in
A. colubris and C. latirostris.
Bill length (±0.1mm)
n A. colubris C. latirostris
1 13.0 17.0
2 14.0 18.0
3 15.0 18.0
4 15.0 18.0
5 15.0 19.0
6 16.0 19.0
7 16.0 19.0
8 18.0 20.0
9 18.0 20.0
10 19.0 20.0
Mean 15.9 18.8
s
Raw data and the mean need to have
consistent decimal places (in line with
uncertainty of the measuring tool)
Uncertainties must be included.
Descriptive table title and number.
51. Standard deviation is a measure of the spread of
most of the data.
Table 1: Raw measurements of bill length in
A. colubris and C. latirostris.
Bill length (±0.1mm)
n A. colubris C. latirostris
1 13.0 17.0
2 14.0 18.0
3 15.0 18.0
4 15.0 18.0
5 15.0 19.0
6 16.0 19.0
7 16.0 19.0
8 18.0 20.0
9 18.0 20.0
10 19.0 20.0
Mean 15.9 18.8
s 1.91 1.03 Standard deviation can have one more
decimal place.=STDEV (highlight RAW data).
Which of the two sets of data has:
a. The longest mean bill length?
a. The greatest variability in the data?
52. Standard deviation is a measure of the spread of
most of the data.
Table 1: Raw measurements of bill length in
A. colubris and C. latirostris.
Bill length (±0.1mm)
n A. colubris C. latirostris
1 13.0 17.0
2 14.0 18.0
3 15.0 18.0
4 15.0 18.0
5 15.0 19.0
6 16.0 19.0
7 16.0 19.0
8 18.0 20.0
9 18.0 20.0
10 19.0 20.0
Mean 15.9 18.8
s 1.91 1.03 Standard deviation can have one more
decimal place.=STDEV (highlight RAW data).
Which of the two sets of data has:
a. The longest mean bill length?
a. The greatest variability in the data?
C. latirostris
A. colubris
53. Standard deviation is a measure of the spread of
most of the data. Error bars are a graphical
representation of the variability of data.
Which of the two sets of data has:
a. The highest mean?
a. The greatest variability in the data?
A
B
Error bars could represent standard deviation, range or confidence intervals.
54. Put the error bars for standard deviation on our graph.
55. Put the error bars for standard deviation on our graph.
56. Put the error bars for standard deviation on our graph.
Delete the horizontal error bars
57. A. colubris,
15.9mm
C. latirostris,
18.8mm
0.0
5.0
10.0
15.0
20.0
MeanBilllength(±0.1mm)
Species of hummingbird
Graph 1: Comparing mean bill lengths in two
hummingbird species, A. colubris and C. latirostris.
(error bars = standard deviation)
Title is adjusted to
show the source of the
error bars. This is very
important.
You can see the clear
difference in the size of
the error bars.
Variability has been
visualised.
The error bars overlap
somewhat.
What does this mean?
58. The overlap of a set of error bars gives a clue as to the
significance of the difference between two sets of data.
Large overlap No overlap
Lots of shared data points
within each data set.
Results are not likely to be
significantly different from
each other.
Any difference is most likely
due to chance.
No (or very few) shared data
points within each data set.
Results are more likely to be
significantly different from
each other.
The difference is more likely
to be ‘real’.
59.
60.
61.
62. A. colubris,
15.9mm
(n=10)
C. latirostris,
18.8mm
(n=10)
-3.0
2.0
7.0
12.0
17.0
22.0
MeanBilllength(±0.1mm)
Species of hummingbird
Graph 1: Comparing mean bill lengths in two
hummingbird species, A. colubris and C.
latirostris.(error bars = standard deviation)
Our results show a very small overlap
between the two sets of data.
So how do we know if the difference is
significant or not?
We need to use a statistical test.
The t-test is a statistical
test that helps us determine
the significance of the
difference between the
means of two sets of data.
63.
64. The Null Hypothesis (H0):
“There is no significant
difference.”
This is the ‘default’ hypothesis that we always test.
In our conclusion, we either accept the null hypothesis or reject it.
A t-test can be used to test whether the difference between two means is significant.
• If we accept H0, then the means are not significantly different.
• If we reject H0, then the means are significantly different.
Remember:
• We are never ‘trying’ to get a difference. We design carefully-controlled experiments and
then analyse the results using statistical analysis.
65. Excel can jump straight to a value of P for our results.
One function (=ttest) compares both sets of data.
As it calculates P directly (the
probability that the difference is due
to chance), we can determine
significance directly.
In this case, P=0.00026
This is much smaller than 0.005, so
we are confident that we can:
reject H0.
The difference is unlikely to be due to
chance.
Conclusion:
There is a significant difference in bill
length between A. colubris and C.
latirostris.
66.
67. Two tails: we assume data are normally distributed, with two ‘tails’ moving away from mean.
Type 2 (unpaired): we are comparing one whole population with the other whole population.
(Type 1 pairs the results of each individual in set A with the same individual in set B).
68.
69.
70.
71.
72.
73. Your correlation coefficient, is your
R^2 value
In Excel, you will want to do a scatter
plot with your data
Next Add a trend line and check the
boxes for displaying the equation as
well as the R-squared value. The
closer to 1.0 that value is, the
stronger the correlation
Table 2: Correlation between bill length and body weight in A. colubris
bill length
(mm) (+/-
0.1mm)
13.0 14.0 15.0 15.0 15.0 16.0 16.0 18.0 18.0 19.0
weight (g)
(+/-0.05g)
2.7 2.8 2.8 2.9 2.9 2.9 3.0 3.1 3.4 3.6
74. http://diabetes-obesity.findthedata.org/b/240/Correlations-between-diabetes-obesity-and-physical-activity
Interpreting Graphs: See – Think – Wonder
See: What is factual about the graph?
• What are the axes?
• What is being plotted
• What values are present?
Think: How is the graph interpreted?
• What relationship is present?
• Is cause implied?
• What explanations are possible and
what explanations are not possible?
Wonder: Questions about the graph.
• What do you need to
know more about?
See – Think - Wonder
Visible Thinking Routine
76. Correlation does not imply causality.
Pirates vs global warming, from http://en.wikipedia.org/wiki/Flying_Spaghetti_Monster#Pirates_and_global_warming
77. Cartoon from: http://www.xkcd.com/552/
Correlation does not imply causation, but it does waggle its eyebrows
suggestively and gesture furtively while mouthing "look over there."
Check out these funny “Correlations”
78. Correlation does not imply causality.
Pirates vs global warming, from http://en.wikipedia.org/wiki/Flying_Spaghetti_Monster#Pirates_and_global_warming
Where correlations exist, we must then design solid scientific experiments to determine the
cause of the relationship. Sometimes a correlation exist because of confounding variables –
conditions that the correlated variables have in common but that do not directly affect each
other.
To be able to determine causality through experimentation we need:
• One clearly identified independent variable
• Carefully measured dependent variable(s) that can be attributed to change in the
independent variable
• Strict control of all other variables that might have a measurable impact on the
dependent variable.
We need: sufficient relevant, repeatable and statistically significant data.
Some known causal relationships:
• Atmospheric CO2 concentrations and global warming
• Atmospheric CO2 concentrations and the rate of photosynthesis
• Temperature and enzyme activity