This presentation is meant to help choose the appropriate statistical analysis for IBDP Biology IAs. It was created as support for teachers but also useful for students.
Within the presentation, we discuss different types of biological data, and how to describe and analyse it using mathematics.
Getting to the Core of Paper 2 - ESS.pdfNigel Gardner
How important are the 9 mark questions in IB Diploma Environmental Systems and Societies?
Where do those questions come from?
How do you teach to answer those questions?
Getting to the Core of Paper 2 - ESS.pdfNigel Gardner
How important are the 9 mark questions in IB Diploma Environmental Systems and Societies?
Where do those questions come from?
How do you teach to answer those questions?
Clinical Research Statistics for Non-StatisticiansBrook White, PMP
Through real-world examples, this presentation teaches strategies for choosing appropriate outcome measures, methods for analysis and randomization, and sample sizes as well as tips for collecting the right data to answer your scientific questions.
Clinical Research Statistics for Non-StatisticiansBrook White, PMP
Through real-world examples, this presentation teaches strategies for choosing appropriate outcome measures, methods for analysis and randomization, and sample sizes as well as tips for collecting the right data to answer your scientific questions.
sience 2.0 : an illustration of good research practices in a real studywolf vanpaemel
a presentation explaining the what, how and why of some of the features of science 2.0 (replication, registration, high power, bayesian statistics, estimation, co-pilot multi-software approach, distinction between confirmatory and exploratory analyses, and open science) using steegen et al. (2014) as a running example.
Census
Everyone in population
Eg. All Cambodian residents
Population
is a set of persons (or objects) having a common observable characteristic.
the entire collection of units about which we would like information
Sample
is a representative subject (subgroup) of a population.
the collection of units we actually measure
Example:
If we want to know many persons in a community
have quit smoking or
have health insurance or
plan to vote for a certain candidate,
Sample
is a representative subject (subgroup) of a population.
the collection of units we actually measure
Example:
If we want to know many persons in a community
have quit smoking or
have health insurance or
plan to vote for a certain candidate,
Sample
is a representative subject (subgroup) of a population.
the collection of units we actually measure
Example:
If we want to know many persons in a community
have quit smoking or
have health insurance or
plan to vote for a certain candidate,
Sample
is a representative subject (subgroup) of a population.
the collection of units we actually measure
Example:
If we want to know many persons in a community
have quit smoking or
have health insurance or
plan to vote for a certain candidate,
Sample
is a representative subject (subgroup) of a population.
the collection of units we actually measure
Example:
If we want to know many persons in a community
have quit smoking or
have health insurance or
plan to vote for a certain candidate,
Sample
is a representative subject (subgroup) of a population.
the collection of units we actually measure
Example:
If we want to know many persons in a community
have quit smoking or
have health insurance or
plan to vote for a certain candidate,
Sample
is a representative subject (subgroup) of a population.
the collection of units we actually measure
Example:
If we want to know many persons in a community
have quit smoking or
have health insurance or
plan to vote for a certain candidate,
Sample
is a representative subject (subgroup) of a population.
the collection of units we actually measure
Example:
If we want to know many persons in a community
have quit smoking or
have health insurance or
plan to vote for a certain candidate,
Statistical inference is the process by which we draw conclusions about a population from data collected on a sample.
In medical research
Population
All patients candidate for treatment
Sample
All patients candidate for treatment who volunteer for your study
Infer results from volunteers (sample) to other candidates for the same treatment (population).
We usually obtain information on an appropriate sample of the community and generalize from it to the entire population.
The way the sample is selected, not its size, determines whether we may draw appropriate inferences about a population.
The primary reason for selecting a sample from a population is to draw inferences about that population.
Statistical inference is the process by which we infer
3 - SamplingTechVarious sampling techniques are employedniques(new1430).pptgharkaacer
In the context of medicine, "medical sampling" generally refers to the collection of biological materials or data for analysis, diagnosis, or research purposes. Various sampling techniques are employed to ensure the integrity and representativeness of the samples. Here are some common medical sampling techniques:
Blood Sampling: One of the most common medical sampling techniques, it involves drawing blood from a vein, usually using a needle. This method is used for countless diagnostic tests, from basic blood counts to more complex disease markers.
Urine Sampling: Urine can be collected randomly or at specific times (e.g., first morning sample, 24-hour urine collection) to assess kidney function, detect metabolic products, and diagnose diseases.
Tissue Biopsy: This involves extracting a small piece of tissue from the body for examination under a microscope. Biopsies can be performed on various body parts, including the skin, liver, and kidneys, to diagnose cancer and other diseases.
K-to-R Workshop: How to Structure the "Approach" Section (Part 1)UCLA CTSI
UCLA CTSI K-to_R Workshop, October 29, 2015
Presenter:
David Elashoff, PhD
Professor of Biostatistics & Medicine
Program Leader, CTSI Biostatistics and Computational Biology
This pdf is about the Schizophrenia.
For more details visit on YouTube; @SELF-EXPLANATORY;
https://www.youtube.com/channel/UCAiarMZDNhe1A3Rnpr_WkzA/videos
Thanks...!
Introduction:
RNA interference (RNAi) or Post-Transcriptional Gene Silencing (PTGS) is an important biological process for modulating eukaryotic gene expression.
It is highly conserved process of posttranscriptional gene silencing by which double stranded RNA (dsRNA) causes sequence-specific degradation of mRNA sequences.
dsRNA-induced gene silencing (RNAi) is reported in a wide range of eukaryotes ranging from worms, insects, mammals and plants.
This process mediates resistance to both endogenous parasitic and exogenous pathogenic nucleic acids, and regulates the expression of protein-coding genes.
What are small ncRNAs?
micro RNA (miRNA)
short interfering RNA (siRNA)
Properties of small non-coding RNA:
Involved in silencing mRNA transcripts.
Called “small” because they are usually only about 21-24 nucleotides long.
Synthesized by first cutting up longer precursor sequences (like the 61nt one that Lee discovered).
Silence an mRNA by base pairing with some sequence on the mRNA.
Discovery of siRNA?
The first small RNA:
In 1993 Rosalind Lee (Victor Ambros lab) was studying a non- coding gene in C. elegans, lin-4, that was involved in silencing of another gene, lin-14, at the appropriate time in the
development of the worm C. elegans.
Two small transcripts of lin-4 (22nt and 61nt) were found to be complementary to a sequence in the 3' UTR of lin-14.
Because lin-4 encoded no protein, she deduced that it must be these transcripts that are causing the silencing by RNA-RNA interactions.
Types of RNAi ( non coding RNA)
MiRNA
Length (23-25 nt)
Trans acting
Binds with target MRNA in mismatch
Translation inhibition
Si RNA
Length 21 nt.
Cis acting
Bind with target Mrna in perfect complementary sequence
Piwi-RNA
Length ; 25 to 36 nt.
Expressed in Germ Cells
Regulates trnasposomes activity
MECHANISM OF RNAI:
First the double-stranded RNA teams up with a protein complex named Dicer, which cuts the long RNA into short pieces.
Then another protein complex called RISC (RNA-induced silencing complex) discards one of the two RNA strands.
The RISC-docked, single-stranded RNA then pairs with the homologous mRNA and destroys it.
THE RISC COMPLEX:
RISC is large(>500kD) RNA multi- protein Binding complex which triggers MRNA degradation in response to MRNA
Unwinding of double stranded Si RNA by ATP independent Helicase
Active component of RISC is Ago proteins( ENDONUCLEASE) which cleave target MRNA.
DICER: endonuclease (RNase Family III)
Argonaute: Central Component of the RNA-Induced Silencing Complex (RISC)
One strand of the dsRNA produced by Dicer is retained in the RISC complex in association with Argonaute
ARGONAUTE PROTEIN :
1.PAZ(PIWI/Argonaute/ Zwille)- Recognition of target MRNA
2.PIWI (p-element induced wimpy Testis)- breaks Phosphodiester bond of mRNA.)RNAse H activity.
MiRNA:
The Double-stranded RNAs are naturally produced in eukaryotic cells during development, and they have a key role in regulating gene expression .
Nutraceutical market, scope and growth: Herbal drug technologyLokesh Patil
As consumer awareness of health and wellness rises, the nutraceutical market—which includes goods like functional meals, drinks, and dietary supplements that provide health advantages beyond basic nutrition—is growing significantly. As healthcare expenses rise, the population ages, and people want natural and preventative health solutions more and more, this industry is increasing quickly. Further driving market expansion are product formulation innovations and the use of cutting-edge technology for customized nutrition. With its worldwide reach, the nutraceutical industry is expected to keep growing and provide significant chances for research and investment in a number of categories, including vitamins, minerals, probiotics, and herbal supplements.
Richard's entangled aventures in wonderlandRichard Gill
Since the loophole-free Bell experiments of 2020 and the Nobel prizes in physics of 2022, critics of Bell's work have retreated to the fortress of super-determinism. Now, super-determinism is a derogatory word - it just means "determinism". Palmer, Hance and Hossenfelder argue that quantum mechanics and determinism are not incompatible, using a sophisticated mathematical construction based on a subtle thinning of allowed states and measurements in quantum mechanics, such that what is left appears to make Bell's argument fail, without altering the empirical predictions of quantum mechanics. I think however that it is a smoke screen, and the slogan "lost in math" comes to my mind. I will discuss some other recent disproofs of Bell's theorem using the language of causality based on causal graphs. Causal thinking is also central to law and justice. I will mention surprising connections to my work on serial killer nurse cases, in particular the Dutch case of Lucia de Berk and the current UK case of Lucy Letby.
Deep Behavioral Phenotyping in Systems Neuroscience for Functional Atlasing a...Ana Luísa Pinho
Functional Magnetic Resonance Imaging (fMRI) provides means to characterize brain activations in response to behavior. However, cognitive neuroscience has been limited to group-level effects referring to the performance of specific tasks. To obtain the functional profile of elementary cognitive mechanisms, the combination of brain responses to many tasks is required. Yet, to date, both structural atlases and parcellation-based activations do not fully account for cognitive function and still present several limitations. Further, they do not adapt overall to individual characteristics. In this talk, I will give an account of deep-behavioral phenotyping strategies, namely data-driven methods in large task-fMRI datasets, to optimize functional brain-data collection and improve inference of effects-of-interest related to mental processes. Key to this approach is the employment of fast multi-functional paradigms rich on features that can be well parametrized and, consequently, facilitate the creation of psycho-physiological constructs to be modelled with imaging data. Particular emphasis will be given to music stimuli when studying high-order cognitive mechanisms, due to their ecological nature and quality to enable complex behavior compounded by discrete entities. I will also discuss how deep-behavioral phenotyping and individualized models applied to neuroimaging data can better account for the subject-specific organization of domain-general cognitive systems in the human brain. Finally, the accumulation of functional brain signatures brings the possibility to clarify relationships among tasks and create a univocal link between brain systems and mental functions through: (1) the development of ontologies proposing an organization of cognitive processes; and (2) brain-network taxonomies describing functional specialization. To this end, tools to improve commensurability in cognitive science are necessary, such as public repositories, ontology-based platforms and automated meta-analysis tools. I will thus discuss some brain-atlasing resources currently under development, and their applicability in cognitive as well as clinical neuroscience.
Observation of Io’s Resurfacing via Plume Deposition Using Ground-based Adapt...Sérgio Sacani
Since volcanic activity was first discovered on Io from Voyager images in 1979, changes
on Io’s surface have been monitored from both spacecraft and ground-based telescopes.
Here, we present the highest spatial resolution images of Io ever obtained from a groundbased telescope. These images, acquired by the SHARK-VIS instrument on the Large
Binocular Telescope, show evidence of a major resurfacing event on Io’s trailing hemisphere. When compared to the most recent spacecraft images, the SHARK-VIS images
show that a plume deposit from a powerful eruption at Pillan Patera has covered part
of the long-lived Pele plume deposit. Although this type of resurfacing event may be common on Io, few have been detected due to the rarity of spacecraft visits and the previously low spatial resolution available from Earth-based telescopes. The SHARK-VIS instrument ushers in a new era of high resolution imaging of Io’s surface using adaptive
optics at visible wavelengths.
THE IMPORTANCE OF MARTIAN ATMOSPHERE SAMPLE RETURN.Sérgio Sacani
The return of a sample of near-surface atmosphere from Mars would facilitate answers to several first-order science questions surrounding the formation and evolution of the planet. One of the important aspects of terrestrial planet formation in general is the role that primary atmospheres played in influencing the chemistry and structure of the planets and their antecedents. Studies of the martian atmosphere can be used to investigate the role of a primary atmosphere in its history. Atmosphere samples would also inform our understanding of the near-surface chemistry of the planet, and ultimately the prospects for life. High-precision isotopic analyses of constituent gases are needed to address these questions, requiring that the analyses are made on returned samples rather than in situ.
2. OUTLINE
1. Why statistics is important?
2. Types of data and sample size
3. Analysis of the mean, range and distribution
4. Standard deviation and standard error
5. Significant figures and outliers
6. Types of graphs
7. Linear regression
8. Pearson correlation coefficient
9. Spearman rank correlation index
10. T-test
11. ANOVA
12. Post-HOC analysis
13. Chi-squared analysis
14. Choosing the appropriate statistics for the biology IA
Descriptive Inferential
3. Statistics
Descriptive Inferential
Is used to describe the data.
For example: the range, average and
spread of data.
Is used to extend the conclusions from a
small sample to a wider population or
another sample.
For example: t-test, ANOVA and Chi-
squared.
4. 1. WHY STATISTICS IS IMPORTANT?
•We cannot survey every individual organism in the population, so we take a sample, analyse it and
extrapolate the tendencies to the whole population.
•Or an experiment with 5 repeats, and limited resources (money and time constraints), how do we know
whether the difference we see is significant statistically or not?
•So we need some kind of a minimal sample to work with.
•In biology, if we do not do the analysis of statistical significance (if the student just does average and range)
then we should NOT state anything about the significance of the results. We then should talk only about
TENDENCIES in the data, but specify why statistics were not applied to show significance (for example, not
enough time to collect the minimum required sample size etc)
•Biostatistics is a subfield of applied statistics. It is used in public health, medicine and biology. It includes
common conventions used by all researchers when reporting the data.
•Biostatisticians report data with 95% confidence in the result, with 5% chance of mistake.
https://www.youtube.com/watch?v=1Q6_LRZwZrc
5. ADVICE FROM IB
•Statistical analysis is expected.
•Percentages, means, standard deviations or other statistics at the end of the column or
row of data they represent will be sufficient.
•For more complex processing using spreadsheets, screenshots are acceptable.
•For other less orthodox processing, a worked example may be necessary.
•The questions that the teacher should be asking are:
• Is the processing appropriate?
• Can the processing be followed?
• Is the processing correct?
• Are conclusions in line with the degree of the data processing?
IB, May 2021
6. 2. TYPES OF DATA AND SAMPLE SIZE
•The more data the stronger is the conclusion
•We are limited to 10 hours of data collection and analysis
•We are also limited by a school budget and available materials
•Sample size should be also reflecting the uncertainty and variability of the measurements, the
larger the uncertainty the bigger should be the sample. For example measurements in humans,
measurements in length of the seedlings etc.
•Biochemical reactions (titration, enzyme activity) can be set up with more controlled variables
and measured with less variabity.
•n – sample size
•Sample size should be large enough to represent the population. For example in quadrant
studies the sample size would be 10% of the total area. In school lab environment this is
constrained by time and resources
15. SAMPLE SIZE
• Sample size depends on the type of data and can be designed with the statistical approach in mind.
• Students will have 10 hours to collect data. So online investigations will require a much larger sample size
than physical investigations.
• If less than a minimum (5) measurements are taken then results will be inconclusive, but still can be
described and evaluated.
• In order to do standard deviation, we need at least 5 measurements.
• 5-14 measurements, therefore, is a minimum for biology IA experiments and is called a very small sample
size.
• 15-30 is a small sample.
• >30 is considered a large sample
• Students need to discuss the limitations of their sample size.
IB, May 2020
16. 3. ANALYSIS OF THE MEAN, RANGE AND
DISTRIBUTION
•In biological data mean and average are the same thing. Be
careful that the student in the report uses one or the other.
•The range shows the extent from minimum to maximum values.
The larger the range the more the data spread around the
mean.
•The distribution shows us how often each value occurs in the
data set.
Sample data set: 3 5 4 7 2 3 9
n: 7
X: 4.71 ≈ 5
Range: 7
Crashcourse statistics #3
https://www.youtube.com/watch?v=kn83BA7cRNM&list=PL8dPuuaLjXtNM_Y-bUAhblSAdWRnmBUcr&index=4
https://cdn.virtualnerd.com/thumbnails/Alg1_14_02_0014-diagram_thumb-lg.png
17. The mean is always distorted by outliers. Therefore it is
important for students to discuss this in their report.
During this discussion, students may indicate what is the
mode of the data.
Mode is the value which appears the most in the set.
There could be more than one mode.
Mode is only useful though if we have a relatively
large sample. Smaller samples will have no mode.
Sample data set: 3 5 4 7 2 3 9
n: 7
X: 4.71 ≈ 5
Range: 7
Mode: 3
http://www.learnersplanet.com/sites/default/files/images/mean-mode-median.png
19. Normal distribution of the data is
important for calculating the mean,
standard deviation and t-test.
https://sciences.usca.edu/biology/zelmer/305/norm/stanorm.jpg
20. To test for normal distribution:
1. Students might do a histogram of the data to
show visually the bell-shaped curve distribution
2. The mathematical alternative is the Shapiro
Wilk test
https://towardsdatascience.com/6-ways-to-test-for-a-normal-distribution-which-one-to-use-9dcf47d8fa93
Values around the mean Values around the mean
Frequency
21. SHAPIRO WILK TEST
Shapiro Wilk test
If the p- value of the Shapiro-Wilk Test is larger
than 0.05, we assume a normal distribution.
If the p- value of the Shapiro-Wilk Test is smaller
than 0.05, we do not assume a normal distribution.
H0: Data is normally distributed.
H1: Data is NOT normally distributed.
https://towardsdatascience.com/6-ways-to-test-for-a-normal-distribution-which-one-to-use-9dcf47d8fa93
Online calculator:
https://scistatcalc.blogspot.com/2013/10/shapiro-wilk-
test-calculator.html
Reporting results
Figure 1. Screenshot of the input data Figure 2. Screenshot of the analysis results
According to Shapiro Wilk test of normality, W=0.981889, p>0.05, therefore the
experimental data set is normally distributed.
22. 4. STANDARD DEVIATION AND STANDARD ERROR
•Standard deviation (SD) or standard error of the mean (SEM) can be useful assuming there
is a sufficient number of replicates to be able to calculate one, otherwise, range bars are
acceptable for max-min values.
•SEM requires usually a larger sample size.
•SD can be done on a sample as small as 5.
•SD describes the characteristics of the data set you collected.
•SEM describes how far is your collected sample mean from the larger population mean.
Basically, it talks about how well your data may represent the population.
•Thus, students explain the appropriate meaning of the value based on what they used SD
or SEM.
https://www.statisticshowto.com/probability-and-statistics/statistics-definitions/what-is-the-standard-error-of-a-sample/
24. SEM
The larger your sample the smaller will be its
difference from the representative population,
and therefore smaller the SE value.
The SEM takes the SD and divides it by the
square root of the sample size.
https://www.statisticshowto.com/probability-and-statistics/statistics-definitions/what-is-the-standard-error-of-a-sample/
https://www.investopedia.com/ask/answers/042415/what-difference-between-standard-error-means-and-standard-deviation.asp
Altman, Douglas G, and J Martin Bland. “Standard deviations and standard errors.” BMJ (Clinical research ed.) vol.
331,7521 (2005): 903. doi:10.1136/bmj.331.7521.903. Accessed Jan. 17, 2022.
https://www.scribbr.com/statistics/standard-error/
25. 5. SIGNIFICANT FIGURES AND OUTLIERS
•Decimal places in the recorded data should be consistent with degrees of precision.
•Decimal places in the Mean should be the same as in the raw data.
•Uncertainties should appear in the column headings along with the units.
•Uncertainties for counts (±1) are not necessary.
However, data derived from these counts may possess a degree of precision (e.g. percentage
germination of a sample of 25 seeds will have an error margin of ±4% or a heart rate after a 15 s palpation ±4
beats per min). Error propagation is not needed, but it is good if a student shows awareness of this in the
evaluation.
•For other calculated values, two numbers after the decimal point are acceptable when
reporting in high-school sciences.
26. OUTLIERS
IB, May 2021
• Outliers should not be excluded from processing just because
they do not “fit well” in the general trend of the data.
• Outliers can be identified mathematically.
• Exclusion requires a justification.
• Outliers can only be excluded if there is evidence of a mistake
in the data collection.
• If data was accurately collected, then an outlier actually can
be new insight into the new trend or discovery.
• Outliers’ significance should be discussed taking this into
account.
Example:
Measuring heights in 13 year old boys.
One of the boys is clearly much taller
than others.
Is he an outlier? Mathematically yes, but
it is not a mistake and therefore should
not be excluded. Instead report should
address the possibility of results
affected by age of onset of puberty
and what it means for their choice of
dependent and independent variables.
27. CALCULATING OUTLIERS
• If a number is less than Q1 – 1.5×IQR or
greater than Q3 + 1.5×IQR, then it is an
outlier.
• Q is the quartile boundary
• The interquartile range (IQR) is a measure of
statistical dispersion, being equal to the
difference between the third quartile (Q3)
and first quartile (Q1), that is, IQR = Q3 –
Q1.
• Students also may use the online calculator:
https://miniwebtool.com/outlier-calculator/
In this case, it should be appropriately
referenced.
https://www.khanacademy.org/math/statistics-probability/summarizing-quantitative-data/box-whisker-plots/a/identifying-outliers-iqr-rule
5, 7, 10, 15, 19, 21, 21, 22, 22, 23, 23, 23, 23, 23, 24, 24, 24, 24, 25
Example:
Q1 = 19
Q3 = 24
IQR = 24-19 = 5
Q1 - 1.5*IQR = 19-1.5*5 = 11.5 Outliers are 5, 7 and 10.
Q3+ 1.5*IQR = 24+1.5*5 = 31.5 There are no upper
outliers.
28. 6. TYPES OF GRAPHS
•Graphing is a type of descriptive statistics which helps us to easily make conclusions
about the data. It represents data in a simplified visually engaging format.
•In high school biology, an experimental report graph should serve a purpose.
•Only graphs that are discussed in the report should be included.
•For example ---- graph showing the trend in data over time.
•One graph is enough for the IA.
•By looking at a graph alone reader should easily see the conclusion from the data in
response to the research question asked.
30. •A bar chart represents two or more categories
and measurements within those categories.
•Technically it is categorical (IV) and quantitative
(DV) data combined in one chart.
•Therefore, this type of chart is suitable for testing
different conditions or locations, where the
question is which condition/location is the best.
Bar charts
Pie charts
http://www.biostathandbook.com/pix/graph4.gif
https://media.cheggcdn.com/study/59c/59c9da3a-e277-49b9-b4b5-
df3549ef4af7/13469-21-1IEFA1.png
•The pie chart is used only when one category is
applied.
•In Biology IA we insist on 2-5 categories, therefore
this type of chart is not recommended.
•Also, there is no way to express error bars on this
type of chart.
31. Scatterplots
Line graphs
http://www.saburchill.com/IBbiology/graphs/images/039.jpg
https://www.westernsydney.edu.au/__data/assets/image/0018
/533601/Biology_4.2_line_graphs.jpg
•Scatterplots are the most versatile graph to present
in biology reports.
•Usually, it presents all individual data points against
two measurements.
•Because of this, this is the best graph to represent in
database analyses and in any correlation studies.
•It is possible to just present the averages and SD
from the single condition on the x-axis.
•The line graph is used to show changes over one
continuous range, for example, over time.
•They can be useful for displaying data where other
than a linear relationship is expected between two
variables.
•Most often point represent the averages and SD from
the single condition on the x-axis.
•Line graphs are acceptable in DP biology, but not in
physics or chemistry.
32. MAKING CUSTOM ERROR BARS ON GRAPHS IN EXCEL
•Note: many students just choose SD suggested by Excel for error
bars. That is incorrect; because Excel will calculate SD between
averages presented in the graph for that option.
•Instead, choose “More error bars options…” and enter the custom
values.
•See the video for reference on how to make error bars:
https://www.youtube.com/watch?v=JeqCl_aD_8Y
33. REPORTING GRAPHS
•Graphs can be made using Excel or any other program.
•Each graph should have a title.
Example: Graph 1. Mean heights of the seedlings after 8 days of exposure to various salt
concentrations. Error bars represent the SD.
•Error bars, if used on the graphs, should be identified in the title of the graph
(range/SEM/SD).
•Both, y and x axes need to be labelled, with units and uncertainty indicated.
•x is the IV, y is DV.
•The graph should be referenced in the text of the report and appear as close to the
paragraph mentioning it as possible.
34. OUTLINE
1. Why statistics is important?
2. Types of data and sample size
3. Analysis of the mean, range and distribution
4. Standard deviation and standard error
5. Significant figures and outliers
6. Types of graphs
7. Linear regression
8. Pearson correlation index
9. Spearman rank correlation index
10. T-test
11. ANOVA
12. Post-HOC analysis
13. Chi-squared analysis
14. Choosing the appropriate statistics for the biology IA
Descriptive Inferential
35.
36. 7. LINEAR REGRESSION
•Used to predict the values when the line of
best fit is extended. For example – osmolarity
experiments.
• Regression analysis is appropriate
when finding the effect of an “x” variate (IV)
on a “y” variate (DV).
•Regression is used on scatterplot data.
•Regression analysis DOES NOT include
statistics.
http://www.biosci.global/customer-stories-en/pearson-correlation-vs-simple-linear-regression/
Pearson
37. REPORTING
•Regression analysis will be reported as an equation that fits the data in the scatterplot.
•We can use the resulting equation (there is an option to calculate equation in the Excel) to estimate the
unknown values.
Petal Length = (Petal Width * 1.8693) + 1.7813
https://www.colby.edu/bio/statistics-and-scientific-writing/regression-analysis/
38. R SQUARED
R2 – describes how well the data fits the trend, on a 0-100% scale.
It can be applied when calculating regression or correlation.
•0% represents a model that does not explain any of the variations in the response variable around its
mean. The mean of the dependent variable predicts the dependent variable as well as the regression
model.
•100% represents a model that explains all the variations in the response variable around its mean.
•R2 calculation is usually done by online calculator or Excel
https://statisticsbyjim.com/regression/how-high-r-squared/
https://www.theseattledataguy.com/wp-content/uploads/2017/09/squared-error-r2.png
39. 8. PEARSON CORRELATION COEFFICIENT
•Important to note that ANY correlation, even if
statistically significant does NOT mean causation.
Students have to be very careful when writing about
this.
•The Pearson coefficient is a measure of the strength
of the linear association
•In order for this test to be valid, all data needs to be
quantitative
https://statistics.laerd.com/statistical-guides/pearson-correlation-coefficient-statistical-guide.php
Requirements for Pearson's correlation coefficient
• Scale of measurement should be interval or ratio
• Variables should be approximately normally distributed
• The association should be linear
• There should be no outliers in the data
41. REPORTING
• Students do not need to know how to calculate the Person
correlation. They can simply use the online calculator.
• For example
https://www.socscistatistics.com/tests/pearson/default2.
aspx
• When reporting results, the test should be properly
referenced and screenshots of the input and output data
can be included.
• Reporting of the results should always be accompanied
by the graph made by the student (scatter plot with a
line of best fit).
Reporting results
Figure 1. Screenshot of the input
data
Figure 2. Screenshot of the analysis results
42. REPORTING SIGNIFICANCE
•It is possible to calculate the p-value for Pearson correlation r.
•In this case, N is the number of pairs in your sample. (3 is minimum.)
•Significance level a is a confidence (significance) level in the results
reported.
•Biostatisticians report data with 95% confidence in the result, with a
5% chance of mistake.
•It is accepted as a standard in science reporting that the possibility
of error should not exceed 5%, thus a is always set up to be 0.05.
•At a = 0.05, p values less than 0.05 a reference value will be
deemed significant and p-value more than 0.05 a reference value
will be deemed insignificant.
•The p-value is the probability that you would have found the current
result if the correlation coefficient were in fact zero.
https://statisticsbyjim.com/glossary/significance-level/
https://www.medcalc.org/manual/correlation.php
https://www.webassign.net/bbunderstat9/10-table-06.gif
•If p is lower than the conventional 5%
(p<0.05) the correlation coefficient is
called statistically significant.
•Since p value here is just taking into
account r and N, then you can see that
weaker is the r the more samples are
required for the result to be deemed
significant
43. REPORTING SIGNIFICANCE
Reporting results
Figure 3. Screenshot of the p calculation.
https://www.socscistatistics.com/tests/pearson/default2.aspx
https://www.webassign.net/bbunderstat9/10-table-06.gif
In the example here the p > 0.05. Therefore indicating that
the results is not statistically significant. So we cannot make
any conclusions applied to the wider population based on
the data analyzed.
Note: students can just report the data as shown in Fig 1-3.
The table of significance above is shown here just for
facilitating our understanding of the values.
p=0.058
a>0.05 a<0.01
n= number of samples
44. 9. SPEARMAN RANK CORRELATION
•Spearman rank correlation is the nonparametric version
of the Pearson correlation.
•Requirements
Scale of measurement must be ordinal for at least one parameter
Data must be in the form of matched pairs
The association must be monotonic (i.e., variables increase in value together, or
one increases while the other decreases)
It can be used when requirements for Pearson test are not met.
https://www.gstatic.com/education/formulas2/397133473/en/spearman_s_ra
nk_correlation_coefficient.svg
https://statistics.laerd.com/statistical-guides/spearmans-rank-order-correlation-statistical-guide.php
45. REPORTING
• Students do not need to know how to calculate the
Spearman correlation. They can simply use the online
calculator.
• For example
https://www.socscistatistics.com/tests/spearman/default
3.aspx
• When reporting results, the test should be properly
referenced and screenshots of the input and output data
can be included.
• Reporting of the results should always be accompanied
by the graph made by the student (scatter plot with a
line of best fit).
Reporting results
Figure 1. Screenshot of the input
data
Figure 2. Screenshot of the analysis results
Significance table for your reference
n= number of samples
46. 10. T-TEST
•If you want to compare differences in both directions (positive and negative) then it is a two-tailed test.
•For DP biology reports almost always students should use a two-tailed test.
• A one-tailed test is only justified if you have a specific prediction about the direction of the difference (e.g., Group
A scoring higher than Group B), and you are completely uninterested in the possibility that the opposite outcome
could be true.
https://www.statisticssolutions.com/should-you-use-a-one-tailed-test-or-a-two-tailed-test-for-your-data-analysis/
https://keydifferences.com/wp-content/uploads/2017/01/one-tailed-vs-two-tailed-test.jpg
•t-test (Student’s t-test) is used when comparing one or
two sets of data.
• When choosing the t-test you will need to know if your
data is one-tailed or two-tailed.
• If you want to compare overlap in only one direction
then it is a one-tailed test.
48. ONE SAMPLE T-TEST
https://datatab.net/assets/tutorial/one_Sample_t-Test.png
Requirements
1. The data is normally distributed
2. Quantitative data
3. A randomized sample from a defined population
It is used to compare data set recorded from a population to the mean reported in the
literature. We use it when we want to know if a sample and do not have the full population.
We want to know if this particular sample came from a particular suggested population.
Students may use the online calculator:
https://www.socscistatistics.com/tests/tsinglesample/default2.aspx
49. ONE SAMPLE T-TEST- REPORTING
The result (p<0.05) means that the
data set is statistically significantly
different from the expected value.
H0: Sample mean = Hypothesized
Population mean (µ)
H1: Sample mean (x̅) ≠
Hypothesized Population mean (µ)
Reporting results
Figure 1. Screenshot of the input data
Figure 2. Screenshot of the analysis results
https://www.socscistatistics.com/tests/tsinglesample/default2.aspx
Significance table for your reference
https://www.machinelearningplus.com/wp-content/uploads/2020/10/t-table-one-sample-t-test-min.png
df = n - 1
50. INDEPENDENT SAMPLES T-TEST
Requirements
1. The data is normally distributed
2. Quantitative data
3. Two independent samples
4. The two samples should have the same variance
It is used to compare two populations and estimate if the values are different or overlap significantly.
Students may use the online calculator:
https://www.socscistatistics.com/tests/studentttest/default.aspx
https://www.statstest.com/wp-content/uploads/2020/02/Screen-Shot-2020-02-03-at-9.39.36-PM-1024x497.png
51. INDEPENDENT SAMPLES T-TEST - REPORTING
The result (p>0.05) means that two
data sets are not statistically
significantly different from each
other.
H0: Sample mean of population 1 =
Sample mean of population 2
H1: Sample mean of population 1 ≠
Sample mean of population 2
Reporting results
Figure 1. Screenshot of the input data
Figure 2. Screenshot of the analysis results
https://www.socscistatistics.com/tests/studentttest/default2.aspx
Significance table for your reference
https://www.machinelearningplus.com/wp-content/uploads/2020/10/t-table-one-sample-t-test-min.png
The t-value is -1.84173. The p-value is
.090354. The result is not significant at p <
.05.
DF=N1 + N2 – 2
52. PAIRED T-TEST
https://www.statstest.com/wp-content/uploads/2020/10/Paired-Samples-T-Test.jpg
Requirements
1. The data is normally distributed
2. Quantitative data
3. The two sets of scores are paired or matched in some way
It is used to compare data set recorded from a population to the data from the same
population later on (for example, before and after the treatment)
Students may use the online calculator:
https://www.socscistatistics.com/tests/ttestdependent/default.aspx
53. PAIRED T-TEST- REPORTING
The result (p<0.05) means that two
data sets are statistically significantly
different from each other.
H0: Sample mean of population
before = Sample mean of population
after
H1: Sample mean of population
before ≠ Sample mean of population
after
Reporting results
Figure 1. Screenshot of the input data
Figure 2. Screenshot of the analysis results
https://www.socscistatistics.com/tests/ttestdependent/default2.aspx
Significance table for your reference
https://cdn1.byjus.com/wp-content/uploads/2019/11/paired-t-test-table.png
The value of t is 6.714549. The value
of p is .00053. The result is significant
at p < .05.
df = n - 1
54. 11. ANOVA
•Data sets should be independent of each other, meaning not the repeat measurements of the
same population (that would be repeated measurement ANOVA).
•There could be one way or two way ANOVA. One way ANOVA is used when only one factor
was measure from all groups; two way ANOVA is used when two factors were measured in all
groups.
•For high school biology most often used is one way ANOVA for independent measurements.
https://www.tibco.com/sites/tibco/files/media_entity/2020-09/anova-diagram.svg
•ANOVA compares the sets of three or
more data simultaneously.
•It is done because repeated t-tests would
give too much cumulative error.
55. ONE WAY ANOVA REQUIREMENTS
1. The data should be normally distributed.
2. Samples must be independent.
3. Groups must have equal sample size.
• A one-way ANOVA will tell you that at least two groups were different from each other.
But it won’t tell you which groups were different.
• Students will always have to run post-hoc analysis to say exactly which group is
significantly different from others.
• Students don’t need to know how to perform the test, they can just use the online
calculator.
https://www.socscistatistics.com/tests/anova/default2.aspx
https://www.statisticshowto.com/probability-and-statistics/hypothesis-testing/anova/
56. ANOVA- REPORTING
The result (p<0.05) means that some of
the data sets are statistically significantly
different from others.
H0: there is no difference in sample
means
H1: there is a difference in sample
means
Reporting results
Figure 1. Screenshot of the input data. Treatment 1 is vermicast, treatment 2 is garden
soil , treatment 3 is compost, treatment 4 is sand, treatment 5 is hydroponics medium.
Figure 2. Screenshot of the analysis results
https://www.socscistatistics.com/tests/anova/default2.aspx
The f-ratio value is 17.01845. The p-
value is < .00001. The result is
significant at p < .05.
Numerator degrees of freedom =
treatments – 1 = t – 1
Denominator degrees of freedom = total
observations minus treatments = N – t
Because there are so many variables in the
ANOVA test, instead of single table there are
separate tables calculated for each level of
significance (a).
Significance table for your reference
https://www.dummies.com/article/business-careers-
money/business/accounting/calculation-analysis/how-to-find-the-critical-values-for-
an-anova-hypothesis-using-the-f-table-146050
57. 12. POST-HOC ANALYSIS
•Post hoc (Latin, meaning “after this”) means to analyze the results of your experimental data
after some previous analysis already conducted.
•The only situation when students are expected to do this in high school biology is a statistically
significant ANOVA result.
•Students don’t need to know how to perform the test, they can just use the online calculator.
https://www.socscistatistics.com/tests/anova/default2.aspx
•There are many post-hoc tests, but for ANOVA Tukey HSD is recommended.
•Tukey's HSD (honestly significant difference) procedure facilitates pairwise comparisons within
ANOVA data.
https://www.statisticshowto.com/probability-and-statistics/statistics-definitions/post-hoc/
58. REPORTING POST-HOC RESULTS
Each significant paired Q result (p<0.05) means
that the two sets are statistically significantly
different from one another.
Post hoc comparisons using the Tukey HSD test
indicated that the mean score for the sand condition
(M4 = 6.14) was significantly different from all
other conditions. Also, compost (M3 = 35.57) was
significantly different from hydroponic medium
(M5 = 64.14). However, the compost was not
different from garden soil (M2 = 54.14), or
vermicast (M1 = 57.14). The hydroponic medium
was not different from garden soil, or vermicast.
Students should remember to discuss this result in the
context of their hypothesis. Was the best/worst
result significantly different from others? What are
the trends? Are they as expected?
Reporting results
Figure 3. Screenshot of the post-hoc results of the
same data as in ANOVA example. Treatment 1 is
vermicast, treatment 2 is garden soil , treatment 3 is
compost, treatment 4 is sand, treatment 5 is
hydroponics medium. Significant p values are in blue
ink.
https://www.socscistatistics.com/tests/anova/default2.aspx
k= Number of Treatments.
Df = SE
Significance table for your reference
For a = 0.05
https://www.real-statistics.com/statistics-tables/studentized-range-q-table/ http://statistics-help-for-
students.com/How_do_I_report_a_1_way_between_subjects_ANOVA_in_APA_
style.htm#.YhC7oBNBzTI
59. 13. CHI-SQUARED ANALYSIS
•The chi-squared test is used to determine whether there is a statistically significant
difference between the expected frequencies and the observed frequencies.
• There are two tests students are expected to know:
Chi-square goodness of fit test
Chi-square test of independence
The chi-squared test is used when one of the parameters is categorical
data.
60. CHI-SQUARE GOODNESS OF FIT TEST
•The Chi-square goodness of fit test compares experimental data to the expected values.
Example of a question: does the distribution of phenotypes after two hybrid
cross matches the expected outcome?
•While students do learn how to calculate this test by hand in DP Biology syllabus, in the IA and
EE it is not expected for them to do so. They are encouraged to use the online calculator.
https://www.socscistatistics.com/tests/goodnessoffit/default2.aspx
•Note that expected values should be calculated by students based on the observed amount of
data points and then expressed as expected frequencies or ratios.
•Expected value calculations should be reported in the IA and EE.
61. REPORTING CHI-SQUARED GOODNESS OF FIT TEST
The result (p<0.05) means that
observed values are statistically
significantly different from
expected values.
H0: expected values and
observed values are the same
H1: expected values and
observed values are different
Reporting results
Figure 1. Screenshot of the input data.
Figure 2. Screenshot of the analysis results
https://www.socscistatistics.com/tests/goodnessoffit/default2.aspx
The Chi^2 value is 519.048.
The p-value is < .00001. The
result is significant at p < .05.
Numerator degrees of freedom =
treatments – 1 = t – 1
Denominator degrees of freedom = total
observations minus treatments = N – t
Significance table for your reference
https://passel2.unl.edu/image.php?uuid=f744d18faf02&extension=PNG&display=
MEDIUM&v=1644531499 https://www.socscistatistics.com/tutorials/chisquare/default.aspx
df = (number of categories – 1)
62. CHI-SQUARE TEST OF INDEPENDENCE
The Chi-square test for independence looks for an association between two categorical variables.
Requirements
Random sample
Observations must be independent of each other (so, for example, no matched pairs)
•While students do learn how to calculate this test by hand in DP Biology syllabus, in the IA and EE it is not
expected for them to do so. They are encouraged to use the online calculator.
https://www.socscistatistics.com/tests/chisquare/default2.aspx
•Note that expected values should be calculated by students based on the observed amount of data points and
then expressed as expected frequencies or ratios.
•We expect here that the distribution of data in different data table cells is equal (note – data is adjusted for
the total sample, see the formula below)
•Expected value calculations should be reported in the IA and EE.
Row total * Column total / Sample Size = Expected value for one table cell
Learn more at: https://www.youtube.com/watch?v=7_cs1YlZoug
63. REPORTING CHI-SQUARED TEST OF INDEPENDENCE
The result (p<0.05) means that the number
of smokers does differ based on the gender.
Further details of the conclusion can be
inferred from the data itself. While the Chi-
squared just tells us if there is association or
not, but does not tell us what it is exactly.
H0: there is no association between two
variables
H1: there is association between two
variables
Reporting results
Figure 1. Screenshot of the input data.
Figure 2. Screenshot of the analysis results
https://www.socscistatistics.com/tests/chisquare/default2.aspx
The chi-square statistic is 5.3333.
The p-value is .020921. Significant
at p < .05.
Significance table for your reference
https://www.statisticssolutions.com/free-resources/directory-of-statistical-
analyses/chi-
square/#:~:text=The%20degrees%20of%20freedom%20for,null%20hypothesis
%20can%20be%20rejected.
https://www.socscistatistics.com/tutorials/chisquare/default.aspx
df = (r-1)(c-1)
64. SUMMARY OF DIFFERENT STATISTICAL TESTS
Test Used for Type of data Null hypothesis
(unbiased
expectation)
Get CV from a
(significance) of 0.05
Conclusion if p<0.05 Conclusion if p>0.05
(Null hypothesis is true)
T-test Significance of
differences
between two
groups
Two groups
(populations) with
the same variable
measured
Two populations are
the same
DF=n1+n2-1 There is significant difference
between two populations
There is no significant difference
between two populations
Chi-
squared
Differences of
data from
expectations
Two or more
categories
Frequencies
No difference
between expected
and observed data
DF= number of categories
-1
There is a difference between
observed and expected data
There is no difference between
observed and expected data
Pearson Correlation
between two
variables
Group of data
points measured
against two
variables
Two measurements
are not correlated
between each other
DF is number of sample
data pairs
Significant correlation No significant correlation
ANOVA Significance of
differences
between three or
more groups
Several groups
(populations) with
the same variable
measured
No significant
overlap between the
populations
DF= number of groups -1 There are differences between the
groups
There is no difference between the
groups
Tukey post-
HOC
Identifying
groups
significantly
different from
others
Done after
ANOVA
All means are equal
65. 13. CHOOSING THE APPROPRIATE STATISTICS
FOR THE BIOLOGY IA
Are you looking for relationship description or for comparison of groups?
Is data categorical or continuous?
Great video for students: https://www.youtube.com/watch?v=ulk_JWckJ78
66. Students could use the online questionnaire to determine which test to use, but they
need to know description of their data first.
https://www.socscistatistics.com/tests/what_stats_test_wizard.aspx
Alternative
For not normal distribution
For normal distribution
67.
68. THANK YOU FOR ATTENTION J
Any questions?
Leave me a message through the website (especially if you notice some mistakes):