How to calculate power in statistics
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Epidemiolgy and biostatistics notes
This document provides an introduction to biostatistics and key concepts. It defines biostatistics as the development and application of statistical techniques to scientific research relating to human life and health. Some key terms discussed include:
- Population, which is the totality of individuals of interest
- Sample, which is a subset of a population
- Variables, which can be qualitative (non-numerical) or quantitative (numerical)
- Levels of measurement for variables, including nominal, ordinal, interval, and ratio scales
- Descriptive methods for qualitative data, including frequency distributions
Biostatistics plays an important role in modern medicine, including determining disease burden, finding new drug treatments, planning resource allocation, and measuring
Medical research and study design
This document discusses the history and importance of clinical research. It notes that while medical research has only recently emerged as a formal discipline, epidemiological practices date back centuries to figures like Hippocrates, James Lind, Edward Jenner, John Snow, Ignaz Semmelweis, and Joseph Goldberger. Their studies helped establish strong methodologies in the 1940s-1950s. The document outlines reasons for conducting research, including fulfilling degree requirements, advancing medical knowledge as the field continues expanding, and contributing to the art and science of medicine. It argues doctors should be trained in research to apply findings wisely, produce research that helps colleagues, and consume research accurately to treat patients. Finally, it describes seven key reasons related to
20140602 statistical power - husnul and nur
This document discusses statistical power in hypothesis testing. It defines statistical power as the probability of correctly rejecting the null hypothesis when the alternative hypothesis is true. An ideal statistical power is 0.80 or higher. Factors that can affect statistical power include effect size, sample size, alpha level, and beta error rate. The document provides steps for calculating statistical power, using an example of studying how a training may improve writing scores: 1) Find the critical value, 2) Standardize the critical value, 3) Find power from tables. Calculating power can help determine necessary sample size to adequately power a study and avoid being underpowered or overpowered.
Fixed-effect and random-effects models in meta-analysis
Systematic review and meta-analysis
Source & acknowledgement
https://www.terripigott.com/meta-analysis
https://mason.gmu.edu/~dwilsonb/ma.html
https://www.campbellcollaboration.org/research-resources/training-courses.html
https://handbook-5-1.cochrane.org/
https://www.youtube.com/user/Biostat100
https://www.youtube.com/user/collaborationtube
https://www.meta-analysis.com/pages/videotutorials.php?cart=BWJJ3522355
Sample size determination
A sample design is a definite plan for obtaining a sample from a given population. Researcher must select/prepare a sample design which should be reliable and appropriate for his research study.
Experimental Studies
This document discusses experimental study designs, specifically randomized clinical trials. It describes key aspects of randomized trials including multiple experimental groups, blinding techniques, objectives related to public health and clinical practice, and historical examples. Randomized trials are identified as the ideal design for evaluating new interventions by comparing outcomes between randomized treatment groups to eliminate selection bias. Key aspects covered include selection and stratification of subjects, data collection on variables like treatment received, outcomes, and prognostic profiles, as well as blinding techniques.
Power Analysis and Sample Size Determination
This document discusses power analysis and sample size determination. It explains key concepts like power, effect size, significance level, and how changing these factors impacts the required sample size. Sample size is important to correctly power a study to detect clinically meaningful effects without excessive subjects. The document provides formulas and examples for calculating sample sizes for various study designs including randomized trials, pre-post, and equivalence studies. Researchers must consider these factors before collecting data to ensure their study is appropriately powered.
Meta analysis techniques in epidemiology
Meta-analysis in Epidemiology is:
Useful tool for epidemiological studies which investigates the relationships between certain risk factors and disease.
Useful tool to improve animal well-being and productivity
Despite of a wealth of suitable studies it is relatively underutilized in animal and veterinary science.
Meta-analysis can provide reliable results about diseases occurrence, pattern and impact in livestock.
It is utmost essential to take benefit of this statistical tool for produce. more reliable estimates of concern effects in animal and veterinary science data.
Recommended
Epidemiolgy and biostatistics notes
This document provides an introduction to biostatistics and key concepts. It defines biostatistics as the development and application of statistical techniques to scientific research relating to human life and health. Some key terms discussed include:
- Population, which is the totality of individuals of interest
- Sample, which is a subset of a population
- Variables, which can be qualitative (non-numerical) or quantitative (numerical)
- Levels of measurement for variables, including nominal, ordinal, interval, and ratio scales
- Descriptive methods for qualitative data, including frequency distributions
Biostatistics plays an important role in modern medicine, including determining disease burden, finding new drug treatments, planning resource allocation, and measuring
Medical research and study design
This document discusses the history and importance of clinical research. It notes that while medical research has only recently emerged as a formal discipline, epidemiological practices date back centuries to figures like Hippocrates, James Lind, Edward Jenner, John Snow, Ignaz Semmelweis, and Joseph Goldberger. Their studies helped establish strong methodologies in the 1940s-1950s. The document outlines reasons for conducting research, including fulfilling degree requirements, advancing medical knowledge as the field continues expanding, and contributing to the art and science of medicine. It argues doctors should be trained in research to apply findings wisely, produce research that helps colleagues, and consume research accurately to treat patients. Finally, it describes seven key reasons related to
20140602 statistical power - husnul and nur
This document discusses statistical power in hypothesis testing. It defines statistical power as the probability of correctly rejecting the null hypothesis when the alternative hypothesis is true. An ideal statistical power is 0.80 or higher. Factors that can affect statistical power include effect size, sample size, alpha level, and beta error rate. The document provides steps for calculating statistical power, using an example of studying how a training may improve writing scores: 1) Find the critical value, 2) Standardize the critical value, 3) Find power from tables. Calculating power can help determine necessary sample size to adequately power a study and avoid being underpowered or overpowered.
Fixed-effect and random-effects models in meta-analysis
Systematic review and meta-analysis
Source & acknowledgement
https://www.terripigott.com/meta-analysis
https://mason.gmu.edu/~dwilsonb/ma.html
https://www.campbellcollaboration.org/research-resources/training-courses.html
https://handbook-5-1.cochrane.org/
https://www.youtube.com/user/Biostat100
https://www.youtube.com/user/collaborationtube
https://www.meta-analysis.com/pages/videotutorials.php?cart=BWJJ3522355
Sample size determination
A sample design is a definite plan for obtaining a sample from a given population. Researcher must select/prepare a sample design which should be reliable and appropriate for his research study.
Experimental Studies
This document discusses experimental study designs, specifically randomized clinical trials. It describes key aspects of randomized trials including multiple experimental groups, blinding techniques, objectives related to public health and clinical practice, and historical examples. Randomized trials are identified as the ideal design for evaluating new interventions by comparing outcomes between randomized treatment groups to eliminate selection bias. Key aspects covered include selection and stratification of subjects, data collection on variables like treatment received, outcomes, and prognostic profiles, as well as blinding techniques.
Power Analysis and Sample Size Determination
This document discusses power analysis and sample size determination. It explains key concepts like power, effect size, significance level, and how changing these factors impacts the required sample size. Sample size is important to correctly power a study to detect clinically meaningful effects without excessive subjects. The document provides formulas and examples for calculating sample sizes for various study designs including randomized trials, pre-post, and equivalence studies. Researchers must consider these factors before collecting data to ensure their study is appropriately powered.
Meta analysis techniques in epidemiology
Meta-analysis in Epidemiology is:
Useful tool for epidemiological studies which investigates the relationships between certain risk factors and disease.
Useful tool to improve animal well-being and productivity
Despite of a wealth of suitable studies it is relatively underutilized in animal and veterinary science.
Meta-analysis can provide reliable results about diseases occurrence, pattern and impact in livestock.
It is utmost essential to take benefit of this statistical tool for produce. more reliable estimates of concern effects in animal and veterinary science data.
observational analytical study
This document discusses different types of observational study designs used in epidemiology, including descriptive and analytical studies. Descriptive studies like case reports and case series describe characteristics of patients but cannot determine causation. Analytical observational studies include cross-sectional studies, which measure exposures and outcomes at one time point, and cohort studies, which follow groups over time. Case-control studies sample based on outcome and look back at exposures. While observational studies are useful for hypothesis generation, experimental randomized controlled trials are needed to prove causation. The odds ratio from case-control studies approximates the risk ratio when studying rare diseases or outcomes.
Statistical Power
Researchers, as a whole, tend to underestimate the need for power. I'm just now starting to get it.
I recently gave a brief, easy-to-follow presentation on statistical power, it's importance, and how to go about getting it.
Hope you find it useful.
Observational analytical and interventional studies
This document provides an overview of different types of epidemiological study designs, including observational analytical studies like cohort and case-control studies, as well as experimental studies. It describes key aspects of cohort and case-control studies such as their designs, advantages, disadvantages, examples, and considerations for conducting them. Cohort studies follow groups over time from exposure to outcome, while case-control studies identify cases and controls and look back from outcome to exposure. Experimental studies actively alter variables to assess relationships between them.
Data Analysis Using Spss T Test
The t-test is used to determine if there are significant differences between the means of two groups. An independent-samples t-test was conducted to compare the affective commitment, continuance commitment, and normative commitment of male and female employees. The t-test results showed a significant difference in affective commitment between males (M=3.49720) and females (M=3.38016), but no significant differences in continuance commitment or normative commitment between the two groups.
Sample size calculation in medical research
A short description on estimation of sample size in health care research. It describes the basic concepts in sample size estimation and various important formulae used for it.
Statistics in medical research
1) Statistics play an important role in medical research by describing diseases, making estimates from samples, determining significance of differences and associations, and making forecasts.
2) A statistician should be consulted at the planning, data collection, and reporting stages of research. At planning, they can help frame questions, determine sample size and sampling methods, and identify variables and scales of measurement.
3) It is important to utilize statisticians properly in research by involving them in the entire process and communicating effectively between clinical and statistical perspectives.
Chi square tests using SPSS
Chi-Square test for independence of attributes / Chi-Square test for checking association between two categorical variables, Chi-Square test for goodness of fit
Parametric and non parametric test
Statistical tests can be used to analyze data in two main ways: descriptive statistics provide an overview of data attributes, while inferential statistics assess how well data support hypotheses and generalizability. There are different types of tests for comparing means and distributions between groups, determining if differences or relationships exist in parametric or non-parametric data. The appropriate test depends on the question being asked, number of groups, and properties of the data.
observational analytical and interventional studies
This document discusses different types of epidemiological studies, including observational analytical studies like cohort and case-control studies, as well as interventional experimental studies. Cohort studies follow groups over time from exposure to disease outcome, while case-control studies compare cases and controls retrospectively from disease outcome back to exposure. Experimental studies actively manipulate variables to evaluate new drugs, technologies, programs, and more. Both observational and experimental studies have advantages like establishing causality, but also disadvantages like costs or ethical concerns.
Sample Size Estimation
This document discusses sample size estimation and the factors that influence determining an appropriate sample size for research studies. It provides examples of calculating sample sizes based on prevalence of a disease, mean values, standard deviations, permissible errors, and confidence levels. The key points are:
- Sample size depends on prevalence/magnitude of the attribute being studied, permissible error, and power of the statistical test
- Larger sample sizes are needed to detect smaller differences and have sufficient power
- Examples are provided to demonstrate calculating sample sizes based on prevalence of anemia, mean blood pressure values, and acceptable margins of error
Inferential statistics
The document provides an overview of inferential statistics. It defines inferential statistics as making generalizations about a larger population based on a sample. Key topics covered include hypothesis testing, types of hypotheses, significance tests, critical values, p-values, confidence intervals, z-tests, t-tests, ANOVA, chi-square tests, correlation, and linear regression. The document aims to explain these statistical concepts and techniques at a high level.
Two-way Repeated Measures ANOVA
This document provides information on two-way repeated measures designs, including when to use them, their structure, and how to analyze the data. A two-way repeated measures design is used to investigate the effects of two within-subjects factors on a dependent variable simultaneously. All subjects are tested at each level of both factors. This design allows comparison of mean differences between groups split on the two within-subject factors. The document describes the analysis process, including testing for main effects, interactions, and simple effects using SPSS. An example is provided to illustrate a two-way repeated measures design investigating the effects of music and environment on work performance.
Nested case control,
This document discusses nested case-control studies, case-cohort studies, and case-crossover studies. It provides examples and discusses the advantages and disadvantages of each study design. Nested case-control studies select controls from within a prospective cohort study. Case-cohort studies select a random subcohort of controls from the entire cohort. Case-crossover studies use individuals as their own controls by comparing exposure during case periods to control periods.
Medical Statistics Part-II:Inferential statistics
This document provides an overview of key concepts in inferential statistics. Inferential statistics allows researchers to make inferences about populations based on samples. It includes techniques like hypothesis testing, t-tests, analysis of variance (ANOVA), regression analysis, and more. The goal is to determine if observed differences are statistically significant rather than due to chance. Inferential statistics helps estimate parameters and analyze variability using statistical models and software.
Introduction to Descriptive Statistics
Lecture on Introduction to Descriptive Statistics - Part 1 and Part 2. These slides were presented during a lecture at the Colombo Institute of Research and Psychology.
Sample size and power
1. Sample size planning is important as it specifies outcome variables, clinically meaningful effect sizes, statistical procedures, recruitment goals, timelines and budgets.
2. Estimating sample size requires specifying hypotheses, statistical tests, minimum detectable effect sizes, outcome variability, and Type I and II error rates.
3. Software can help estimate sample sizes for different study designs, while smaller samples may be feasible with adjustments like changing error rates, hypotheses, effect sizes, or outcome measures.
05 intervention studies
This document discusses intervention studies and randomized controlled trials. It begins by defining causality using the counterfactual model and comparing exposed and unexposed groups. It then describes the importance of randomization in intervention studies, noting that randomization helps ensure the unexposed group is a valid control, controls for unknown confounders, facilitates blinding, and provides a foundation for statistical tests. The document discusses types of intervention studies, issues like compliance, analysis approaches like intention-to-treat, and ethical considerations.
Non parametric test
This document discusses non-parametric tests, which are statistical tests that make fewer assumptions about the population distribution compared to parametric tests. Some key points:
1) Non-parametric tests like the chi-square test, sign test, Wilcoxon signed-rank test, Mann-Whitney U-test, and Kruskal-Wallis test are used when the population is not normally distributed or sample sizes are small.
2) They are applied in situations where data is on an ordinal scale rather than a continuous scale, the population is not well defined, or the distribution is unknown.
3) Advantages are that they are easier to compute and make fewer assumptions than parametric tests,
Cross sectional study
This document discusses cross-sectional studies. It defines a cross-sectional study as an observational study that measures exposure and health outcomes in a population at a single point in time, providing a "snapshot" of prevalence. It describes key characteristics, including simultaneously collecting exposure and outcome data, estimating prevalence rather than incidence, and inability to determine temporal relationships between variables. The document outlines advantages as being quick and inexpensive but also limitations such as inability to establish causation.
Categorical data analysis
This document discusses various statistical tests used to analyze categorical data, including contingency tables and chi-square tests. It begins by defining continuous and categorical variables. It then discusses how to represent associations between categorical variables using contingency tables. It explains how to calculate expected frequencies and chi-square values to test for relationships between categorical variables. Finally, it discusses other tests that can be used for contingency tables like Fisher's exact test, McNemar's test, and Yates correction.
CORE: May the “Power” (Statistical) - Be with You!
About CORE:
The Culture of Research and Education (C.O.R.E.) webinar series is spearheaded by Dr. Bernice B. Rumala, CORE Chair & Program Director of the Ph.D. in Health Sciences program in collaboration with leaders and faculty across all academic programs.
This innovative and wide-ranging series is designed to provide continuing education, skills-building techniques, and tools for academic and professional development. These sessions will provide a unique chance to build your professional development toolkit through presentations, discussions, and workshops with Trident’s world-class faculty.
For further information about CORE or to present, you may contact Dr. Bernice B. Rumala at Bernice.rumala@trident.edu
Hypothesis testing
Statistics is used to interpret data and draw conclusions about populations based on sample data. Hypothesis testing involves evaluating two statements (the null and alternative hypotheses) about a population using sample data. A hypothesis test determines which statement is best supported.
The key steps in hypothesis testing are to formulate the hypotheses, select an appropriate statistical test, choose a significance level, collect and analyze sample data to calculate a test statistic, determine the probability or critical value associated with the test statistic, and make a decision to reject or fail to reject the null hypothesis based on comparing the probability or test statistic to the significance level and critical value.
An example tests whether the proportion of internet users who shop online is greater than 40% using
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observational analytical study
This document discusses different types of observational study designs used in epidemiology, including descriptive and analytical studies. Descriptive studies like case reports and case series describe characteristics of patients but cannot determine causation. Analytical observational studies include cross-sectional studies, which measure exposures and outcomes at one time point, and cohort studies, which follow groups over time. Case-control studies sample based on outcome and look back at exposures. While observational studies are useful for hypothesis generation, experimental randomized controlled trials are needed to prove causation. The odds ratio from case-control studies approximates the risk ratio when studying rare diseases or outcomes.
Statistical Power
Researchers, as a whole, tend to underestimate the need for power. I'm just now starting to get it.
I recently gave a brief, easy-to-follow presentation on statistical power, it's importance, and how to go about getting it.
Hope you find it useful.
Observational analytical and interventional studies
This document provides an overview of different types of epidemiological study designs, including observational analytical studies like cohort and case-control studies, as well as experimental studies. It describes key aspects of cohort and case-control studies such as their designs, advantages, disadvantages, examples, and considerations for conducting them. Cohort studies follow groups over time from exposure to outcome, while case-control studies identify cases and controls and look back from outcome to exposure. Experimental studies actively alter variables to assess relationships between them.
Data Analysis Using Spss T Test
The t-test is used to determine if there are significant differences between the means of two groups. An independent-samples t-test was conducted to compare the affective commitment, continuance commitment, and normative commitment of male and female employees. The t-test results showed a significant difference in affective commitment between males (M=3.49720) and females (M=3.38016), but no significant differences in continuance commitment or normative commitment between the two groups.
Sample size calculation in medical research
A short description on estimation of sample size in health care research. It describes the basic concepts in sample size estimation and various important formulae used for it.
Statistics in medical research
1) Statistics play an important role in medical research by describing diseases, making estimates from samples, determining significance of differences and associations, and making forecasts.
2) A statistician should be consulted at the planning, data collection, and reporting stages of research. At planning, they can help frame questions, determine sample size and sampling methods, and identify variables and scales of measurement.
3) It is important to utilize statisticians properly in research by involving them in the entire process and communicating effectively between clinical and statistical perspectives.
Chi square tests using SPSS
Chi-Square test for independence of attributes / Chi-Square test for checking association between two categorical variables, Chi-Square test for goodness of fit
Parametric and non parametric test
Statistical tests can be used to analyze data in two main ways: descriptive statistics provide an overview of data attributes, while inferential statistics assess how well data support hypotheses and generalizability. There are different types of tests for comparing means and distributions between groups, determining if differences or relationships exist in parametric or non-parametric data. The appropriate test depends on the question being asked, number of groups, and properties of the data.
observational analytical and interventional studies
This document discusses different types of epidemiological studies, including observational analytical studies like cohort and case-control studies, as well as interventional experimental studies. Cohort studies follow groups over time from exposure to disease outcome, while case-control studies compare cases and controls retrospectively from disease outcome back to exposure. Experimental studies actively manipulate variables to evaluate new drugs, technologies, programs, and more. Both observational and experimental studies have advantages like establishing causality, but also disadvantages like costs or ethical concerns.
Sample Size Estimation
This document discusses sample size estimation and the factors that influence determining an appropriate sample size for research studies. It provides examples of calculating sample sizes based on prevalence of a disease, mean values, standard deviations, permissible errors, and confidence levels. The key points are:
- Sample size depends on prevalence/magnitude of the attribute being studied, permissible error, and power of the statistical test
- Larger sample sizes are needed to detect smaller differences and have sufficient power
- Examples are provided to demonstrate calculating sample sizes based on prevalence of anemia, mean blood pressure values, and acceptable margins of error
Inferential statistics
The document provides an overview of inferential statistics. It defines inferential statistics as making generalizations about a larger population based on a sample. Key topics covered include hypothesis testing, types of hypotheses, significance tests, critical values, p-values, confidence intervals, z-tests, t-tests, ANOVA, chi-square tests, correlation, and linear regression. The document aims to explain these statistical concepts and techniques at a high level.
Two-way Repeated Measures ANOVA
This document provides information on two-way repeated measures designs, including when to use them, their structure, and how to analyze the data. A two-way repeated measures design is used to investigate the effects of two within-subjects factors on a dependent variable simultaneously. All subjects are tested at each level of both factors. This design allows comparison of mean differences between groups split on the two within-subject factors. The document describes the analysis process, including testing for main effects, interactions, and simple effects using SPSS. An example is provided to illustrate a two-way repeated measures design investigating the effects of music and environment on work performance.
Nested case control,
This document discusses nested case-control studies, case-cohort studies, and case-crossover studies. It provides examples and discusses the advantages and disadvantages of each study design. Nested case-control studies select controls from within a prospective cohort study. Case-cohort studies select a random subcohort of controls from the entire cohort. Case-crossover studies use individuals as their own controls by comparing exposure during case periods to control periods.
Medical Statistics Part-II:Inferential statistics
This document provides an overview of key concepts in inferential statistics. Inferential statistics allows researchers to make inferences about populations based on samples. It includes techniques like hypothesis testing, t-tests, analysis of variance (ANOVA), regression analysis, and more. The goal is to determine if observed differences are statistically significant rather than due to chance. Inferential statistics helps estimate parameters and analyze variability using statistical models and software.
Introduction to Descriptive Statistics
Lecture on Introduction to Descriptive Statistics - Part 1 and Part 2. These slides were presented during a lecture at the Colombo Institute of Research and Psychology.
Sample size and power
1. Sample size planning is important as it specifies outcome variables, clinically meaningful effect sizes, statistical procedures, recruitment goals, timelines and budgets.
2. Estimating sample size requires specifying hypotheses, statistical tests, minimum detectable effect sizes, outcome variability, and Type I and II error rates.
3. Software can help estimate sample sizes for different study designs, while smaller samples may be feasible with adjustments like changing error rates, hypotheses, effect sizes, or outcome measures.
05 intervention studies
This document discusses intervention studies and randomized controlled trials. It begins by defining causality using the counterfactual model and comparing exposed and unexposed groups. It then describes the importance of randomization in intervention studies, noting that randomization helps ensure the unexposed group is a valid control, controls for unknown confounders, facilitates blinding, and provides a foundation for statistical tests. The document discusses types of intervention studies, issues like compliance, analysis approaches like intention-to-treat, and ethical considerations.
Non parametric test
This document discusses non-parametric tests, which are statistical tests that make fewer assumptions about the population distribution compared to parametric tests. Some key points:
1) Non-parametric tests like the chi-square test, sign test, Wilcoxon signed-rank test, Mann-Whitney U-test, and Kruskal-Wallis test are used when the population is not normally distributed or sample sizes are small.
2) They are applied in situations where data is on an ordinal scale rather than a continuous scale, the population is not well defined, or the distribution is unknown.
3) Advantages are that they are easier to compute and make fewer assumptions than parametric tests,
Cross sectional study
This document discusses cross-sectional studies. It defines a cross-sectional study as an observational study that measures exposure and health outcomes in a population at a single point in time, providing a "snapshot" of prevalence. It describes key characteristics, including simultaneously collecting exposure and outcome data, estimating prevalence rather than incidence, and inability to determine temporal relationships between variables. The document outlines advantages as being quick and inexpensive but also limitations such as inability to establish causation.
Categorical data analysis
This document discusses various statistical tests used to analyze categorical data, including contingency tables and chi-square tests. It begins by defining continuous and categorical variables. It then discusses how to represent associations between categorical variables using contingency tables. It explains how to calculate expected frequencies and chi-square values to test for relationships between categorical variables. Finally, it discusses other tests that can be used for contingency tables like Fisher's exact test, McNemar's test, and Yates correction.
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CORE: May the “Power” (Statistical) - Be with You!
About CORE:
The Culture of Research and Education (C.O.R.E.) webinar series is spearheaded by Dr. Bernice B. Rumala, CORE Chair & Program Director of the Ph.D. in Health Sciences program in collaboration with leaders and faculty across all academic programs.
This innovative and wide-ranging series is designed to provide continuing education, skills-building techniques, and tools for academic and professional development. These sessions will provide a unique chance to build your professional development toolkit through presentations, discussions, and workshops with Trident’s world-class faculty.
For further information about CORE or to present, you may contact Dr. Bernice B. Rumala at Bernice.rumala@trident.edu
Hypothesis testing
Statistics is used to interpret data and draw conclusions about populations based on sample data. Hypothesis testing involves evaluating two statements (the null and alternative hypotheses) about a population using sample data. A hypothesis test determines which statement is best supported.
The key steps in hypothesis testing are to formulate the hypotheses, select an appropriate statistical test, choose a significance level, collect and analyze sample data to calculate a test statistic, determine the probability or critical value associated with the test statistic, and make a decision to reject or fail to reject the null hypothesis based on comparing the probability or test statistic to the significance level and critical value.
An example tests whether the proportion of internet users who shop online is greater than 40% using
Hypothesis TestingThe Right HypothesisIn business, or an.docx
Hypothesis Testing
The Right Hypothesis
In business, or any other discipline, once the question has been asked there must be a statement as to what will or will not occur through testing, measurement, and investigation. This process is known as formulating the right hypothesis. Broadly defined a hypothesis is a statement that the conditions under which something is being measured or evaluated holds true or does not hold true. Further, a business hypothesis is an assumption that is to be tested through market research, data mining, experimental designs, quantitative, and qualitative research endeavors. A hypothesis gives the businessperson a path to follow and specific things to look for along the road.
If the research and statistical data analysis supports and proves the hypothesis that becomes a project well done. If, however, the research data proved a modified version of the hypothesis then re-evaluation for continuation must take place. However, if the research data disproves the hypothesis then the project is usually abandoned.
Hypotheses come in two forms: the null hypothesis and the alternate hypothesis. As a student of applied business statistics you can pick up any number of business statistics textbooks and find a number of opinions on which type of hypothesis should be used in the business world. For the most part, however, and the safest, the better hypothesis to formulate on the basis of the research question asked is what is called the null hypothesis. A null hypothesis states that the research measurement data gathered will not support a difference, relationship, or effect between or amongst those variables being investigated. To the seasoned research investigator having to accept a statement that no differences, relationships, and/or effects will occur based on a statistical data analysis is because when nothing takes place or no differences, effects, or relationship are found there is no possible reason that can be given as to why. This is where most business managers get into trouble when attempting to offer an explanation as to why something has not happened. Attempting to provide an answer to why something has not taken place is akin to discussing how many angels can be placed on the head of a pin—everyone’s answer is plausible and possible. As such business managers need to accept that which has happened and not that which has not happened.
Many business people will skirt the null hypothesis issue by attempting to set analternative hypothesis that states differences, effects and relationships will occur between and amongst that which is being investigated if certain conditions apply.Unfortunately, however, this reverse position is as bad. The research investigator might well be safe if the data analysis detects differences, effect or relationships, but what if it does not? In that case the business manager is back to square one in attempting to explain what has not happened. Although the hypothesis situation may seem c.
Power Analysis: Determining Sample Size for Quantitative Studies
In this webinar, we go over how to determine the appropriate sample size for a quantitative study by using power analysis. The presentation includes an explanation of what a power analysis is and examples of how to conduct power analyses for common statistical tests. The presentation focuses on power analysis using G*Power and Intellectus Statistics software programs. Sample size calculations for more advanced analyses are briefly discussed.
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This document discusses determining sample size for research studies. It defines key terms like sample size, population, and discusses factors that affect sample size like desired accuracy and available resources. It describes common methods for calculating sample size like formulas, tables, and software. Formulas use specifications like confidence level, margin of error, and population proportion to determine the needed sample size. The document emphasizes that determining an appropriate sample size is essential for research validity and making inferences to the target population.
Hypothesis Testing Definitions A statistical hypothesi.docx
Hypothesis Testing
Definitions:
A statistical hypothesis is a guess about a population parameter. The guess may or not be
true.
The null hypothesis, written H0, is a statistical hypothesis that states that there is no
difference between a parameter and a specific value, or that there is no difference between
two parameters.
The alternative hypothesis, written H1 or HA, is a statistical hypothesis that specifies a
specific difference between a parameter and a specific value, or that there is a difference
between two parameters.
Example 1:
A medical researcher is interested in finding out whether a new medication will have
undesirable side effects. She is particularly concerned with the pulse rate of patients who
take the medication. The research question is, will the pulse rate increase, decrease, or
remain the same after a patient takes the medication?
Since the researcher knows that the mean pulse rate for the population under study is 82
beats per minute, the hypotheses for this study are:
H0: µ = 82
HA: µ ≠ 82
The null hypothesis specifies that the mean will remain unchanged and the alternative
hypothesis states that it will be different. This test is called a two-tailed test since the
possible side effects could be to raise or lower the pulse rate. Notice that this is a non
directional hypothesis. The rejection region lies in both tails. We divide the alpha in two
and place half in each tail.
Example 2:
An entrepreneur invents an additive to increase the life of an automobile battery. If the
mean lifetime of the automobile battery is 36 months, then his hypotheses are:
H0: µ ≤ 36
HA: µ > 36
Here, the entrepreneur is only interested in increasing the lifetime of the batteries, so his
alternative hypothesis is that the mean is greater than 36 months. The null hypothesis is
that the mean is less than or equal to 36 months. This test is one-tailed since the interest
is only in an increased lifetime. Notice that the direction of the inequality in the alternate
hypothesis points to the right, same as the area of the curve that forms the rejection
region.
Example 3:
A landlord who wants to lower heating bills in a large apartment complex is considering
using a new type of insulation. If the current average of the monthly heating bills is $78,
his hypotheses about heating costs with the new insulation are:
H0: µ ≥ 78
HA: µ < 78
This test is also a one-tailed test since the landlord is interested only in lowering heating
costs. Notice that the direction of the inequality in the alternate hypothesis points to the
left, same as the area of the curve that forms the rejection region.
Study Design:
After stating the hypotheses, the researcher’s next step is to design the study. In designing
the study, the researcher selects an appropriate statistical test, chooses a level of
significance, and formulates a plan for conducting the study..
TEST #1Perform the following two-tailed hypothesis test, using a.docx
TEST #1
Perform the following two-tailed hypothesis test, using a .05 significance level:
· Intrinsic by Gender
· State the null and an alternate statement for the test
· Use Microsoft Excel (Data Analysis Tools) to process your data and run the appropriate test. Copy and paste the results of the output to your report in Microsoft Word.
· Identify the significance level, the test statistic, and the critical value.
· State whether you are rejecting or failing to reject the null hypothesis statement.
· Explain how the results could be used by the manager of the company.
TEST #2
Perform the following two-tailed hypothesis test, using a .05 significance level:
· Extrinsic variable by Position Type
· State the null and an alternate statement for the test
· Use Microsoft Excel (Data Analysis Tools) to process your data and run the appropriate test.
· Copy and paste the results of the output to your report in Microsoft Word.
· Identify the significance level, the test statistic, and the critical value.
· State whether you are rejecting or failing to reject the null hypothesis statement.
· Explain how the results could be used by the manager of the company.
GENERAL ANALYSIS (Research Required)
Using your textbook or other appropriate college-level resources:
· Explain when to use a t-test and when to use a z-test. Explore the differences.
· Discuss why samples are used instead of populations.
The report should be well written and should flow well with no grammatical errors. It should include proper citation in APA formatting in both the in-text and reference pages and include a title page, be double-spaced, and in Times New Roman, 12-point font. APA formatting is necessary to ensure academic honesty.
Be sure to provide references in APA format for any resource you may use to support your answers.
Making Inferences
When data are collected, various summary statistics and graphs can be used for describing data; however, learning about what the data mean is where the power of statistics starts. For example, is there really a difference between two leading cola products? Hypothesis testing is an example of making these types of inferences on data sets.
Hypothesis Tests
Claims are made all the time, such as a particular light bulb will last a certain number of hours.
Claims like this are tested with hypothesis testing. It is a straight forward procedure that consists of the following steps:
1. A claim is made.
2. A value for probability of significance is chosen.
3. Data are collected.
4. The test is performed.
5. The results are analyzed.
Hypothesis tests are performed on the mean of the population. µ
It is not possible to test the full population. For example, it would be impossible to test every light bulb. Instead, the hypothesis test is performed on a sample of the population.
Setting up a Hypothesis Test
When performing hypothesis testing, the test is setup with a null hypothesis (or claim) and the alternative hypothesis. ...
Hypothesis testing 1.0
This presentation discusses the following topics:
Hypothesis Test
Potential Outcomes in Hypothesis Testing
Significance level
P-value
Sampling Errors
Type I Error
What causes Type I errors?
What causes Type II errors?
4 possible outcomes
STATISTICS : Changing the way we do: Hypothesis testing, effect size, power, ...
Researchers should take several steps to make statistical results meaningful:
1. Perform a power analysis to determine adequate sample size and ensure power is above .50, ideally .80. Power is the probability of detecting real effects.
2. Never set the alpha level lower than .05 and try to set it higher to .10 if acceptable.
3. Report effect sizes and confidence intervals to provide context around statistical significance. Effect sizes indicate the magnitude of differences between groups.
Brmedj00047 0038
1) The article discusses the importance of properly determining sample size in medical research studies. Sample size is one of the most common reasons researchers consult statisticians.
2) Studies with too small of a sample size will likely be unable to detect clinically important effects and thus be scientifically useless and unethical. However, studies with unnecessarily large samples can also be deemed unethical due to unnecessary involvement of extra subjects.
3) The concept of statistical power, which is the likelihood of a test detecting a true difference or effect of a given size, is important for determining an appropriate sample size that balances scientific validity with ethical considerations. Methods like power calculations, graphs, and nomograms can help researchers prospectively determine adequate
Page 266LEARNING OBJECTIVES· Explain how researchers use inf.docx
Page 266
LEARNING OBJECTIVES
· Explain how researchers use inferential statistics to evaluate sample data.
· Distinguish between the null hypothesis and the research hypothesis.
· Discuss probability in statistical inference, including the meaning of statistical significance.
· Describe the t test and explain the difference between one-tailed and two-tailed tests.
· Describe the F test, including systematic variance and error variance.
· Describe what a confidence interval tells you about your data.
· Distinguish between Type I and Type II errors.
· Discuss the factors that influence the probability of a Type II error.
· Discuss the reasons a researcher may obtain nonsignificant results.
· Define power of a statistical test.
· Describe the criteria for selecting an appropriate statistical test.
Page 267IN THE PREVIOUS CHAPTER, WE EXAMINED WAYS OF DESCRIBING THE RESULTS OF A STUDY USING DESCRIPTIVE STATISTICS AND A VARIETY OF GRAPHING TECHNIQUES. In addition to descriptive statistics, researchers use inferential statistics to draw more general conclusions about their data. In short, inferential statistics allow researchers to (a) assess just how confident they are that their results reflect what is true in the larger population and (b) assess the likelihood that their findings would still occur if their study was repeated over and over. In this chapter, we examine methods for doing so.
SAMPLES AND POPULATIONS
Inferential statistics are necessary because the results of a given study are based only on data obtained from a single sample of research participants. Researchers rarely, if ever, study entire populations; their findings are based on sample data. In addition to describing the sample data, we want to make statements about populations. Would the results hold up if the experiment were conducted repeatedly, each time with a new sample?
In the hypothetical experiment described in Chapter 12 (see Table 12.1), mean aggression scores were obtained in model and no-model conditions. These means are different: Children who observe an aggressive model subsequently behave more aggressively than children who do not see the model. Inferential statistics are used to determine whether the results match what would happen if we were to conduct the experiment again and again with multiple samples. In essence, we are asking whether we can infer that the difference in the sample means shown in Table 12.1 reflects a true difference in the population means.
Recall our discussion of this issue in Chapter 7 on the topic of survey data. A sample of people in your state might tell you that 57% prefer the Democratic candidate for an office and that 43% favor the Republican candidate. The report then says that these results are accurate to within 3 percentage points, with a 95% confidence level. This means that the researchers are very (95%) confident that, if they were able to study the entire population rather than a sample, the actual percentage who preferred th ...
Sample Size Determination
This presentation will address the issue of sample size determination for social sciences. A simple example is provided for every to understand and explain the sample size determination.
PAGE O&M Statistics – Inferential Statistics Hypothesis Test.docx
PAGE
O&M Statistics – Inferential Statistics: Hypothesis Testing
Inferential Statistics
Hypothesis testing
Introduction
In this week, we transition from confidence intervals and interval estimates to hypothesis testing, the basis for inferential statistics. Inferential statistics means using a sample to draw a conclusion about an entire population. A test of hypothesis is a procedure to determine whether sample data provide sufficient evidence to support a position about a population. This position or claim is called the alternative or research hypothesis.
“It is a procedure based on sample evidence and probability theory to determine whether the hypothesis is a reasonable statement” (Mason & Lind, pg. 336).
This Week in Relation to the Course
Hypothesis testing is at the heart of research. In this week, we examine and practice a procedure to perform tests of hypotheses comparing a sample mean to a population mean and a test of hypotheses comparing two sample means.
The Five-Step Procedure for Hypothesis Testing (you need to show all 5 steps – these contain the same information you would find in a research paper – allows others to see how you arrived at your conclusion and provides a basis for subsequent research).
Step 1
State the null hypothesis – equating the population parameter to a specification. The null hypothesis is always one of status quo or no difference. We call the null hypothesis H0 (H sub zero). It is the hypothesis that contains an equality.
State the alternate hypothesis – The alternate is represented as H1 or HA (H sub one or H sub A). The alternate hypothesis is the exact opposite of the null hypothesis and represents the conclusion supported if the null is rejected. The alternate will not contain an equal sign of the population parameter.
Most of the time, researchers construct tests of hypothesis with the anticipation that the null hypothesis will be rejected.
Step 2
Select a level of significance (α) which will be used when finding critical value(s).
The level you choose (alpha) indicates how confident we wish to be when making the decision.
For example, a .05 alpha level means that we are 95% sure of the reliability of our findings, but there is still a 5% chance of being wrong (what is called the likelihood of committing a Type 1 error).
The level of significance is set by the individual performing the test. Common significance levels are .01, .05, and .10. It is important to always state what the chosen level of significance is.
Step 3
Identify the test statistic – this is the formula you use given the data in the scenario. Simply put, the test statistic may be a Z statistic, a t statistic, or some other distribution. Selection of the correct test statistic will depend on the nature of the data being tested (sample size, whether the population standard deviation is known, whether the data is known to be normally distributed).
The sampling distribution of the test statistic is divided into t.
2016 Symposium Poster - statistics - Final
This document discusses common pitfalls in statistical analysis and provides examples to illustrate typical mistakes. It notes that statistical significance does not always imply practical significance. Even with the same means and variances, different datasets can have very different distributions. Correlation does not necessarily indicate causation. Qualitative scales should not always be treated as quantitative variables. Choosing the appropriate statistical test is important to get the right results. Sample size calculations depend on study details and objectives. Involving statisticians early in the research process helps ensure proper experimental design and analysis.
Hypothesis Testing.pptx
A hypothesis test examines two opposing hypotheses: the null hypothesis and alternative hypothesis. The null hypothesis is the statement being tested, usually stating "no effect". The alternative hypothesis is what the researcher hopes to prove true. A hypothesis test uses a sample to determine whether to reject the null hypothesis based on a p-value and significance level. There are 5 steps: specify null and alternative hypotheses, set significance level, calculate test statistic and p-value, and draw a conclusion. Type I and II errors are possible - type I rejects a true null hypothesis, type II fails to reject a false null hypothesis.
Inferential statistics.ppt
This document discusses inferential statistics, which uses sample data to make inferences about populations. It explains that inferential statistics is based on probability and aims to determine if observed differences between groups are dependable or due to chance. The key purposes of inferential statistics are estimating population parameters from samples and testing hypotheses. It discusses important concepts like sampling distributions, confidence intervals, null hypotheses, levels of significance, type I and type II errors, and choosing appropriate statistical tests.
BUS308 – Week 5 Lecture 1 A Different View Expected Ou.docx
BUS308 – Week 5 Lecture 1
A Different View
Expected Outcomes
After reading this lecture, the student should be familiar with:
1. What a confidence interval for a statistic is.
2. What a confidence interval for differences is.
3. The difference between statistical and practical significance.
4. The meaning of an Effect Size measure.
Overview
Years ago, a comedy show used to introduce new skits with the phrase “and now for
something completely different.” That seems appropriate for this week’s material.
This week we will look at evaluating our data results in somewhat different ways. One of
the criticisms of the hypothesis testing procedure is that it only shows one value, when it is
reasonably clear that a number of different values would also cause us to reject or not reject a
null hypothesis of no difference. Many managers and researchers would like to see what these
values could be; and, in particular, what are the extreme values as help in making decisions.
Confidence intervals will help us here.
The other criticism of the hypothesis testing procedure is that we can “manage” the
results, or ensure that we will reject the null, by manipulating the sample size. For example, if
we have a difference in a customer preference between two products of only 1%, is this a big
deal? Given the uncertainty contained in sample results, we might tend to think that we can
safely ignore this result. However, if we were to use a sample of, say, 10,000, we would find
that this difference is statistically significant. This, for many, seems to fly in the face of
reasonableness. We will look at a measure of “practical significance,” meaning the likelihood of
the difference being worth paying any attention to, called the effect size to help us here.
Confidence Intervals
A confidence interval is a range of values that, based upon the sample results, most likely
contains the actual population parameter. The “most likely” element is the level of confidence
attached to the interval, 95% confidence interval, 90% confidence interval, 99% confidence
interval, etc. They can be created at any time, with or without performing a statistical test, such
as the t-test.
A confidence interval may be expressed as a range (45 to 51% of the town’s population
support the proposal) or as a mean or proportion with a margin of error (48% of the town
supports the proposal, with a margin of error of 3%). This last format is frequently seen with
opinion poll results, and simply means that you should add and subtract this margin of error from
the reported proportion to obtain the range. With either format, the confidence percent should
also be provided.
Confidence intervals for a single mean (or proportion) are fairly straightforward to
understand, and relate to t-test outcomes simply. Details on how to construct the interval will be
given in this week’s second lecture. We want to understand how to interpret and understa.
Hypothesis testing
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.
Basics of Sample Size Estimation
A short introduction to sample size estimation for Research methodology workshop at Dr. BVP RMC, Pravara Institute of Medical Sciences(DU), Loni by Dr. Mandar Baviskar
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PAGE O&M Statistics – Inferential Statistics Hypothesis Test.docx
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- 3. As a statistics student you should know how to calculate power in statistics. If you are still not finding the best ways to calculate power in statistics. Then don’t worry we are going to share with you the best and efficient ways to do it.The statistical strength of a study (sometimes called sensitivity) is likely to be the probability of how likely the study is to distinguish the actual effect from a chance. Likely, the test is properly rejecting the hypothesis (i.e. “Your hypothesis to prove). For example, a study that has 80% strength means that the study has an 80% chance of testing significant results.
- 5. A Type I error is a false rejection of a true null hypothesis. Alpha is the size of the test. A Type II error is where you do not reject a false infirm hypothesis.
- 6. Beta (β) is likely that you will not reject a null hypothesis when you are false. Statistical power complements this probability: 1-β
- 7. Statistical power is considerably difficult to calculate by hand. This article on Moresteam explains it well. Calculate power in SAS. Calculate power in PASS.
- 8. The Power analysis is a method for finding statistical power: the possibility of finding an effect, assuming that the effect is. To put it the other way, power is likely to dismiss a zero hypothesis when it is wrong. Note that power differs from a Type II error, which occurs when you fail to reject a false null hypothesis. So you can say that power is likely not to make your Type II error.
- 9. Suppose you were doing a drug test and this medicine was working. You run a series of tests with effective medication and a placebo. If you have the power of .9, it means that 90% of that time will give you statistically significant results.In 10% of cases, your results will not be statistically significant. The power, in this case, tells you the possibility to find the difference between the two means, which is 90%. But 10% of the time, you won’t get a difference
- 10. You can run a power analysis for many reasons, including:To find out the number of tests needed to achieve a certain size effect. This is probably the most common use for power analysis—it explains how many tests you need to avoid incorrectly rejecting the null hypothesis.To find power, given an impact size and number of tests available. This is often useful when you have a limited budget, say, 100 tests, and you want to know if testing that number is enough to detect an effect.To validate your research. Power analysis is an easy science conducted.The calculation of power is complex and is usually always done with the computer. You can find the list of links to the online power calculator here.The power of any test of statistical importance is defined as the possibility that it will dismiss a false disturbance.
- 11. Specify the hypothesis test. Specify the importance level of the test Then specify the smallest effect size that is of scientific interest. Estimate the values of other parameters needed to calculate the power function. Specify the desired power of the test.
- 12. Now you have seen the plenty of ways to calculate the power in statistics. If you are still finding it difficult to calculate the power in statistics, then get into touch with our experts.Get the best statistics homework help from the experts at nominal charges. We are offering the world class help with statistics homework to the students across the globe.
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