Podcast
Questions and Answers
What statistical test would you use to compare the medians of two groups when the data is not normally distributed?
What statistical test would you use to compare the medians of two groups when the data is not normally distributed?
Mann-Whitney U Test (Wilcoxon rank-sum test)
What statistical test is used to compare the means of two linked values when the data is parametric?
What statistical test is used to compare the means of two linked values when the data is parametric?
Paired Student T Test
What test would you use to compare the means of several groups?
What test would you use to compare the means of several groups?
F Test
When would you use a Fisher Exact Test for a 2-by-2 table?
When would you use a Fisher Exact Test for a 2-by-2 table?
When would you use a Chi-square test for a 2-by-2 table?
When would you use a Chi-square test for a 2-by-2 table?
What test would you use to compare the mean of one group to a hypothetical value when the data is normally distributed?
What test would you use to compare the mean of one group to a hypothetical value when the data is normally distributed?
What test would you use to compare the means of two unpaired groups when the data is normally distributed?
What test would you use to compare the means of two unpaired groups when the data is normally distributed?
What test would you use to compare the means of two paired groups when the data is normally distributed?
What test would you use to compare the means of two paired groups when the data is normally distributed?
What does the null hypothesis (H0) suggest about an observed difference?
What does the null hypothesis (H0) suggest about an observed difference?
How does the alternative hypothesis (HA) differ from the null hypothesis (H0)?
How does the alternative hypothesis (HA) differ from the null hypothesis (H0)?
What forms can the alternative hypothesis (HA) take in hypothesis testing?
What forms can the alternative hypothesis (HA) take in hypothesis testing?
What is a test statistic in hypothesis testing?
What is a test statistic in hypothesis testing?
List the first three steps of significance testing in hypothesis testing.
List the first three steps of significance testing in hypothesis testing.
What is the significance level in hypothesis testing?
What is the significance level in hypothesis testing?
What is the purpose of performing a hypothesis test?
What is the purpose of performing a hypothesis test?
In hypothesis testing, what do we use to compute uncertainty in our results?
In hypothesis testing, what do we use to compute uncertainty in our results?
Define the purpose of using a Chi-Square test in biostatistics.
Define the purpose of using a Chi-Square test in biostatistics.
What is the formula for calculating expected values in a Chi-Square test?
What is the formula for calculating expected values in a Chi-Square test?
What are two common goals when analyzing data in a biostatistical context?
What are two common goals when analyzing data in a biostatistical context?
In the context provided, how many total individuals were sampled?
In the context provided, how many total individuals were sampled?
If comparing two unpaired groups, what is a potential goal of analysis?
If comparing two unpaired groups, what is a potential goal of analysis?
What information about the sample groups can be derived from the mean and variance?
What information about the sample groups can be derived from the mean and variance?
What does a high chi-square statistic suggest about the categorical variables being analyzed?
What does a high chi-square statistic suggest about the categorical variables being analyzed?
What are the degrees of freedom used for in the context of the Chi-Square test?
What are the degrees of freedom used for in the context of the Chi-Square test?
What is a nonparametric test used for?
What is a nonparametric test used for?
Name one test that compares two unpaired groups.
Name one test that compares two unpaired groups.
What does the Wilcoxon test compare?
What does the Wilcoxon test compare?
Under what conditions should you use nonparametric tests?
Under what conditions should you use nonparametric tests?
What is the purpose of the Kruskal-Wallis test?
What is the purpose of the Kruskal-Wallis test?
Why might parametric tests be unreliable with small sample sizes?
Why might parametric tests be unreliable with small sample sizes?
What type of distribution do Chi-Square tests rely on?
What type of distribution do Chi-Square tests rely on?
What is a situation where nonparametric tests lack statistical power?
What is a situation where nonparametric tests lack statistical power?
What is the null hypothesis (H0) in a hypothesis test?
What is the null hypothesis (H0) in a hypothesis test?
What does the alternative hypothesis (HA) state?
What does the alternative hypothesis (HA) state?
In the Wedding Cake Study, what was the null hypothesis regarding attack rates?
In the Wedding Cake Study, what was the null hypothesis regarding attack rates?
What alternative hypotheses (HA) were proposed in the Wedding Cake Study?
What alternative hypotheses (HA) were proposed in the Wedding Cake Study?
How should you choose between using a z-score or t-score in hypothesis testing?
How should you choose between using a z-score or t-score in hypothesis testing?
What statistical test is typically used for comparing two means?
What statistical test is typically used for comparing two means?
What type of statistical test is the Chi-square test used for?
What type of statistical test is the Chi-square test used for?
What defines a parametric test?
What defines a parametric test?
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Study Notes
Hypotheses
- Null Hypothesis (H0): Indicates no real difference, implying observed variations are due to chance.
- Alternative Hypothesis (HA): Posits that the observed effect is real and not attributable to chance.
Types of Hypotheses
- H0 example: Observed HIV positivity difference between drug users and non-users is due to chance.
- HA example: Observed HIV positivity difference between drug users and non-users is NOT due to chance.
Forms of Hypotheses
- Upper-tailed Test (H1: μ > μ0): Suggests increase in parameter of interest.
- Lower-tailed Test (H1: μ < μ0): Indicates decrease in parameter.
- Two-tailed Test (H1: μ ≠μ0): Suggests a change without indicating direction.
Hypothesis Testing Steps
- State null hypothesis (H0) and alternative hypothesis (HA).
- Choose appropriate statistical test suitable for variable scales and study design.
- Specify significance level for decision-making.
- Perform statistical test and compute P-value.
- Make a decision to accept or reject the null hypothesis.
Example of Hypothesis Testing
- Wedding Cake Study:
- H0: Attack rates for groups who ate cake and those who didn’t are the same.
- HA: Attack rates differ between the two groups.
Statistical Tests
- Test statistics aggregate sample data, depending on measurement types and sample size.
- Small samples (<30): use t-test; larger samples: use z-test.
Types of Statistical Tests
- Parametric Tests: Suitable for continuous data from normally distributed populations.
- Nonparametric Tests: Used when data may not follow a normal distribution; focus on medians or ranks.
- Chi-square Tests: Compare proportions, applicable for dichotomous variables.
Specific Statistical Tests for 2-by-2 Tables
- Fisher's Exact Test: Used when expected frequencies in any cell are <5.
- Chi-square Test: Applied when expected frequencies >5, includes uncorrected and corrected variations.
Examples of Parametric Tests
- One-sample t-test: Compares group mean to a hypothetical value.
- Unpaired t-test: Compares means of two independent groups.
- One-way ANOVA: Compares three or more unmatched groups.
Choosing Nonparametric Tests
- Applied when data are not normally distributed or based on ranks.
- Robust for large sample sizes even if normally distributed.
Addressing Small Sample Sizes
- Parametric tests may yield inaccurate P-values; nonparametric tests may lack statistical power in normally distributed samples.
Additional Significance Tests
- Chi-square, Fisher's test, McNemar's test, useful for varying data types and sample populations.
Questions for Choosing Statistical Tests
- Consider data types (continuous/binary), sample size, study goals, and group comparisons (independent/matched).
Case Study: Oswego Data on Gastroenteritis
- Analysis included comparing attack rates based on whether attendees ate vanilla ice cream:
- Attack rate for ice cream eaters was 79.6% versus 14.3% for non-eaters.
Chi-Square Test for Independence
- Formula: Chi-square statistic = Σ((observed - expected)²/expected).
- Degrees of freedom calculated as (rows−1) × (columns−1).
- Expected values determined by (Row total × Column total) / Grand total.
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