Hypothesis Testing in Statistics

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Questions and Answers

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?

Paired Student T Test

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 any expected value is less than 5 Signup and view all the answers

When would you use a Chi-square test for a 2-by-2 table?

When all expected values are greater than 5 Signup and view all the answers

What test would you use to compare the mean of one group to a hypothetical value when the data is normally distributed?

One-sample t test Signup and view all the answers

What test would you use to compare the means of two unpaired groups when the data is normally distributed?

Unpaired t test Signup and view all the answers

What test would you use to compare the means of two paired groups when the data is normally distributed?

Paired t test Signup and view all the answers

What does the null hypothesis (H0) suggest about an observed difference?

H0 suggests that the observed difference is due to chance and is not real. Signup and view all the answers

How does the alternative hypothesis (HA) differ from the null hypothesis (H0)?

HA indicates that the observed difference is not due to chance, whereas H0 states that it is. Signup and view all the answers

What forms can the alternative hypothesis (HA) take in hypothesis testing?

HA can be upper-tailed, lower-tailed, or two-tailed depending on the research question. Signup and view all the answers

What is a test statistic in hypothesis testing?

A test statistic summarizes sample information and helps in making decisions about the hypotheses. Signup and view all the answers

List the first three steps of significance testing in hypothesis testing.

<ol> <li>State the null hypothesis. 2. State the alternative hypothesis. 3. Choose a statistical test.</li> </ol> Signup and view all the answers

What is the significance level in hypothesis testing?

The significance level is a criterion for making decisions regarding rejecting H0. Signup and view all the answers

What is the purpose of performing a hypothesis test?

The purpose is to determine if there is enough evidence to reject the null hypothesis in favor of the alternative. Signup and view all the answers

In hypothesis testing, what do we use to compute uncertainty in our results?

We compute a P-value to assess the uncertainty regarding the null hypothesis. Signup and view all the answers

Define the purpose of using a Chi-Square test in biostatistics.

The Chi-Square test determines if deviations between observed and expected frequencies are significant, indicating that the differences are unlikely due to chance. Signup and view all the answers

What is the formula for calculating expected values in a Chi-Square test?

The expected value is calculated as: (Row total x Column total) / Overall total. Signup and view all the answers

What are two common goals when analyzing data in a biostatistical context?

Common goals include describing a group (e.g., mean, median) and comparing two or more groups. Signup and view all the answers

In the context provided, how many total individuals were sampled?

The total number of individuals sampled is 75. Signup and view all the answers

If comparing two unpaired groups, what is a potential goal of analysis?

A potential goal is to compare the means or proportions of the two groups. Signup and view all the answers

What information about the sample groups can be derived from the mean and variance?

The mean provides the average value, while variance indicates the degree of variation within the sample. Signup and view all the answers

What does a high chi-square statistic suggest about the categorical variables being analyzed?

A high chi-square statistic suggests that there is a significant difference between observed and expected frequencies. Signup and view all the answers

What are the degrees of freedom used for in the context of the Chi-Square test?

Degrees of freedom in the Chi-Square test are calculated as (rows - 1) x (columns - 1), used to determine the distribution for significance testing. Signup and view all the answers

What is a nonparametric test used for?

A nonparametric test is used when data cannot be assumed to follow a normal distribution. Signup and view all the answers

Name one test that compares two unpaired groups.

The Mann-Whitney test. Signup and view all the answers

What does the Wilcoxon test compare?

The Wilcoxon test compares one group to a hypothetical value or two paired groups. Signup and view all the answers

Under what conditions should you use nonparametric tests?

Use nonparametric tests when the data is not normally distributed or the sample size is small. Signup and view all the answers

What is the purpose of the Kruskal-Wallis test?

The Kruskal-Wallis test is used to compare three or more unmatched groups. Signup and view all the answers

Why might parametric tests be unreliable with small sample sizes?

Parametric tests may generate inaccurate P-values when the distribution is not normal. Signup and view all the answers

What type of distribution do Chi-Square tests rely on?

Chi-Square tests rely on the Binomial distribution. Signup and view all the answers

What is a situation where nonparametric tests lack statistical power?

Nonparametric tests lack power when the population is normally distributed. Signup and view all the answers

What is the null hypothesis (H0) in a hypothesis test?

The observed difference is not real, indicating it is the result of chance. Signup and view all the answers

What does the alternative hypothesis (HA) state?

The alternative hypothesis states that the observed difference is not due to chance. Signup and view all the answers

In the Wedding Cake Study, what was the null hypothesis regarding attack rates?

H0: The attack rates in the two groups are the same (RR=1). Signup and view all the answers

What alternative hypotheses (HA) were proposed in the Wedding Cake Study?

HA: The attack rates in the two groups are not the same (RR ≠ 1) or those who ate cake have a higher attack rate (RR > 1). Signup and view all the answers

How should you choose between using a z-score or t-score in hypothesis testing?

Use a t-score for small sample sizes (under 30) or when the population standard deviation is unknown; otherwise, use a z-score. Signup and view all the answers

What statistical test is typically used for comparing two means?

The Student t-test is used for comparing two means. Signup and view all the answers

What type of statistical test is the Chi-square test used for?

The Chi-square test is used for comparing proportions, like attack rates in categorical data. Signup and view all the answers

What defines a parametric test?

Parametric tests operate on continuous data sampled from normally distributed populations. Signup and view all the answers

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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Description

This quiz covers fundamental concepts of hypothesis testing, focusing on null and alternative hypotheses. Participants will explore examples related to HIV positivity in drug users versus non-users, emphasizing the significance of statistical differences. Enhance your understanding of these critical statistical principles.