736: Comparing 2 Groups

unrevised

What are the main learning objectives for comparing two groups?

Understand comparing means, difference versus variance, the t distribution, identifying independent and dependent variables, choosing appropriate inferential tests, distinguishing independent and dependent samples, and interpreting results.

What is the purpose of comparing two group means?

To determine whether the observed difference between groups is statistically meaningful.

What statistical test is commonly used to compare two group means?

The t-test, also called Student's t-test.

In the experimental-design example, what do groups A and B represent?

A is the control group; B is the experimental group.

What is the null hypothesis when comparing two groups?

H₀: A = B; there is no difference between the group means.

If an intervention is ineffective, what result is expected?

No difference in responses between the control and experimental groups.

If an intervention is effective, what result is expected?

A difference in responses between the control and experimental groups.

Why is it unrealistic to expect every person in a group to receive exactly the same score?

Individual scores vary; there is usually variability within each group.

What is variance within groups?

Variation among individual scores within the same group.

What is error variance?

Unexplained variation in scores that is not accounted for by the intervention or group difference.

How can overlap between control and experimental group scores affect interpretation?

More overlap means the intervention may not fully explain the differences among scores.

What does a t statistic compare?

The separation between group means relative to error or variability.

What is the numerator of a t statistic conceptually?

The difference or separation between the groups.

What is the denominator of a t statistic conceptually?

The variability or standard error used to account for error.

If the null hypothesis is false and a treatment works, what should happen to the t statistic?

The group difference should be larger relative to error, producing a larger absolute t value.

What is the t distribution used for?

To judge whether an observed t value is likely or unlikely under the null hypothesis.

How does a standardized score help interpret an observation?

It expresses the observation relative to a reference distribution; the slides discuss converting a value into a z score.

What is homogeneity of variance?

The assumption that the groups have equal or roughly equivalent variances.

What does it mean if group variances are homogeneous?

The variances are roughly equivalent or not significantly different.

According to the slides, how can sample size relate to finding equal variances?

Larger samples have a better chance of showing equal variances.

What is an independent-samples t-test?

A test comparing the means of two independent groups.

What are other names for the independent-samples t-test?

Independent t-test or unpaired t-test.

What does the numerator of the independent-samples t statistic represent?

The difference between the group means.

What does the denominator of the independent-samples t statistic represent?

The pooled variance and standard error of the difference between means.

What is the standard error of the difference between means?

The estimated standard deviation of the sampling distribution of the difference between means.

How do you determine whether an independent-samples t value is significant?

Compare its absolute value with the appropriate critical value.

What is a critical value?

A cutoff value used to decide whether a test statistic is sufficiently extreme to reject the null hypothesis.

What is the difference between a one-tailed and a two-tailed test?

A one-tailed test evaluates an effect in one specified direction; a two-tailed test evaluates differences in either direction.

How are degrees of freedom relevant to a t-test?

Degrees of freedom, related to sample size, help determine the critical t value.

When should the null hypothesis be rejected using a critical t value?

When the absolute t value exceeds the applicable critical value.

How are positive and negative t values evaluated against a two-tailed criterion?

The same absolute-value criterion is used for positive and negative t values.

What are the main steps in running an independent-samples t-test?

Prepare and load data, identify variable types, describe the sample, calculate descriptive statistics, check assumptions, run the test, and interpret results.

What data types should be identified before analysis?

Nominal, ordinal, or scale.

What should descriptive statistics summarize?

Central tendency and variation; the slides also mention the interquartile range (IQR).

Which assumptions are checked before an independent-samples t-test?

Normality and equality of variances.

Which test is used when assumptions are satisfied for the standard independent t-test?

Student's independent-samples t-test.

What alternative is listed when the normality assumption is not satisfied?

A nonparametric test such as the Mann–Whitney test.

What test is listed when variances are unequal?

The Welch t-test.

What results should be interpreted after an independent-samples t-test?

The t score, p value, and effect size, such as Cohen's d.

What is the Mann–Whitney test?

A nonparametric alternative listed for comparing two independent groups when assumptions for the parametric test are not met.

What is Welch's t-test used for?

Comparing two independent group means when variances are unequal.

What is a paired-samples t-test?

A test that compares paired or correlated observations, often from the same people in two conditions.

When is a paired-samples t-test used?

In repeated-measures designs when subjects serve as their own controls.

What does it mean that subjects serve as their own controls?

The same individuals are measured under both conditions, so each person is compared with themselves.

What does the paired t-test analyze?

The difference scores within each pair.

How can a paired t-test reduce total error variance?

Many extraneous influences are shared across conditions for the same individual, reducing their contribution to error.

What do the symbols in the paired t-test formula represent in the slides?

The mean of the difference scores and the standard error of the difference scores.

Does a paired t-test require testing homogeneity of variances?

No; the slides state that testing this assumption is unnecessary for a paired t-test.

How is significance determined for a paired t-test?

Compare the calculated t statistic with the critical value to decide whether to reject the null hypothesis.

What is statistical power analysis for a t-test based on in the slides?

The effect-size index d, also called Cohen's d.

What is Cohen's d?

A standardized effect-size measure used to describe the magnitude of a difference.

What is the conventional small effect size for Cohen's d?

d = 0.20.

What is the conventional medium effect size for Cohen's d?

d = 0.50.

What is the conventional large effect size for Cohen's d?

d = 0.80.

What is used to calculate effect size for an independent t-test?

The difference between group means standardized by a common standard deviation.

What does S represent in the independent t-test effect-size formula described in the slides?

The common standard deviation.

If group variances are not significantly different, how can the common standard deviation be chosen?

Use either group's standard deviation or the average of the two groups' standard deviations, as described in the slides.

What effect-size formula does the presentation identify for a paired t-test?

It identifies a separate Cohen's d formula for the paired t-test, but the extracted slide text does not show the equation.

What is the key difference between independent and paired samples?

Independent samples come from separate, unrelated groups; paired samples are linked, such as repeated measurements on the same individuals.

What should be considered when selecting an inferential test for two groups?

Whether samples are independent or paired and whether the relevant parametric assumptions are satisfied.

What does a p value contribute to t-test interpretation?

It helps assess the evidence against the null hypothesis.

What does an effect size contribute beyond statistical significance?

It describes the magnitude of the observed difference.

What should be included when reporting a t-test result based on the slides?

The test statistic (t), p value, and effect size such as Cohen's d.