PSY 302 Stats Midterm #2

Why is the t-distribution used when the population standard deviation is unknown?

The t-distribution has a wider shape to account for the increased variability and uncertainty associated with estimating σ.

What is a defining property of the t-distribution compared to the z-distribution?

It has critical values that depend on the sample size (degrees of freedom).

How do degrees of freedom (df) affect the shape of the t-distribution?

As the degrees of freedom increase, the t-distribution approaches the shape of the z-distribution.

What is the assumption of homogeneity of variance in an independent samples t-test?

It assumes that the variance in both groups is approximately equal.

Why do we use difference scores in a paired samples t-test?

To isolate and compare changes within the same individuals, minimizing the effect of individual differences.

Why is a paired samples t-test more effective at controlling for individual differences?

Because it compares each participant to themselves, reducing the variability caused by individual differences.

How does using a within-groups design help in paired samples t-tests?

It helps control for individual differences, making it a more powerful test.

Why is it problematic to perform multiple t-tests when comparing more than two groups?

It increases the probability of making a Type I error.

When is it appropriate to use post-hoc tests following an ANOVA?

If the omnibus ANOVA is significant, to identify specific group differences.

Why do larger sample sizes provide more stable estimates in the t-distribution?

Larger sample sizes yield more stable estimates, reducing the uncertainty of population parameter estimates.

What best describes 'between-group variability' in an ANOVA context?

It captures the differences between the overall means of the groups.

How does matching participants in a paired samples t-test influence the results?

It controls for variability between different individuals, increasing power.

Which metric involves creating a combined estimate of variance from two samples to represent the variance of the null hypothesis?

Pooled Variance.

What is the mean of the sampling distribution in a paired samples t-test under the null hypothesis?

𝑀𝐷 = 0.

What does a significant F-ratio in a one-way ANOVA indicate?

At least one group mean is significantly different from the others.

What is the null hypothesis for a one-way ANOVA?

All group means are equal.

Which situation is appropriate for using a one-way ANOVA?

Comparing the average heights of plants grown under three different types of fertilizers.

What is the main difference between an independent samples t-test and a paired samples t-test?

An independent samples t-test compares means from two different groups, while a paired samples t-test compares means from the same group at two time points.

What does it mean if the mean of the difference scores is significantly different from zero in a paired samples t-test?

There is a significant change or difference between the two related samples.

Which scenario would require a paired samples t-test?

Measuring the performance of students before and after a training program.

What assumptions should be checked when performing a paired samples t-test?

Independence of cases, Normality, Random sample.

How are the null and alternative hypotheses formulated in hypothesis testing?

The null hypothesis typically assumes no effect or difference, while the alternative hypothesis reflects the expected effect or difference.

What is the significance of effect size in statistical analysis?

Effect size measures the strength of the relationship or the magnitude of the difference.

What is the purpose of confidence intervals in statistical interpretation?

Confidence intervals provide a range of values within which we expect the true population parameter to fall.

What is the importance of understanding assumptions in t-tests and ANOVA?

Satisfying the assumptions ensures the validity of the test results and conclusions.