Terms and Definitions
Independent-Samples t-Test and Related Concepts
Power and Effect Size
Scenario Identification and Analysis
100

True/False: The dependent variable is the outcome variable measured by the researcher. 

True

100

True/False: An independent-samples t-test is used when comparing the means of two related groups. 

False

100

True/False: A larger effect size indicates a stronger relationship between the independent and dependent variables. 

True

100

A researcher compares the test scores of students who took a prep course and those who did not. The mean scores for the two groups are 75 and 68, respectively. 

  • Identify the independent and dependent variables.

  • State the null and alternative hypotheses for this study.

  • Independent variable: Prep course (yes/no). Dependent variable: Test scores.
  • Null hypothesis: There is no difference in test scores between the groups. Alternative hypothesis: Students who took the prep course will score differently than those who did not.
200

The __________ variable is the one that is manipulated in an experiment. 

independent

200

The standard error in a t-test represents: 

A) The total variance in the data. 

B) The variability of sample means. 

C) The degree of correlation between variables. 

D) The mean difference between groups. 

B) The variability of sample means. 

200

True/False: If two groups' means differ by more than 0.8 standard deviations, the effect is small, even if it is statistically significant.

False

200

In a clinical trial, patients are randomly assigned to receive a new medication or a placebo. The outcome measure is reduction in symptom severity. A significant t-test result is found. 

  • What does this result suggest about the medication?

  • Explain how effect size could further clarify the findings.

  • The significant result suggests that the medication had an effect on reducing symptom severity.
  • Effect size provides additional information about the magnitude of the difference, which helps interpret the practical importance of the findings.
300

The null hypothesis in an independent-samples t-test typically states: 

A) The two group means are equal. 

B) The two group means are different. 

C) One group mean is greater than the other. 

D) The standard deviation is zero. 

A) The two group means are equal. 

300

Degrees of freedom (df) for an independent-samples t-test are calculated as __________.

df = (n1 - 1) + (n2 - 1)

df = (N1 + N2) - 2

300

Cohen's d is a measure of: 

A) The variability within each group. 

B) The standardized mean difference between groups. 

C) The proportion of variance explained. 

D) The error rate in hypothesis testing. 

B) The standardized mean difference between groups. 

300

A psychology researcher wants to test whether caffeine affects how long people sleep. She randomly assigns 20 participants to two groups. One group drinks a cup of caffeinated coffee before bed, and the other drinks decaf. She then records the number of hours each participant sleeps that night. 

  • If the t-test result is not significant, what decision should be made about the null hypothesis? 

  • If Cohen’s d is calculated to be 0.90, how would you interpret the effect size?
  • Fail to reject the null.
  • A large effect size, meaning caffeine has a strong effect on sleep even if sample size is small.
400

Estimated standard error is ________________.

the difference between the means (𝑆𝑀1−𝑀2)

  • Denominator of the t test equation

400

The independent variable utilizes ___________ variables, while the dependent variable utilizes ___________ variables.

discrete (nominal); continuous (interval/ratio)

400

Which of the following is NOT a way to increase power?

    A) Increasing your sample size.

    B) Having a larger rejection/critical region.

    C) Changing it from two-tailed to one-tailed.

    D) Changing it from one-tailed to two-tailed.

 D) Changing it from one-tailed to two-tailed.

400

Two groups of students prepare for a standardized test. Group 1 uses a new prep program, while Group 2 studies using traditional methods. After taking the test, their average scores are compared using an independent-samples t-test. 

  • If the calculated t = 2.12, and the critical t = 2.31 (df = 18), what is the decision?

  • What would increasing the sample size do to the power of the test?

  • If r² = 0.36, interpret what this means in context. 

  • Since calculated t < critical t (2.12 < 2.31), we fail to reject the null hypothesis.

  • Increasing sample size would increase power (higher chance of detecting a true effect).

  • r² = 0.36 means that 36% of the variance in test scores is explained by the type of prep method used.

500

The ___________ hypothesis predicts a difference between the groups being compared.

alternative

500

What are the 4 steps to an Independent Samples t-test Hypothesis Test?

Step 1: State hypotheses 

Step 2: Find critical value and state decision rule 

Step 3: Calculate test statistic 

Step 4: Make decision

500

The coefficient of determination (r^2) represents __________________________________.

The proportion of variance in the dependent variable explained by the independent variable

500

Two groups of participants were tested for reaction time (in seconds): 

Group A: 5, 6, 7, 5, 6 

Group B: 7, 8, 9, 8, 7 

Instructions: 

  1. Calculate the mean and variance for each group. 

  1. Compute the t statistic. 

  1. Compare the calculated t value with the critical t value (use df = N1 + N2 - 2).

1. Group A Mean: 5.8, Variance: 0.7 

Group B Mean: 7.8, Variance: 0.7

2. t = (7.8 - 5.8) / sqrt(0.7*(1/5 + 1/5)) = 4.77

3. Degrees of Freedom (df): 5 + 5 - 2 = 8

M
e
n
u