**Chapter 5: Comparing Group Means Using the Independent Samples t Test**

** **

**Multiple Choice**

- A variable with only two values is described as ____________ variable:
- dichotomous
- bivariate
- quantitative
- categorical

Ans: a

- The null hypothesis for the independent samples t test is:
- H
_{0}: μ_{1}≠ μ_{2} - H
_{0}: μ_{1}< μ_{2} - H
_{0}: μ_{1}> μ_{2} - H
_{0}: μ_{1}= μ_{2}

Ans: d

- What is
__not__an assumption about the dependent variable in an independent samples t test: - the Y outcome variable must be quantitative.
- the outcome variable should at least have an interval level of measurement.
- the variance of the outcome variable should be different between the two groups that are compared.
- the outcome variable should be normally distributed.

Ans: c

- A
*t*-test is considered to be*robust*if the: - variances of the outcome variable is relatively the same for both comparison groups.
- risk of Type I error does not increase much if a violation of assumptions occurs.
- sample sizes are large enough to have sufficient statistical power.
- outcome variable scale of measurement is large enough to have good variability.

Ans: b

- The appropriate parametric test for a within-subject design with two groups is the:
- independent samples
*t-*test - analysis of variance
- paired samples
*t*-test - repeated measures analysis of variance

Ans: c

- The independent samples
*t*-test is robust if which assumption is violated: - the outcome variable is not quantitative.
- the outcome variable is not normally distributed.
- there is no homogeneity of variance.
- theample size is too small.

Ans: c

- If variances are unequal, which would be an alternate test for the independent samples
*t*-test: - Wilcoxon rank sum test.
- Kruskal-Wallis test.
- Wilcoxon signed-rank test.
- Friedman analysis of variance.

Ans: a

- Which combination of variables is used to calculate the pooled variance in an independent
*t*-test: - n
_{1}, n_{2}, x_{1}, x_{2} - x
_{1}, x_{2}, s_{1}, s_{2} - n
_{1}, n_{2}, s_{1}, s_{2} - n
_{1}, n_{2}, s_{1}, s_{2}, x_{1}, x_{2}

Ans: c

- Essentially, the independent samples
*t*-test is the: - square root of the mean difference divided by the variance of the mean difference.
- sum of the means divided by the pooled sample size.
- mean difference divided by the variance of the mean difference.
- mean difference divided by the standard error of the mean difference.

Ans: d

- The degrees of freedom for the independent samples
*t-*test is: - √[(n
_{1}– 1)(n_{2}– 1)] - (n
_{1}– 1) * (n_{2}– 1) - (n
_{1 }+ n_{2}) / 2 - n
_{1 }+ n_{2 }– 2

Ans: d

- If all other values are held constant, what happens to the value of
*t*when*n*_{1}and*n*_{2}increase: *t*increases*t*decreases- (
*m*_{1 }–*m*_{2}) increases - (
*m*_{1 }–*m*_{2}) decreases

Ans: a

- If all other values are held constant, what happens to the value of
*t*when*s*decreases:_{p} *t*increases*t*decreases- (
*m*_{1 }–*m*_{2}) increases - (
*m*_{1 }–*m*_{2}) decreases

Ans: a

- Which of the following design decisions affects the value of (
*m*_{1 }–*m*_{2}): - having homogenous participants in regard to the dependent variable.
- procedures in conducting the study are standardized.
- the degree of separation in treatment effects between participant groups.
- the number of participants in the two treatment groups.

Ans: c

- Which of the following is
__not__a measure of effect size: - η
^{2} *e*- Cohen’s
*d* *r*_{pb}

Ans: b

- The primary advantage of using estimates of effect size is that they :
- are unitless measures of the outcome variable.
- are standardized measures of the outcome variable.
- indicate how large the value of
*t*should be in order to have significance. - are independent of the sample size.

Ans: d

**True/False**

- An independent-samples
*t-*test is appropriate for measuring differences between two uncorrelated groups.

Ans: True

- If the Levene test is statistically significant, the variances are considered equal and can be pooled.

Ans: False

- We reject H
_{0}for the independent samples*t-*test if obtained values of*t*are larger in absolute value than the critical values.

Ans: True

- A very small difference in the means between groups can be statistically significant with a very large sample size.

Ans: True

- The maximum value of η
^{2}is ∞.

Ans: False.

**Short Answer**

1.What measure is an example of an ordinal dependent variable in a t test?

Ans: Likert scale

- Describe what is meant by H
_{0}: σ_{1}^{2}= σ_{2}^{2}.

Ans: This is the null hypothesis for the assumption of homogeneity of variance. That is, the variance of Y is the same for both treatment groups.

- The formula to calculate the degrees of freedom for the Levene test is _________.

Ans: (k-1, N-k) where N is the total sample size and k is the number of groups.

**Essay**

- Describe issues in designing a study design with independent groups.

Ans: reasonable sample size within groups, enough groups to determine the effect of the independent variable, enough variance to detect a difference across groups.

Category: Statistics

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