Question

SCORES: -3, -3, -3, -3, -3, -3, -3, -3, -3,

-2, -2, -2, -2, -2, -2, -2, -2, -2,

2,

-1, -1, -1, -1, -1, -1, -1

0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Sample size                                                                             ____36________________

Sample mean                                                                           __-1.39______________

Sample standard deviation                                                     ____1.29_____________

Estimated standard error                                                         _____.22________________

Based on the table shown in SPSS, state the following values associated with the test statistic:

Mean difference                                                                      ___-1.39___________________

t obtained (t)                                                                            ______-6.44___________________

Degrees of freedom (df)                                                          _______35___________________

Significance (2-tailed)                                                             _______.00____________________

Based on the value of the test statistic, what is the decision for a one-sample t test? (Circle one)

                        Retain the null hypothesis                               Reject the null hypothesis

Compute Cohen's d and state the size of the effect as small, medium, or large. (Show your work.) In a sentence, also state the number of standard deviations that scores have shifted in the population. Note: The tables in SPSS give you all the data you need to compute effect size.

  

Compute proportion of variance using eta-squared or omega-squared, and state the size of the effect as small, medium, or large. (Show your work.) In a sentence, also state the proportion of variance in the dependent variable that can be explained by the factor. The tables in SPSS give you all the information you need to compute proportion of variance.

Answer 1

The decision for a one-sample t-test is: Reject the null hypothesis, since the p-value is less than the 0.05 alpha level.

d = absolute value of Mean difference/sample standard deviation = 1.39/1.29 = 1.0776. This indicates that the effect size is large. The scores have shifted in the population by 1.0776 standard deviations.

r² = d²/(d² + 4) = 0.2250. This indicates that the effect size is small. This means that 22.5% of the proportion of variance in the dependent variable can be explained by the factor.