A research article included the following table:

Mean Score on Four Questionnarie Scales Before and After the Experimental Manipulation.

Questionnaire Before After Change
Dominance 18.42 16.31 -2.11
Independence 17.25 21.38 4.13**
Conformity 18.97 17.20 -1.77*
Nurturance 16.11 13.89 -2.22*
_________________________
* p<.05 **p<.01

Which of the following is most likely to be true given the information on this table?
-The hypothesis testing probably used one-tailed test.

-The various scales all probably had just about the same population variances

-The t scores are all larger than the raw change scores.

-The hypothesis testing probably used a t test for dependent means.

-The t scores are all larger than the raw change scores.

To determine which statement is most likely to be true given the information on the table, let's analyze each of the options:

1. The hypothesis testing probably used one-tailed test:
To determine whether a one-tailed test was used, we need to look at the provided significance levels (p-values) and their corresponding annotations. In this case, the annotations are *p<.05 and **p<.01. These indicate the significance levels at which the observed differences are considered statistically significant. Since the notation includes a double asterisk (**p<.01), it suggests that a two-tailed test was conducted, rather than a one-tailed test. Therefore, this statement is unlikely to be true.

2. The various scales all probably had just about the same population variances:
This statement cannot be determined solely from the information provided in the table. The table only shows the mean scores before and after the experimental manipulation, as well as the change scores. It does not provide any information about the variances of different scales. Therefore, we cannot conclude whether the various scales had similar population variances. This statement is uncertain.

3. The t scores are all larger than the raw change scores:
To determine if the t scores are larger than the raw change scores, we need to calculate the t scores. The t score is typically calculated by dividing the raw change scores by the standard error of the mean difference. Unfortunately, the table does not provide the standard error of the mean difference, so we are unable to compare the t scores and raw change scores. Therefore, we cannot conclude whether this statement is true or false. This statement is uncertain.

4. The hypothesis testing probably used a t test for dependent means:
Based on the information provided in the table, we can see that the table compares "Before" and "After" scores, indicating a pre-test and post-test design. The differences between the scores are also given, suggesting a comparison of the mean changes. In such cases, a common statistical test used is the t test for dependent means (or paired t-test). Therefore, it is likely that the hypothesis testing used a t test for dependent means. This statement is most likely to be true.

In summary, the statement that is most likely to be true given the information on the table is: "The hypothesis testing probably used a t test for dependent means."