# Chapter 5: Testing for a Difference: Two Conditons

1. The standard error of the mean ______ as the ______ increases.

1. Decreases, n
2. Decreases, variance
3. Decreases, mean
4. Increases, n
5. Increases, mean

2. When testing for the difference between two conditions resulting from a between-subject design, we statistically need to take into account _______.

1. The two means.
2. The two variances.
3. The number of subjects in each condition.
4. All of the above.
5. Both A. and C.

3. We are more likely to find a significant difference (α< .05) between two means if _____.

1. The variance is relatively large.
2. The subject are randomly assigned to conditions.
3. The null hypothesis is true.
4. All of the above
5. None of the above.

4. The results of a t-test can be compromised by which of the following?

1. Outliers.
2. Heterogeneous variance.
3. Skewness.
4. All of the above.
5. None of the above.

5. As a p-value decreases ________.

1.  Effect size necessarily increases.
2. Sample size necessarily increases.
3. Effect size necessarily decreases.
4. The importance of the findings increases.
5. None of the above.

6. If a researcher wishes to test for a large difference between two means (d = .80), how many subjects would she require per condition with α = .05?

1. Cannot be determined from the information provided.
2. 10
3. 26
4. 64
5. 100

7. The critical value for a t-test (α= .05) with 29 degrees-of-freedom is _____.

1. Cannot be determined from the information provided.
2. 2.045
3. 12.706
4. 1.96
5. 29

8. In a within-subject design, if the mean of condition one is 5.5 and the mean of condition two is 3.2, the mean of the d-scores is _____.

1. Cannot be determined from the information provided.
2. 8.8
3. 0.0
4. 3.2
5. 2.3

9. The assumptions for the Mann-Whitney U test include ______.

1. Independent observations.
2. At least ordinal data.
3. Interval data.
4. Normality distributions.
5. Both A and B.

10. Assume there are 5 observations in condition #1, 7 observations in condition 2, and the total of the ranking in condition #1 is 20. Using the Mann-Whitney U test, what is the value of the U to be evaluated?

1. 5
2. 4
3. 20
4. 58
5. None of the above.

1. In a paragraph, describe the logic of a repeated-measures t-test (related samples). For the purpose of constructing the “sampling distribution of the difference between means,” which variance is used? What is the null hypothesis?
Main Points:

1. In a repeated measures t-test we examine the difference scores (d-score), which represent the difference between each subject’s scores in the two experimental conditions. If the scores are random with respect to the two conditions, e.g., there is no treatment effect, you would expect roughly an equal number of positive and negative d-scores. More accurately, you would expect the total values of the negative and positive d-scores to be equal. If there is no treatment effect, the Expected Value of the mean d-score is 0.0. If the H1 is correct, the two condition means are estimating two different population means and the expected value of the mean d-score will be non-zero.
2. Variance of d-score is used.
3. H0 is that the average d-score will be 0, such that any difference in the condition means is due solely to error.

2. How does the randomization test differ from the traditional parametric t-test?
Main Points:

1. Parametric t-tests are based on estimates of population parameters, such as means and variances, and thus require assumptions about the shape of underlying distribution.
2. Randomization test was designed to calculate the probability of randomness, and is free from any assumptions concerning the shape of the underlying distribution.

3. Imagine you have analyzed your data thinking that they were collected using a within-subject (repeated-measures) design. The t-value was non-significant (p . .05). Subsequently you are told the data were collected using a between-subject (independent samples) design. Is there any chance that the findings will be significant after you re-analyze the data with an independent-samples t-test? If no, why not? If yes, under what circumstances?
Main Points:

1. No.
2. Procedures for a within-subject design remove all of the factors associated with the individual subject which are responsible for making his or her performance different from that of other subjects. All of these individual differences are sources of variance. As a result, within-subject designs have more power.
3. (Actually there is a particular circumstance under which power can increase when a within-subject design is (inappropriately) analyzed as a between-subject design. (Degrees-of-freedom will increase. If there are very few individual differences, the sum-of-squares error will increase very little. Thus, power can increase. This is very rare.)

4. What is the difference between the sign test and signed rank test?
Main Points:

1. The sign test utilizes only the sign of the d-scores.
2. The Signed Rank Test uses both the sign and the magnitude.

5. How do we calculate the standard error for a “difference between two means?” What is its use?
Main Points:

1. Our estimate of the standard error of the difference between two means is made using the Variance Sum Law.
2. The Variance Sum Law states that the variance in the difference between (or a sum of) two independent variables is estimated by the sum of the variances of the two variables.

6. Why is a mean d-score the expected value used in the null hypothesis for a repeated measures t-test?
Main Points:

1. A positive d-score means that a subject scored higher in condition 1 than he or she scored in condition 2.
2. A negative d-score indicates the opposite. If there is no treatment effect, you would expect roughly an equal number of positive and negative d-scores.
3. If there is no treatment effect, the Expected Value of the mean d-score is 0.0. Thus, our H0 is that the average d-score will be 0.0.

#### Data set questions.

1. You want to know whether people are able to identify emotions correctly when we are extremely tired. We know that in the general population (who are not tired), accuracy ratings are on average 82% with a variance of 20. In the present study however, you test 50 people after they participate in strenuous cardiovascular exercise for 45 minutes. You find a mean of 78%. What is the most appropriate test? What can you conclude?

1. We test a sample mean using a Z-test when we know the population mean & variance.

2. What simple change can you make to the scores in the shaded condition in Table 5.1 so that the resulting t-value will have a p-value less than .05? (The variance in the condition should not be changed.)

1. Add a large constant (e.g., 50) to each score in the shaded condition. This increases the mean while keeping variance the same.

3. Professor Pigeon hypothesized that Long Evans rats are smarter than the common Norway brown rats. To test out his idea he randomly selected 10 rats from each of the two populations. He tests the rats on the standard rat intelligence test: a maze. His data are depicted in the table below. The scores indicate the number of days it took a rat to learn the maze. Did Professor Pigeon find sufficient evidence to support his idea? Include descriptive statistics, tests of assumptions and outliers, an appropriate graph, 95% confidence intervals, and standard effect size estimate, if necessary.

Reject H0. It takes less time for Long-Evans rats to learn the maze in comparison to Brown Norway Rats with a medium effect size.

4. A clinical psychologist wanted to know if a new form of relaxation therapy would reduce the symptoms of her anxious patients. She had her patients report the number of daily symptoms both before and after four weeks of the new therapy. Do the data in the below table provide evidence for the effectiveness of the new form of relaxation therapy?

Because she believed anxiety symptoms are not normally distributed, she used a non-parametric test. Do the data in the below table still provide evidence for the effectiveness of the new form of relaxation therapy? What do you think about the normality of the distribution of the symptoms?