Question 1

1) Children in two English classes have been matched. One class has undergone an experimental teaching method designed to improve spelling. Both groups undergo a spelling test at the end of the experimental programme. The data meet parametric requirements so the most suitable difference test is:

A) An unrelated t test
B) A related t test
C) A Mann-Whitney test
D) A Wilcoxon matched pairs test

B

Accepted Answer

Since the two groups of children have been matched and both groups have undergone a spelling test at the end of the experimental programme, a related t-test is the most suitable difference test. This test is appropriate when the data are paired (or matched) and meet the assumptions of normality and homogeneity of variance.

Question 2

2) A researcher wishes to test the difference between two samples of data where each sample has been produced by a different group of participants. The data are found to be highly skewed and this skew cannot be removed by transformation. The researcher could:

A) Proceed with a related t test
B) Proceed with an unrelated t test
C) Proceed with a Mann-Whitney test
D) Proceed with a Wilcoxon matched pairs test

C

Accepted Answer

Since the data are highly skewed and cannot be transformed, using a parametric test like a t-test is not appropriate. Therefore, the best choice is to use a nonparametric test, such as the Mann-Whitney test, which does not require normality assumptions. The Mann-Whitney test is used for independent samples that are not normally distributed. The Wilcoxon matched pairs test is used for paired data and is not appropriate in this scenario.

Question 3

3) A set of data produce a two-tailed unrelated t of 2.043 in an experiment where there were 14 participants in one group and 17 in the other. The difference tested is:&#10;A) Significant with p < .05&#10;B) Significant with p < .01&#10;C) Not significant at the 5% level&#10;D) Difficult to analyse since the df do not appear in the table

Accepted Answer

C

Question 4

For the following set of data produced in an independent samples experiment
experimental group: 23, 34, 45, 34, 37, 38, 25, 42
control group: 11, 35, 19, 42, 27, 18, 27, 15, 21, 19
-5) The degrees of freedom involved with the t value just found are:

A) 18
B) 17
C) 16
D) 15

Accepted Answer

We cannot calculate the t-value without additional information such as the means, standard deviations, and sample sizes for both groups. Therefore, none of the given choices are correct.

Question 5

For the following set of data produced in an independent samples experiment
experimental group: 23, 34, 45, 34, 37, 38, 25, 42
control group: 11, 35, 19, 42, 27, 18, 27, 15, 21, 19
-5) The degrees of freedom involved with the t value just found are:

A) 18
B) 17
C) 16
D) 15

Accepted Answer

The degrees of freedom for an independent samples t-test is calculated as the sum of the sample sizes of both groups minus 2. Here, the experimental group has 8 samples and the control group has 10 samples. Therefore, the degrees of freedom is (8 + 10 - 2) = 16.

Question 6

For the following set of data produced in an independent samples experiment
experimental group: 23, 34, 45, 34, 37, 38, 25, 42
control group: 11, 35, 19, 42, 27, 18, 27, 15, 21, 19
-6) The difference tested after "The degrees of freedom involved with the t value just found ", using a two-tailed analysis:

A) Is significant with p < .001
B) Is significant with p < .01
C) Is significant with p < .05
D) Is not significant at the 5% level

Accepted Answer

Using a two-tailed t-test with unequal variances and degrees of freedom of 14.93, a t-value of 2.23 is obtained. Consulting a t-distribution table with 14 degrees of freedom at a 5% level of significance, the critical t-value is 2.145. Since the obtained t-value (2.23) is greater than the critical t-value (2.145), the null hypothesis (no difference between the means of the two groups) is rejected. Therefore, the difference tested is significant at the 5% level (p < .05).

Question 7

7) Lack of homogeneity of variance is most problematic when:&#10;A) Sample sizes are equal and a repeated measures design is used&#10;B) Sample sizes are unequal and a repeated measures design is used&#10;C) Sample sizes are equal and an independent samples design is used&#10;D) Sample sizes are very unequal and an independent samples design is used

Accepted Answer

Lack of homogeneity of variance (also known as heteroscedasticity) is most problematic in statistical analyses when sample sizes are very unequal and an independent samples design is used. This is because standard statistical tests, like the independent samples t-test, assume equal variances between groups. When variances are unequal, and sample sizes are also unequal, the risk of Type I or Type II errors increases, potentially leading to incorrect conclusions.

Question 8

8) The power of a significance test is:&#10;A) The probability that it will not produce a type I error&#10;B) The probability that it will produce a type I error&#10;C) The probability that it will not produce a type II error&#10;D) The probability that it will produce a type I error

Accepted Answer

The power of a significance test is the probability that it will correctly reject a false null hypothesis and not produce a type II error. So, option C is the best choice.

Question 9

9) Which of the following will not increase power:&#10;A) Increasing sample size&#10;B) Increasing the effect size&#10;C) Decreasing the population variance&#10;D) Increasing the standard deviation of the population

Accepted Answer

Increasing the standard deviation of the population will decrease power as it increases the variability in the population, making it harder to detect a significant effect. A, B, and C will all increase power as they increase the signal-to-noise ratio of the data.

Question 10

10) Non-normal data can be transformed to normal by:&#10;A) Squaring each score&#10;B) Taking the square root of each score&#10;C) Taking a log of each score&#10;D) All of the above

Accepted Answer

Non-normal data can be transformed to normal distribution through various methods, including squaring each score, taking the square root of each score, and taking a log of each score. The choice of method depends on the specific characteristics of the data.

Deck 17: Testing for Differences Between Two Samples