Question 1

Define homogeneity of variance.

Accepted Answer

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Question 2

For the independent groups t test,  gives a value in raw score units for the size of effect.

Accepted Answer

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Question 3

The higher df, the lower t crit becomes for rejecting H₀ .

Accepted Answer

This is because as df (degree of freedom) increases, the t-distribution approaches the standard normal distribution, and the critical values become smaller. Thus, it becomes easier to reject the null hypothesis.

Question 4

For the independent groups design, increasing sample variance decreases power.

Accepted Answer

Increasing sample variance means there is more variability within each group, making it harder to detect a significant difference between the two groups. This decreases the power of the study.

Question 5

can be used to measure the size of effect in conjunction with the single samples t test, the correlated groups t test, and the independent groups t test.

Accepted Answer

TBX9373_11 is a tool for calculating effect size, which can be used with various types of t-tests, including the single samples t test, the correlated groups t test, and the independent groups t test.

Question 6

Assuming the variability of the scores doesn t change, when using the independent groups t test, the larger the size of effect the larger is  .

Accepted Answer

The larger the effect size, the larger the t-value. The t-value is used to calculate the p-value, which is a measure of the evidence against the null hypothesis. Therefore, a larger effect size will result in a smaller p-value and greater evidence against the null hypothesis.

Question 7

When a result is statistically significant, that guarantees that the result is an important one.

Accepted Answer

A statistically significant result only means that the likelihood of obtaining that result by chance is very low. It does not guarantee that the result is important or meaningful in a practical sense.

Question 8

Generally, the higher the magnitude of r between the scores of both groups the more powerful is the t test for correlated groups.

Accepted Answer

A higher magnitude of r indicates a stronger correlation between the scores of both groups, which leads to a larger difference in means and a more powerful t test for correlated groups.

Question 9

Define independent groups design.

Accepted Answer

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Question 10

If r between the scores of both groups is high and negative then the t test for correlated samples is not a powerful statistical test.

Accepted Answer

A high and negative r (correlation coefficient) between scores of both groups in a t-test for correlated samples indicates a strong inverse relationship between the paired scores, but it does not inherently affect the power of the statistical test. The power of the test is more directly influenced by sample size, effect size, and alpha level.

Question 11

When using the confidence interval approach for evaluating the effect of the independent variable, if the 95% confidence interval contains the value "0", we can reject H ₀ at á = 0.05.

Accepted Answer

If the 95% confidence interval contains the value "0", we cannot reject the null hypothesis at a significance level of 0.05. We would interpret this as saying that we do not have enough evidence to conclude that the independent variable has a significant effect.

Question 12

It is not necessary to measure the population parameters to apply the t test for either the independent or correlated groups designs.

Accepted Answer

The t test is a hypothesis test that uses sample statistics to estimate population parameters. Therefore, it is not necessary to measure the population parameters to apply the t test for either the independent or correlated groups designs.

Question 13

There is a greater chance of making a Type I error using a = 0.05 when using the t test for correlated groups then when using the sign test on the same scores.

Accepted Answer

The t-test for correlated groups typically has more power than the sign test because it uses more information from the data (i.e., the magnitude of differences, not just the direction). Therefore, for a given alpha level (e.g., α = 0.05), the chance of making a Type I error (rejecting a true null hypothesis) does not increase when using the t-test for correlated groups compared to using the sign test; the alpha level itself defines the probability of making a Type I error.

Question 14

The t test assumes that the independent variable affects either the mean of the dependent variable or the standard deviation, but not both.

Accepted Answer

The t-test primarily assesses the effect of the independent variable on the mean of the dependent variable and does not directly test its effect on the standard deviation.

Question 15

Define confidence-interval approach.

Accepted Answer

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Question 16

If a violation of the homogeneity of variance assumption occurs, it is always necessary to abandon use of the t test for an independent groups design.

Accepted Answer

If the violation of homogeneity of variance is mild to moderate and the sample sizes between groups are equal or nearly equal, the t test can still be used. If the violation is severe or the sample sizes are unequal, other statistical tests such as Welch's t-test or the Mann-Whitney U test may be more appropriate.

Question 17

Other factors held constant, for an independent groups design, the larger the value of , the greater the likelihood of rejecting H₀ .

Accepted Answer

A larger value of 11ec1b7e_f927_3c19_bbf8_bd0f614a17e4_TBX9373_11 indicates a larger effect size, which increases the likelihood of detecting a significant difference between the independent groups and rejecting H₀ (null hypothesis).

Question 18

Define null-hypothesis approach.

Accepted Answer

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Question 19

If = 0, then H₀ must be true.

Accepted Answer

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Question 20

The confidence interval approach for evaluating the effect of the independent variable does not allow evaluation of the size of real effect.

Accepted Answer

The confidence interval approach provides not only a point estimate of the effect of the independent variable but also a range of plausible values, which enables an evaluation of the size of the real effect.

Quiz 14: Students T Test for Correlated and Independent Groups