Question

​Which set of sample characteristics is most likely to produce a significant value for the independent-measures t statistic and a large effect size?

a. A small mean difference and small sample variances ​
b. A large mean difference and small sample variances ​
c. A small mean difference and large sample variances ​
d. A large mean difference and large sample variances

Answer 1

Correct option: (b).

Explanation:

Effect size (η) is a statistical measure that determines the strength of the association (numerically) between two variables. For example, if we have data on the weight of male and female candidates and we realize that, on average, males are heavier than females, the difference between the weight of male and the weight of female candidates is known as the effect size.

The larger the effect size, the larger the weight difference between male and female will be.

Statistic effect size helps us in analyzing if the difference is factual or if it is affected by a change of factors.

In hypothesis testing, effect size, power, sample size, and critical significance level are related to each other.

The effect size formula for a hypothesis test of mean difference is:

`\eta =\frac{\bar x_(1)-\bar x_(2)}{\sqrt{s^(2)}}`

The denominator s² is combined sample variance.

`s^(2)=(n_(1)s_(1)^(2)+n_(2)s_(2)^(2))/(n_(1)+n_(2)-2)`

The effect size is affected by two components:

1. Sample mean difference
2. Sample variance.

As the sample mean difference is directly proportional to the effect size, on increasing the sample mean difference value the effect size will also increase.

Ans the sample variance is inversely proportional to the the effect size, on decreasing the sample variance value the effect size will increase and vice-versa.

Thus, the correct option is (b).