# Statistics

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What are independent samples?

What is a pooled estimate of variance and why do you need to calculate it?

When do you use a dependent versus an independent sample t test?

Which is the more powerful t test?

What are the assumptions of the independent t test?

What are the mechanics of conducting an independent samples t test?

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The expert examines independent samples and pooled estimates of variances. A complete, neat and correct answers to all the questions are provided in the solution.

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(1) Samples which are independent of each other, the choice of items in the first sample in no way affecting the choice of items in the other. Example: Samples of tooth paste tubes of the same type picked up from two different departmental stores to check for the mean weight.

(2) One of the assumptions of the t test or ANOVA is that all groups have the same variance. We estimate this with a weighted average. This is called pooled estimate of the variance. As such, we calculate the pooled estimate of variance whenever we assume homogeneity of variance between the groups. The standard error calculated on the basis of pooled estimate of variance yields standard error bars for different groups that depend only on the sample size. Done this way, the standard error bars on a graph would correspond closely to the statistical tests, and would allow

the reader to 'eyeball' the statistical ...

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