T-test for Two Independent Means

What is the null hypothesis in a t test for two independent means?

What must be true about the data to satisfy the assumptions of the t test?

What is the relationship between the degrees of freedom and sample size in a t test?

Which assumption can be checked visually using a histogram?

If the variances of two samples are significantly different, what can be done?

What happens to the t distribution as the degrees of freedom increases beyond 100?

In what situation is the t test considered less robust?

What might be a consequence if the assumptions of the t test do not hold?

T-test for Two Independent Means

Compares means from two independent samples
Based on the sampling distribution of the difference between two sample means (Normal distribution).

Assumptions

Continuous data, normally distributed:
- Can be visually checked for symmetry using dot plots, histograms, or normal plots
Variances (standard deviations) are the same:
- This can be checked by inspecting the standard deviations.
- If variances are different, the Satterthwaite approximation may be used (available in some statistical programs).

Null Hypothesis

Two samples come from populations with the same mean.

The T-distribution

Has one parameter: degrees of freedom.
Degrees of freedom = n1 + n2 - 2 (where n1 and n2 are the sample sizes)
Each combination of n1 and n2 results in a different shape of t-distribution.
For large degrees of freedom (n1 + n2 - 2 > 100), the t distribution approaches the normal distribution.

Consequences of Violating Assumptions

The statistical test becomes dubious, and the P-value might be incorrect.
Consider transforming the data to address non-normality and unequal variances.
The t-test is relatively robust to slight skewness if the sample sizes are equal but less robust if variances are significantly different.
Skewness and unequal variances are often interconnected, and transforming the data to address one may improve the other as well.

Explore the fundamental concepts of the T-test for two independent means, including its assumptions, null hypothesis, and the characteristics of the T-distribution. This quiz will check your understanding of continuous data, the equality of variances, and the consequences of violating assumptions. Perfect for students learning statistics!