The estimated standard error in the context of the independent-measures t statistic measures the standard deviation of the sampling distribution of the difference between two sample means. It reflects how much variability can be expected in the difference between the means of two independent groups.

1. The denominator of the independent-measures t statistic provides an estimate of the standard deviation between a sample mean and the population mean. This helps to gauge how much the sample means might deviate from the true population mean.

2. When the null hypothesis is true, the standard error is the standard deviation between a sample mean and the other sample mean. This indicates the variability expected in the differences between the two groups under the null hypothesis, which posits that there is no effect or difference.

Summary:

• The estimated standard error quantifies the expected variation in the difference between two means.
• It is crucial for determining the statistical significance of the observed difference.

Would you like more details or have any questions about this concept? Here are some related questions for further exploration:

1. What factors influence the estimated standard error?
2. How is the estimated standard error calculated in practice?
3. What is the role of the null hypothesis in hypothesis testing?
4. How does sample size affect the estimated standard error?
5. Can the independent-measures t statistic be used for more than two groups, and if so, how?

Tip: Always consider sample sizes and variability when interpreting standard errors, as they directly affect the power of statistical tests.