# t-Distribution Table

The t-distribution table is a valuable tool in statistical analysis, particularly when dealing with small sample sizes and unknown population variances. Here’s an explanation of what it is and how to use it:

What is it?:

The t-distribution table summarizes the critical values of the t-statistic, a statistical test used for various purposes, including:

• Student’s t-test: Comparing the means of two independent groups.
• Paired t-test: Comparing the means of two related samples.
• Confidence intervals: Estimating the range within which the population mean is likely to lie.

Structure:

The table features two main sections:

• One-tailed: Used for one-sided tests, where we are interested only in the probability of a value falling in one tail of the distribution (e.g., higher than a certain value).
• Two-tailed: Used for two-sided tests, where we consider both tails of the distribution (e.g., significantly different from a specific value).

Within each section, you’ll find:

• Degrees of freedom (df): Represents the number of independent pieces of information in your data, affecting the shape of the t-distribution.
• Significance level (α): Represents the probability of rejecting the null hypothesis (H0) when it’s actually true, typically 0.05 (5%) or 0.01 (1%).
• Critical values: These are specific thresholds for your calculated t-statistic based on df and α.

How to use it:

1. Calculate your t-statistic: This involves using your sample data and the appropriate formula for your chosen test (e.g., Student’s t-test, paired t-test).

2. Identify the appropriate section: One-tailed for one-sided tests, two-tailed for two-sided tests.

3. Locate the row with your degrees of freedom (df).

4. Find the column with your chosen significance level (α).

5. Compare your calculated t-statistic to the critical value:

• Reject H0 if your t-statistic is more extreme (greater in absolute value) than the critical value. This indicates a statistically significant difference or effect.
• Fail to reject H0 if your t-statistic falls within the range defined by the critical values. This suggests insufficient evidence for a significant difference or effect.

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