For a one-sample or paired t-test, df = N – 1. For an independent samples t-test, df = (N₁ – 1) + (N₂ – 1), where N is the sample size.
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P-value:
Conclusion:
Significance:
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Further Information
What does the t-test tell you?
A t-test determines if there's a significant difference between two group means. It calculates a t-value and p-value, indicating how likely the observed difference occurred by chance. A low p-value (usually <0.05) suggests the difference is statistically significant, not just random variation.
When to use t-test vs anova?
Use a t-test when comparing means between two groups. Choose ANOVA (Analysis of Variance) when comparing means across three or more groups. T-tests are simpler but limited to two-group comparisons. ANOVA is more versatile, allowing for multiple group comparisons and analysis of interaction effects between variables. ANOVA reduces the risk of Type I errors in multiple comparisons.
What is the difference between a t-test and a z-test?
T-tests and z-tests both compare sample means to population parameters. T-tests are used for smaller samples (typically n < 30) and when population standard deviation is unknown. Z-tests are for larger samples or when population standard deviation is known. T-tests use the t-distribution, which has heavier tails, accounting for greater uncertainty in smaller samples.
When to use t-test vs chi-square?
Use a t-test for comparing means of continuous data between two groups. Use chi-square for analyzing relationships between categorical variables. T-tests work with numerical data (like heights or test scores), while chi-square tests are for categorical data (like gender or preferences). Chi-square also tests goodness-of-fit for observed vs. expected frequencies.
