t-test Assumptions
Before running a t-test, you need to check that your data meets several key assumptions. These assumptions are crucial — if they are not satisfied, the results of your t-test may not be valid. The three main assumptions are:
1. Normality
- The data in each group should be approximately normally distributed;
- This is especially important for small sample sizes (usually less than 30 observations per group);
- If the sample size is large, the Central Limit Theorem allows some flexibility, but for small samples, non-normal data can make p-values and confidence intervals unreliable;
- Common signs of non-normality include strong skewness or outliers in your sample.
Why it matters: the t-test calculates probabilities based on the normal distribution. If your data is not normal, especially with small samples, the test may give misleading results.
2. Independence
- Each observation in your dataset should be independent from the others;
- This means that the value of one observation cannot influence or predict the value of another;
- Independence is often violated if you use repeated measurements from the same subject, or if your data comes from related groups (such as siblings or matched pairs without accounting for the pairing).
Why it matters: violating independence can result in underestimated variability, leading to incorrect significance results and invalid conclusions.
3. Equal Variances (Homogeneity of Variance)
- The variability (spread) of scores in each group should be roughly equal;
- This is also called the homogeneity of variance assumption;
- If one group has much higher or lower variance than the other, the standard t-test is not appropriate;
- In such cases, use a version of the t-test that does not assume equal variances, such as Welch’s t-test.
Why it matters: the t-test assumes equal variances to calculate the pooled estimate of variability. If this assumption is violated, the test may over- or under-estimate the true significance of the difference between groups.
Always check these assumptions before running a t-test. If any assumption is not met, choose a more suitable statistical method or adjust your approach to ensure valid results.
To check the normality assumption in practice, you can use visual tools like Q-Q plots or statistical tests such as the Shapiro-Wilk test. For equal variances, you can apply Levene’s test or compare group standard deviations. Always explore your data before running a t-test to confirm these assumptions are met.
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Before running a t-test, you need to check that your data meets several key assumptions. These assumptions are crucial — if they are not satisfied, the results of your t-test may not be valid. The three main assumptions are:
1. Normality
- The data in each group should be approximately normally distributed;
- This is especially important for small sample sizes (usually less than 30 observations per group);
- If the sample size is large, the Central Limit Theorem allows some flexibility, but for small samples, non-normal data can make p-values and confidence intervals unreliable;
- Common signs of non-normality include strong skewness or outliers in your sample.
Why it matters: the t-test calculates probabilities based on the normal distribution. If your data is not normal, especially with small samples, the test may give misleading results.
2. Independence
- Each observation in your dataset should be independent from the others;
- This means that the value of one observation cannot influence or predict the value of another;
- Independence is often violated if you use repeated measurements from the same subject, or if your data comes from related groups (such as siblings or matched pairs without accounting for the pairing).
Why it matters: violating independence can result in underestimated variability, leading to incorrect significance results and invalid conclusions.
3. Equal Variances (Homogeneity of Variance)
- The variability (spread) of scores in each group should be roughly equal;
- This is also called the homogeneity of variance assumption;
- If one group has much higher or lower variance than the other, the standard t-test is not appropriate;
- In such cases, use a version of the t-test that does not assume equal variances, such as Welch’s t-test.
Why it matters: the t-test assumes equal variances to calculate the pooled estimate of variability. If this assumption is violated, the test may over- or under-estimate the true significance of the difference between groups.
Always check these assumptions before running a t-test. If any assumption is not met, choose a more suitable statistical method or adjust your approach to ensure valid results.
To check the normality assumption in practice, you can use visual tools like Q-Q plots or statistical tests such as the Shapiro-Wilk test. For equal variances, you can apply Levene’s test or compare group standard deviations. Always explore your data before running a t-test to confirm these assumptions are met.
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