Does paired t-test assume equal variances?
A paired t-test is designed to compare the means of the same group or item under two separate scenarios. An unpaired t-test compares the means of two independent or unrelated groups. In an unpaired t-test, the variance between groups is assumed to be equal. In a paired t-test, the variance is not assumed to be equal.
What if equal variances are not assumed?
When equal variances are assumed, the calculation uses pooled variances; when equal variances cannot be assumed, the calculation utilizes un-pooled variances and a correction to the degrees of freedom.
Should equal variance be assumed?
If the variances are relatively equal, that is one sample variance is no larger than twice the size of the other, then you can assume equal variances. By looking at the output of the Levene’s test you decide which row to use.
What do you do if t-test assumptions are not met?
When t test assumptions are violated
- Check the data – in particular, make sure that that the problematic data are true outliers and not errors in copying.
- Ignore the problem – not recommended since this will often yield inaccurate results, although often acceptable if the violation of the assumptions is not too severe.
What are the assumptions of a paired t-test?
Paired t-test assumptions
Subjects must be independent. Measurements for one subject do not affect measurements for any other subject. Each of the paired measurements must be obtained from the same subject. For example, the before-and-after weight for a smoker in the example above must be from the same person.
What does it mean to assume equal variance?
What Is the Assumption of Equal Variance? In simple terms, variance refers to the data spread or scatter. Statistical tests, such as analysis of variance (ANOVA), assume that although different samples can come from populations with different means, they have the same variance.
What does it mean when variances are not equal?
Equal variances (homoscedasticity) is when the variances are approximately the same across the samples. Unequal variances (heteroscedasticity) can affect the Type I error rate and lead to false positives.
What happens if Levene’s test is significant?
If the Levene’s Test is significant (the value under “Sig.” is less than . 05), the two variances are significantly different. If it is not significant (Sig. is greater than . 05), the two variances are not significantly different; that is, the two variances are approximately equal.
What does assuming equal variances mean?
How do you assume equal variances with two samples?
Use the Variance Rule of Thumb.
For example, suppose we have the following two samples: What is this? Sample 1 has a variance of 24.86 and sample 2 has a variance of 15.76. Since this ratio is less than 4, we could assume that the variances between the two groups are approximately equal.
What are the assumptions for a paired t-test?
The paired sample t-test has four main assumptions:
- The dependent variable must be continuous (interval/ratio).
- The observations are independent of one another.
- The dependent variable should be approximately normally distributed.
- The dependent variable should not contain any outliers.
Does paired t-test assume normality?
The paired t–test does not assume that observations within each group are normal, only that the differences are normal.
How do you know if a paired t-test is significant?
Paired T Test Hypotheses
If the p-value is less than your significance level (e.g., 0.05), you can reject the null hypothesis. Your sample provides strong enough evidence to conclude that the mean paired difference does not equal zero in the population.
How would you know if your data have equal variances?
If the p-value is larger than the alpha level, then you can say that the null hypothesis stands — that the variances are equal; if the p-value is smaller than the alpha level, then the implication is that the variances are unequal.
What does it mean when equal variance is assumed?
The assumption of equal variances (i.e. assumption of homoscedasticity) assumes that different samples have the same variance, even if they came from different populations. The assumption is found in many statistical tests, including Analysis of Variance (ANOVA) and Student’s T-Test.
How do you interpret the Levene’s test for equality of variances?
How do you interpret Levene’s test? If the p-value of Levene’s test is less than the significance level (for example 0.05), the variances of at least two groups are not equal.
How do you know if t-test is statistically significant?
Interpret the value of t
If the computed t-score equals or exceeds the value of t indicated in the table, then the researcher can conclude that there is a statistically significant probability that the relationship between the two variables exists and is not due to chance, and reject the null hypothesis.
What are the assumptions of a two-sample t-test?
In the two-sample t-test, the assumptions are that the observations of different individuals are outcomes of statistically independent, normally distributed, random variables, with the same expected value for all individuals within the same group, and the same variance for all individuals in both groups.
What does a paired t-test assume?
A paired samples t-test assumes that the differences between the pairs should be approximately normally distributed. This is a crucial assumption because if the differences between the pairs are not normally distributed then it isn’t valid to use the p-value from the test to draw conclusions.
What assumptions do paired t tests make?
How do you interpret the p-value in a paired t-test?
The p-value gives the probability of observing the test results under the null hypothesis. The lower the p-value, the lower the probability of obtaining a result like the one that was observed if the null hypothesis was true. Thus, a low p-value indicates decreased support for the null hypothesis.
What does it mean if variances are equal?
If the variances of two random variables are equal, that means on average, the values it can take, are spread out equally from their respective means.
What to do if Levene’s test is significant in t-test?
You said that if Levene’s test is statistically significant, one should use a non-parametric test rather than a t-test, and suggested a Chi-square test.
What statistic tells you if your assumptions of equal variance are correct?
Levene’s test ( Levene 1960) is used to test if k samples have equal variances. Equal variances across samples is called homogeneity of variance.
What is the t-test statistic and how is it interpreted?
A t-test is a statistical test that compares the means of two samples. It is used in hypothesis testing, with a null hypothesis that the difference in group means is zero and an alternate hypothesis that the difference in group means is different from zero.