What if equal variances are not assumed?
Equal variances not assumed If the calculated t value > critical t value, then we reject the null hypothesis. This is why both the denominator of the test statistic and the degrees of freedom of the critical value of t are different than the equal variances form of the test statistic.
What are the assumptions for a one-sample t-test?
Assumptions
- Assumption #1: Your dependent variable should be measured at the interval or ratio level (i.e., continuous).
- Assumption #2: The data are independent (i.e., not correlated/related), which means that there is no relationship between the observations.
- Assumption #3: There should be no significant outliers.
What are the three assumptions for one-sample t-test?
The common assumptions made when doing a t-test include those regarding the scale of measurement, random sampling, normality of data distribution, adequacy of sample size, and equality of variance in standard deviation.
What is the main difference between the z-test and the one sample t test?
We perform a One-Sample t-test when we want to compare a sample mean with the population mean. The difference from the Z Test is that we do not have the information on Population Variance here. We use the sample standard deviation instead of population standard deviation in this case.
Why do independent samples t test not assume equal variances?
Note that this form of the independent samples t test statistic does not assume equal variances. This is why both the denominator of the test statistic and the degrees of freedom of the critical value of t are different than the equal variances form of the test statistic.
Which is the null hypothesis in one sample t test?
Homogeneity of variances (i.e., variances approximately equal in both the sample and population) The null hypothesis ( H0) and (two-tailed) alternative hypothesis ( H1) of the one sample T test can be expressed as: where µ is the “true” population mean and µ 0 is the proposed value of the population mean.
When to use a two sample t test?
A two sample t-test is used to test whether or not the means of two populations are equal. 1. Independence: The observations in one sample are independent of the observations in the other sample. 2. Normality: Both samples are approximately normally distributed. 3. Homogeneity of Variances: Both samples have approximately the same variance.
Which is the most important assumption in a t test?
Assumption 2: Normality A two sample t-test makes the assumption that both samples are approximately normally distributed. This is a crucial assumption because if the samples are not normally distributed then it isn’t valid to use the p-values from the test to draw conclusions about the differences between the samples.