Why Are Unequal Sample Sizes A Problem?
Why are unequal sample sizes a problem? Unequal sample sizes can lead to: Unequal variances between samples, which affects the assumption of equal variances in tests like ANOVA. Having both unequal sample sizes and variances dramatically affects statistical power and Type I error rates (Rusticus & Lovato, 2014). A general loss of power.
What is Welch's t-test used for?
The Welch t-test is an adaptation of Student's t-test. It is used to compare the means of two groups of samples when the variances are different.
What is unequal variance t-test?
For the unequal variance t test, the null hypothesis is that the two population means are the same but the two population variances may differ. The unequal variance t test reports a confidence interval for the difference between two means that is usable even if the standard deviations differ.
Can you do a paired t-test with unequal sample sizes?
All Answers (13) Hey Luke. A paired t-test when you have unequal sample sizes does not make any sense, conceptually or mathematically. Conceptually, a paired t-test is good for when your "before" values have a lot of variance, relative to the difference between your before and after values.
What is an unpaired t-test?
An unpaired t-test (also known as an independent t-test) is a statistical procedure that compares the averages/means of two independent or unrelated groups to determine if there is a significant difference between the two.
Related faq for Why Are Unequal Sample Sizes A Problem?
What is p value in Welch t-test?
Since Welch's t-test maintains the nominal Type 1 error rate with unequal variances, the p-values in this quadrant represent the bias in Student's t-test when groups are unequal and variances are unequal (i.e., the studies that yield a p < .
Which t-test is equal or unequal variance?
Welch's t-test: Assumes that both groups of data are sampled from populations that follow a normal distribution, but it does not assume that those two populations have the same variance. So, if the two samples do not have equal variance then it's best to use the Welch's t-test.
What do unequal variances mean?
The conservative choice is to use the "Unequal Variances" column, meaning that the data sets are not pooled. This doesn't require you to make assumptions that you can't really be sure of, and it almost never makes much of a change in your results.
Should I use equal or unequal variance?
Shall you use the test for equal or unequal variances? If you have equal numbers of data points, or the numbers are nearly the same, then you should be able to safely use the two-sample test for equal variances.
In which two ways does the Welch t-test differ from the Student t-test?
The most important difference between Student's t-test and Welch's t-test, and indeed the main reason Welch's t-test was developed, is when both the variances and the sample sizes differ between groups, the t-value, degrees of freedom, and p-value all differ between Student's t-test and Welch's t-test.
What do you need to do if you have unequal sample sizes and want to use the independent samples t-test?
Should sample size and paired t-test be the same?
By definition a paired t-test is performed on two random samples of the same size. If they are not of the same size then you just can't do it.
What does t-test tell you?
The t test tells you how significant the differences between groups are; In other words it lets you know if those differences (measured in means) could have happened by chance. A t test can tell you by comparing the means of the two groups and letting you know the probability of those results happening by chance.
Is a paired t-test two tailed?
Like many statistical procedures, the paired sample t-test has two competing hypotheses, the null hypothesis and the alternative hypothesis. The alternative hypothesis can take one of several forms depending on the expected outcome. If the direction of the difference does not matter, a two-tailed hypothesis is used.
How does an unpaired t-test work?
The unpaired t test works by comparing the difference between means with the standard error of the difference, computed by combining the standard errors of the two groups. If the data are paired or matched, then you should choose a paired t test instead.
What kind of t-test should I use?
If you are studying two groups, use a two-sample t-test. If you want to know only whether a difference exists, use a two-tailed test. If you want to know if one group mean is greater or less than the other, use a left-tailed or right-tailed one-tailed test.
What is the difference between an independent t-test and a dependent t-test?
What is the difference between a test of independent means and a test of dependent means? A t-test for independent means test two distinct groups of participants, each group is tested once. -A test for dependent means tests one group of participants, and each participant is tested twice.
How do you interpret t-test results?
Higher values of the t-value, also called t-score, indicate that a large difference exists between the two sample sets. The smaller the t-value, the more similarity exists between the two sample sets. A large t-score indicates that the groups are different. A small t-score indicates that the groups are similar.
How do you compare populations of different sizes?
One way to compare the two different size data sets is to divide the large set into an N number of equal size sets. The comparison can be based on absolute sum of of difference. THis will measure how many sets from the Nset are in close match with the single 4 sample set.
Which test is relevant for unequal variances?
Welch's Test for Unequal Variances (also called Welch's t-test, Welch's adjusted T or unequal variances t-test) is a modification of Student's t-test to see if two sample means are significantly different.
What is a t-test two sample assuming UNequal variances?
This tool executes a two-sample student's t-Test on data sets from two independent populations with unequal variances. This test can be either two-tailed or one-tailed contingent upon if we are testing that the two population means are different or if one is greater than the other.
What is the difference between t-test equal variance and UNequal variance?
The Two-Sample assuming Equal Variances test is used when you know (either through the question or you have analyzed the variance in the data) that the variances are the same. The Two-Sample assuming UNequal Variances test is used when either: You do not know if the variances are the same or not.
What does hypothesized difference mean?
Hypothesized Mean Difference
You're basically telling the program what's in your hypothesis statements, so you must know your null hypothesis. For example, let's say you had the following hypothesis statements: Null Hypothesis: M1 – M2 = 10. Alternative Hypothesis: M1 – M2 ≠ 10.
What does equal variances mean?
Equal variances (homoscedasticity) is when the variances are approximately the same across the samples. If you are comparing two or more sample means, as in the 2-Sample t-test and ANOVA, a significantly different variance could overshadow the differences between means and lead to incorrect conclusions.
When should you assume equal variances?
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.
How do you know if variances are equal?
If the variances are equal, the ratio of the variances will equal 1. For example, if you had two data sets with a sample 1 (variance of 10) and a sample 2 (variance of 10), the ratio would be 10/10 = 1. You always test that the population variances are equal when running an F Test.
What is t-test paired two sample for means?
The t-Test Paired Two Sample for Means tool performs a paired two-sample Student's t-Test to ascertain if the null hypothesis (means of two populations are equal) can be accepted or rejected. This test does not assume that the variances of both populations are equal.