How do you know when to 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. By looking at the output of the Levene’s test you decide which row to use.
Why do we assume equal variances in t-test?
Very simple answer: if you assume that two groups are coming from the sample population, you need the proper sampling distribution for this case. So you construct a null hypothesis with “equal variances”. There is only one population, so there is only one variance. Both samples are used to estimate this one variance.
Why is independent samples t-test two sample assuming equal variances are used?
A two sample t test assuming equal variances is used to test data to see if there is statistical significance or if the results may have occurred randomly. This is one of three t tests available in Excel and of the three, it’s the one least likely to be used.
Should I assume equal or unequal variance t-test?
Use the Variance Rule of Thumb. As a rule of thumb, if the ratio of the larger variance to the smaller variance is less than 4 then we can assume the variances are approximately equal and use the Student’s t-test.
What does assuming equal variances mean?
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 are the assumptions of a two sample t-test with variances not assumed equal?
Test Assumptions When running a two-sample equal-variance t-test, the basic assumptions are that the distributions of the two populations are normal, and that the variances of the two distributions are the same.
Why is it important to have equal variances?
It is important because it is a formal requirement for statistical analyses such as ANOVA or the Student’s t-test. The unequal variance doesn’t have much impact on ANOVA if the data sets have equal sample sizes. However, if the sample sizes are different, ANOVA will end up with inaccurate results.
What is a two-sample t-test used for?
The two-sample t-test (Snedecor and Cochran, 1989) is used to determine if two population means are equal. A common application is to test if a new process or treatment is superior to a current process or treatment. There are several variations on this test. The data may either be paired or not paired.
What type of t-test should you use if you want to compare a your sample group with a known mean?
The one-sample t-test compares a sample’s mean with a known value, when the variance of the population is unknown.
Why do we need equal variances?
It is important because it is a formal requirement for statistical analyses such as ANOVA or the Student’s t-test. The unequal variance doesn’t have much impact on ANOVA if the data sets have equal sample sizes.
Which one of the following is an assumption made when using a two sample test of means with equal population standard deviations?
Which two of the following are assumptions made when using a two sample test of means with equal standard deviations? The sampling distribution of the difference of means is a t-distribution. The populations have equal but unknown standard deviations; therefore, we “pool” the sample standard deviations.
What is an example of a two sample t test?
Two-Sample t-Test Example The following two-sample t-test was generated for the AUTO83B.DATdata set. The data set contains miles per gallon for U.S. cars (sample 1) and for Japanese cars (sample 2); the summary statistics for each sample are shown below. SAMPLE 1: NUMBER OF OBSERVATIONS = 249 MEAN = 20.14458
How to interpret t-test results?
Create the Data Suppose a biologist want to know whether or not two different species of plants have the same mean height.
What are the assumptions of a t test?
Independence: The observations in one sample are independent of the observations in the other sample.
How to interpret a t test result?
x,y: The names of the two vectors that contain the data.