Two-Sample T-Tests for Equivalence Allowing Unequal Variance The Method column denotes which test is being used for that row, and the Variances column indicates what assumption about variances is being made. The pooled test assumes that the two populations have equal variances and uses degrees of freedom , where and are the sample sizes for the two populations. The remaining two tests do not assume that

## Unequal Variances jmp.com

Unequal Variances jmp.com. 17.11. "Equal Variances" and "Unequal Variances" in Two-Sample Inferences. Applies to: StatTools 6.x/7.x. In StatTools, I'm selecting a confidence interval or hypothesis test about the difference in means of two independent samples. StatTools gives two columns of results, headed "Equal Variances" and "Unequal Variances". What do those mean, When the variances across groups are not equal, the usual analysis of variance assumptions are not satisfied and the ANOVA F test is not valid. JMP provides four tests for equality of group variances and an ANOVA that is valid when the group population variances are unequal..

t-tests. The t.test( ) function produces a variety of t-tests. Unlike most statistical packages, the default assumes unequal variance and applies the Welsh df modification.# independent 2-group t-test t.test(y~x) # where y is numeric and x is a binary factor # independent 2-group t-test t.test(y1,y2) # where y1 and y2 are numeric If LeveneвЂ™s test indicates that the variances are not equal across the two groups (i.e., p-value small), you will need to rely on the second row of output, Equal variances not assumed, when you look at the results of the Independent Samples t Test (under the heading t-test вЂ¦

17.11. "Equal Variances" and "Unequal Variances" in Two-Sample Inferences. Applies to: StatTools 6.x/7.x. In StatTools, I'm selecting a confidence interval or hypothesis test about the difference in means of two independent samples. StatTools gives two columns of results, headed "Equal Variances" and "Unequal Variances". What do those mean This example teaches you how to perform a t-Test in Excel. The t-Test is used to test the null hypothesis that the means of two populations are equal. Below you can find the study hours of 6 female students and 5 male students. To perform a t-TestвЂ¦

Two-Sample T-Tests for Equivalence Allowing Unequal Variance Introduction This procedure allows you to study the power and sample size of equivalence tests of the means of two independent groups using the two-sample unequal-variance t-test. SchuirmannвЂ™s (1987) two one-sided tests (TOST) approach is used to test equivalence. Only a brief For such small samples, a test of equality between the two population variances would not be very powerful. Since the sample sizes are equal, the two forms of the two-sample t-test will perform similarly in this example. Unequal variances. If the approach for unequal variances (discussed above) is followed, the results are

If LeveneвЂ™s test indicates that the variances are not equal across the two groups (i.e., p-value small), you will need to rely on the second row of output, Equal variances not assumed, when you look at the results of the Independent Samples t Test (under the heading t-test вЂ¦ When the variances across groups are not equal, the usual analysis of variance assumptions are not satisfied and the ANOVA F test is not valid. JMP provides four tests for equality of group variances and an ANOVA that is valid when the group population variances are unequal.

This example teaches you how to perform a t-Test in Excel. The t-Test is used to test the null hypothesis that the means of two populations are equal. Below you can find the study hours of 6 female students and 5 male students. To perform a t-TestвЂ¦ For such small samples, a test of equality between the two population variances would not be very powerful. Since the sample sizes are equal, the two forms of the two-sample t-test will perform similarly in this example. Unequal variances. If the approach for unequal variances (discussed above) is followed, the results are

For such small samples, a test of equality between the two population variances would not be very powerful. Since the sample sizes are equal, the two forms of the two-sample t-test will perform similarly in this example. Unequal variances. If the approach for unequal variances (discussed above) is followed, the results are Two sample t test - equal variances not assumed - overview This page offers structured overviews of one or more selected methods. Add additional methods for comparisons by clicking on the dropdown button in the right-hand column.

When the variances across groups are not equal, the usual analysis of variance assumptions are not satisfied and the ANOVA F test is not valid. JMP provides four tests for equality of group variances and an ANOVA that is valid when the group population variances are unequal. Two-Sample T-Tests for Equivalence Allowing Unequal Variance Introduction This procedure allows you to study the power and sample size of equivalence tests of the means of two independent groups using the two-sample unequal-variance t-test. SchuirmannвЂ™s (1987) two one-sided tests (TOST) approach is used to test equivalence. Only a brief

Two-Sample T-Tests for Equivalence Allowing Unequal Variance Introduction This procedure allows you to study the power and sample size of equivalence tests of the means of two independent groups using the two-sample unequal-variance t-test. SchuirmannвЂ™s (1987) two one-sided tests (TOST) approach is used to test equivalence. Only a brief Two sample t test - equal variances not assumed - overview This page offers structured overviews of one or more selected methods. Add additional methods for comparisons by clicking on the dropdown button in the right-hand column.

The Method column denotes which test is being used for that row, and the Variances column indicates what assumption about variances is being made. The pooled test assumes that the two populations have equal variances and uses degrees of freedom , where and are the sample sizes for the two populations. The remaining two tests do not assume that 17.11. "Equal Variances" and "Unequal Variances" in Two-Sample Inferences. Applies to: StatTools 6.x/7.x. In StatTools, I'm selecting a confidence interval or hypothesis test about the difference in means of two independent samples. StatTools gives two columns of results, headed "Equal Variances" and "Unequal Variances". What do those mean

This example teaches you how to perform a t-Test in Excel. The t-Test is used to test the null hypothesis that the means of two populations are equal. Below you can find the study hours of 6 female students and 5 male students. To perform a t-TestвЂ¦ For such small samples, a test of equality between the two population variances would not be very powerful. Since the sample sizes are equal, the two forms of the two-sample t-test will perform similarly in this example. Unequal variances. If the approach for unequal variances (discussed above) is followed, the results are

### Unequal Variances jmp.com

Two-Sample T-Tests for Equivalence Allowing Unequal Variance. scipy.stats.ttest_ind (a, b, axis=0, equal_var=True, nan_policy='propagate') [source] В¶ Calculate the T-test for the means of two independent samples of scores. This is a two-sided test for the null hypothesis that 2 independent samples have identical average (expected) values. This test assumes that the populations have identical variances by, Two sample t test - equal variances not assumed - overview This page offers structured overviews of one or more selected methods. Add additional methods for comparisons by clicking on the dropdown button in the right-hand column..

two-sample t-test with unequal variances Cross Validated. Two-Sample T-Tests for Equivalence Allowing Unequal Variance Introduction This procedure allows you to study the power and sample size of equivalence tests of the means of two independent groups using the two-sample unequal-variance t-test. SchuirmannвЂ™s (1987) two one-sided tests (TOST) approach is used to test equivalence. Only a brief, I am working in R and know of the T-test and Tukey-test to compare levels of a variable, but these require equal sample sizes. Is there a test I can use where equal sample sizes are not a вЂ¦.

### Two-Sample T-Tests for Equivalence Allowing Unequal Variance

Two-Sample T-Tests for Equivalence Allowing Unequal Variance. If LeveneвЂ™s test indicates that the variances are not equal across the two groups (i.e., p-value small), you will need to rely on the second row of output, Equal variances not assumed, when you look at the results of the Independent Samples t Test (under the heading t-test вЂ¦ https://tr.wikipedia.org/wiki/Welch%27in_t-testi This example teaches you how to perform a t-Test in Excel. The t-Test is used to test the null hypothesis that the means of two populations are equal. Below you can find the study hours of 6 female students and 5 male students. To perform a t-TestвЂ¦.

• Unequal Variances jmp.com
• Two-Sample T-Tests for Equivalence Allowing Unequal Variance

• t-tests. The t.test( ) function produces a variety of t-tests. Unlike most statistical packages, the default assumes unequal variance and applies the Welsh df modification.# independent 2-group t-test t.test(y~x) # where y is numeric and x is a binary factor # independent 2-group t-test t.test(y1,y2) # where y1 and y2 are numeric One can quibble whether equal variances are part of the null hypothesis. But, using the pooled t test, equal variances are essential to a fair test of the null hypothesis. Notes about R code: (a) The default 2-sample t test in R is the Welch test, which does not assume equal variances. The parameter var.eq=T leads to use of the pooled test. If

I am working in R and know of the T-test and Tukey-test to compare levels of a variable, but these require equal sample sizes. Is there a test I can use where equal sample sizes are not a вЂ¦ One can quibble whether equal variances are part of the null hypothesis. But, using the pooled t test, equal variances are essential to a fair test of the null hypothesis. Notes about R code: (a) The default 2-sample t test in R is the Welch test, which does not assume equal variances. The parameter var.eq=T leads to use of the pooled test. If

I am working in R and know of the T-test and Tukey-test to compare levels of a variable, but these require equal sample sizes. Is there a test I can use where equal sample sizes are not a вЂ¦ The Method column denotes which test is being used for that row, and the Variances column indicates what assumption about variances is being made. The pooled test assumes that the two populations have equal variances and uses degrees of freedom , where and are the sample sizes for the two populations. The remaining two tests do not assume that

07/10/2018В В· When working with the 2 sample t-test, we must make one of those two assumptions. We also learn how to decide if we can assume equal variance or if we should assume unequal variance. We cover When the variances across groups are not equal, the usual analysis of variance assumptions are not satisfied and the ANOVA F test is not valid. JMP provides four tests for equality of group variances and an ANOVA that is valid when the group population variances are unequal.

If LeveneвЂ™s test indicates that the variances are not equal across the two groups (i.e., p-value small), you will need to rely on the second row of output, Equal variances not assumed, when you look at the results of the Independent Samples t Test (under the heading t-test вЂ¦ t-tests. The t.test( ) function produces a variety of t-tests. Unlike most statistical packages, the default assumes unequal variance and applies the Welsh df modification.# independent 2-group t-test t.test(y~x) # where y is numeric and x is a binary factor # independent 2-group t-test t.test(y1,y2) # where y1 and y2 are numeric

Two sample t test - equal variances not assumed - overview This page offers structured overviews of one or more selected methods. Add additional methods for comparisons by clicking on the dropdown button in the right-hand column. t-tests. The t.test( ) function produces a variety of t-tests. Unlike most statistical packages, the default assumes unequal variance and applies the Welsh df modification.# independent 2-group t-test t.test(y~x) # where y is numeric and x is a binary factor # independent 2-group t-test t.test(y1,y2) # where y1 and y2 are numeric

t-tests. The t.test( ) function produces a variety of t-tests. Unlike most statistical packages, the default assumes unequal variance and applies the Welsh df modification.# independent 2-group t-test t.test(y~x) # where y is numeric and x is a binary factor # independent 2-group t-test t.test(y1,y2) # where y1 and y2 are numeric 17.11. "Equal Variances" and "Unequal Variances" in Two-Sample Inferences. Applies to: StatTools 6.x/7.x. In StatTools, I'm selecting a confidence interval or hypothesis test about the difference in means of two independent samples. StatTools gives two columns of results, headed "Equal Variances" and "Unequal Variances". What do those mean

t-tests. The t.test( ) function produces a variety of t-tests. Unlike most statistical packages, the default assumes unequal variance and applies the Welsh df modification.# independent 2-group t-test t.test(y~x) # where y is numeric and x is a binary factor # independent 2-group t-test t.test(y1,y2) # where y1 and y2 are numeric One can quibble whether equal variances are part of the null hypothesis. But, using the pooled t test, equal variances are essential to a fair test of the null hypothesis. Notes about R code: (a) The default 2-sample t test in R is the Welch test, which does not assume equal variances. The parameter var.eq=T leads to use of the pooled test. If

Two sample t test - equal variances not assumed - overview This page offers structured overviews of one or more selected methods. Add additional methods for comparisons by clicking on the dropdown button in the right-hand column. 17.11. "Equal Variances" and "Unequal Variances" in Two-Sample Inferences. Applies to: StatTools 6.x/7.x. In StatTools, I'm selecting a confidence interval or hypothesis test about the difference in means of two independent samples. StatTools gives two columns of results, headed "Equal Variances" and "Unequal Variances". What do those mean

When the variances across groups are not equal, the usual analysis of variance assumptions are not satisfied and the ANOVA F test is not valid. JMP provides four tests for equality of group variances and an ANOVA that is valid when the group population variances are unequal. I am working in R and know of the T-test and Tukey-test to compare levels of a variable, but these require equal sample sizes. Is there a test I can use where equal sample sizes are not a вЂ¦

I am working in R and know of the T-test and Tukey-test to compare levels of a variable, but these require equal sample sizes. Is there a test I can use where equal sample sizes are not a вЂ¦ Two sample t test - equal variances not assumed - overview This page offers structured overviews of one or more selected methods. Add additional methods for comparisons by clicking on the dropdown button in the right-hand column.

## Two-Sample T-Tests for Equivalence Allowing Unequal Variance

two-sample t-test with unequal variances Cross Validated. scipy.stats.ttest_ind (a, b, axis=0, equal_var=True, nan_policy='propagate') [source] В¶ Calculate the T-test for the means of two independent samples of scores. This is a two-sided test for the null hypothesis that 2 independent samples have identical average (expected) values. This test assumes that the populations have identical variances by, 17.11. "Equal Variances" and "Unequal Variances" in Two-Sample Inferences. Applies to: StatTools 6.x/7.x. In StatTools, I'm selecting a confidence interval or hypothesis test about the difference in means of two independent samples. StatTools gives two columns of results, headed "Equal Variances" and "Unequal Variances". What do those mean.

### Unequal Variances jmp.com

Unequal Variances jmp.com. I am working in R and know of the T-test and Tukey-test to compare levels of a variable, but these require equal sample sizes. Is there a test I can use where equal sample sizes are not a вЂ¦, For such small samples, a test of equality between the two population variances would not be very powerful. Since the sample sizes are equal, the two forms of the two-sample t-test will perform similarly in this example. Unequal variances. If the approach for unequal variances (discussed above) is followed, the results are.

Two sample t test - equal variances not assumed - overview This page offers structured overviews of one or more selected methods. Add additional methods for comparisons by clicking on the dropdown button in the right-hand column. When the variances across groups are not equal, the usual analysis of variance assumptions are not satisfied and the ANOVA F test is not valid. JMP provides four tests for equality of group variances and an ANOVA that is valid when the group population variances are unequal.

scipy.stats.ttest_ind (a, b, axis=0, equal_var=True, nan_policy='propagate') [source] В¶ Calculate the T-test for the means of two independent samples of scores. This is a two-sided test for the null hypothesis that 2 independent samples have identical average (expected) values. This test assumes that the populations have identical variances by 17.11. "Equal Variances" and "Unequal Variances" in Two-Sample Inferences. Applies to: StatTools 6.x/7.x. In StatTools, I'm selecting a confidence interval or hypothesis test about the difference in means of two independent samples. StatTools gives two columns of results, headed "Equal Variances" and "Unequal Variances". What do those mean

If LeveneвЂ™s test indicates that the variances are not equal across the two groups (i.e., p-value small), you will need to rely on the second row of output, Equal variances not assumed, when you look at the results of the Independent Samples t Test (under the heading t-test вЂ¦ For such small samples, a test of equality between the two population variances would not be very powerful. Since the sample sizes are equal, the two forms of the two-sample t-test will perform similarly in this example. Unequal variances. If the approach for unequal variances (discussed above) is followed, the results are

This example teaches you how to perform a t-Test in Excel. The t-Test is used to test the null hypothesis that the means of two populations are equal. Below you can find the study hours of 6 female students and 5 male students. To perform a t-TestвЂ¦ The Method column denotes which test is being used for that row, and the Variances column indicates what assumption about variances is being made. The pooled test assumes that the two populations have equal variances and uses degrees of freedom , where and are the sample sizes for the two populations. The remaining two tests do not assume that

I am working in R and know of the T-test and Tukey-test to compare levels of a variable, but these require equal sample sizes. Is there a test I can use where equal sample sizes are not a вЂ¦ This example teaches you how to perform a t-Test in Excel. The t-Test is used to test the null hypothesis that the means of two populations are equal. Below you can find the study hours of 6 female students and 5 male students. To perform a t-TestвЂ¦

Two sample t test - equal variances not assumed - overview This page offers structured overviews of one or more selected methods. Add additional methods for comparisons by clicking on the dropdown button in the right-hand column. If LeveneвЂ™s test indicates that the variances are not equal across the two groups (i.e., p-value small), you will need to rely on the second row of output, Equal variances not assumed, when you look at the results of the Independent Samples t Test (under the heading t-test вЂ¦

17.11. "Equal Variances" and "Unequal Variances" in Two-Sample Inferences. Applies to: StatTools 6.x/7.x. In StatTools, I'm selecting a confidence interval or hypothesis test about the difference in means of two independent samples. StatTools gives two columns of results, headed "Equal Variances" and "Unequal Variances". What do those mean One can quibble whether equal variances are part of the null hypothesis. But, using the pooled t test, equal variances are essential to a fair test of the null hypothesis. Notes about R code: (a) The default 2-sample t test in R is the Welch test, which does not assume equal variances. The parameter var.eq=T leads to use of the pooled test. If

For such small samples, a test of equality between the two population variances would not be very powerful. Since the sample sizes are equal, the two forms of the two-sample t-test will perform similarly in this example. Unequal variances. If the approach for unequal variances (discussed above) is followed, the results are The Method column denotes which test is being used for that row, and the Variances column indicates what assumption about variances is being made. The pooled test assumes that the two populations have equal variances and uses degrees of freedom , where and are the sample sizes for the two populations. The remaining two tests do not assume that

Two sample t test - equal variances not assumed - overview This page offers structured overviews of one or more selected methods. Add additional methods for comparisons by clicking on the dropdown button in the right-hand column. If LeveneвЂ™s test indicates that the variances are not equal across the two groups (i.e., p-value small), you will need to rely on the second row of output, Equal variances not assumed, when you look at the results of the Independent Samples t Test (under the heading t-test вЂ¦

The Method column denotes which test is being used for that row, and the Variances column indicates what assumption about variances is being made. The pooled test assumes that the two populations have equal variances and uses degrees of freedom , where and are the sample sizes for the two populations. The remaining two tests do not assume that t-tests. The t.test( ) function produces a variety of t-tests. Unlike most statistical packages, the default assumes unequal variance and applies the Welsh df modification.# independent 2-group t-test t.test(y~x) # where y is numeric and x is a binary factor # independent 2-group t-test t.test(y1,y2) # where y1 and y2 are numeric

### Unequal Variances jmp.com

Unequal Variances jmp.com. This example teaches you how to perform a t-Test in Excel. The t-Test is used to test the null hypothesis that the means of two populations are equal. Below you can find the study hours of 6 female students and 5 male students. To perform a t-TestвЂ¦, scipy.stats.ttest_ind (a, b, axis=0, equal_var=True, nan_policy='propagate') [source] В¶ Calculate the T-test for the means of two independent samples of scores. This is a two-sided test for the null hypothesis that 2 independent samples have identical average (expected) values. This test assumes that the populations have identical variances by.

Unequal Variances jmp.com. t-tests. The t.test( ) function produces a variety of t-tests. Unlike most statistical packages, the default assumes unequal variance and applies the Welsh df modification.# independent 2-group t-test t.test(y~x) # where y is numeric and x is a binary factor # independent 2-group t-test t.test(y1,y2) # where y1 and y2 are numeric, t-tests. The t.test( ) function produces a variety of t-tests. Unlike most statistical packages, the default assumes unequal variance and applies the Welsh df modification.# independent 2-group t-test t.test(y~x) # where y is numeric and x is a binary factor # independent 2-group t-test t.test(y1,y2) # where y1 and y2 are numeric.

### two-sample t-test with unequal variances Cross Validated

two-sample t-test with unequal variances Cross Validated. The Method column denotes which test is being used for that row, and the Variances column indicates what assumption about variances is being made. The pooled test assumes that the two populations have equal variances and uses degrees of freedom , where and are the sample sizes for the two populations. The remaining two tests do not assume that https://tr.wikipedia.org/wiki/Welch%27in_t-testi scipy.stats.ttest_ind (a, b, axis=0, equal_var=True, nan_policy='propagate') [source] В¶ Calculate the T-test for the means of two independent samples of scores. This is a two-sided test for the null hypothesis that 2 independent samples have identical average (expected) values. This test assumes that the populations have identical variances by.

For such small samples, a test of equality between the two population variances would not be very powerful. Since the sample sizes are equal, the two forms of the two-sample t-test will perform similarly in this example. Unequal variances. If the approach for unequal variances (discussed above) is followed, the results are 17.11. "Equal Variances" and "Unequal Variances" in Two-Sample Inferences. Applies to: StatTools 6.x/7.x. In StatTools, I'm selecting a confidence interval or hypothesis test about the difference in means of two independent samples. StatTools gives two columns of results, headed "Equal Variances" and "Unequal Variances". What do those mean

07/10/2018В В· When working with the 2 sample t-test, we must make one of those two assumptions. We also learn how to decide if we can assume equal variance or if we should assume unequal variance. We cover For such small samples, a test of equality between the two population variances would not be very powerful. Since the sample sizes are equal, the two forms of the two-sample t-test will perform similarly in this example. Unequal variances. If the approach for unequal variances (discussed above) is followed, the results are

This example teaches you how to perform a t-Test in Excel. The t-Test is used to test the null hypothesis that the means of two populations are equal. Below you can find the study hours of 6 female students and 5 male students. To perform a t-TestвЂ¦ If LeveneвЂ™s test indicates that the variances are not equal across the two groups (i.e., p-value small), you will need to rely on the second row of output, Equal variances not assumed, when you look at the results of the Independent Samples t Test (under the heading t-test вЂ¦

For such small samples, a test of equality between the two population variances would not be very powerful. Since the sample sizes are equal, the two forms of the two-sample t-test will perform similarly in this example. Unequal variances. If the approach for unequal variances (discussed above) is followed, the results are Two-Sample T-Tests for Equivalence Allowing Unequal Variance Introduction This procedure allows you to study the power and sample size of equivalence tests of the means of two independent groups using the two-sample unequal-variance t-test. SchuirmannвЂ™s (1987) two one-sided tests (TOST) approach is used to test equivalence. Only a brief

One can quibble whether equal variances are part of the null hypothesis. But, using the pooled t test, equal variances are essential to a fair test of the null hypothesis. Notes about R code: (a) The default 2-sample t test in R is the Welch test, which does not assume equal variances. The parameter var.eq=T leads to use of the pooled test. If scipy.stats.ttest_ind (a, b, axis=0, equal_var=True, nan_policy='propagate') [source] В¶ Calculate the T-test for the means of two independent samples of scores. This is a two-sided test for the null hypothesis that 2 independent samples have identical average (expected) values. This test assumes that the populations have identical variances by

Two sample t test - equal variances not assumed - overview This page offers structured overviews of one or more selected methods. Add additional methods for comparisons by clicking on the dropdown button in the right-hand column. scipy.stats.ttest_ind (a, b, axis=0, equal_var=True, nan_policy='propagate') [source] В¶ Calculate the T-test for the means of two independent samples of scores. This is a two-sided test for the null hypothesis that 2 independent samples have identical average (expected) values. This test assumes that the populations have identical variances by

07/10/2018В В· When working with the 2 sample t-test, we must make one of those two assumptions. We also learn how to decide if we can assume equal variance or if we should assume unequal variance. We cover If LeveneвЂ™s test indicates that the variances are not equal across the two groups (i.e., p-value small), you will need to rely on the second row of output, Equal variances not assumed, when you look at the results of the Independent Samples t Test (under the heading t-test вЂ¦

Two sample t test - equal variances not assumed - overview This page offers structured overviews of one or more selected methods. Add additional methods for comparisons by clicking on the dropdown button in the right-hand column. One can quibble whether equal variances are part of the null hypothesis. But, using the pooled t test, equal variances are essential to a fair test of the null hypothesis. Notes about R code: (a) The default 2-sample t test in R is the Welch test, which does not assume equal variances. The parameter var.eq=T leads to use of the pooled test. If

scipy.stats.ttest_ind (a, b, axis=0, equal_var=True, nan_policy='propagate') [source] В¶ Calculate the T-test for the means of two independent samples of scores. This is a two-sided test for the null hypothesis that 2 independent samples have identical average (expected) values. This test assumes that the populations have identical variances by t-tests. The t.test( ) function produces a variety of t-tests. Unlike most statistical packages, the default assumes unequal variance and applies the Welsh df modification.# independent 2-group t-test t.test(y~x) # where y is numeric and x is a binary factor # independent 2-group t-test t.test(y1,y2) # where y1 and y2 are numeric

This example teaches you how to perform a t-Test in Excel. The t-Test is used to test the null hypothesis that the means of two populations are equal. Below you can find the study hours of 6 female students and 5 male students. To perform a t-TestвЂ¦ The Method column denotes which test is being used for that row, and the Variances column indicates what assumption about variances is being made. The pooled test assumes that the two populations have equal variances and uses degrees of freedom , where and are the sample sizes for the two populations. The remaining two tests do not assume that

The Method column denotes which test is being used for that row, and the Variances column indicates what assumption about variances is being made. The pooled test assumes that the two populations have equal variances and uses degrees of freedom , where and are the sample sizes for the two populations. The remaining two tests do not assume that When the variances across groups are not equal, the usual analysis of variance assumptions are not satisfied and the ANOVA F test is not valid. JMP provides four tests for equality of group variances and an ANOVA that is valid when the group population variances are unequal.