T-testing is used in hypothesis testing, when you are deciding if you should support or reject a null hypothesis.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.
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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.If your p-value is greater than .05 you fail to reject the null (meaning the difference in means is likely due to chance or sampling error).
Why do we assume equal variances in t test?
Equal variances assumed
If the calculated t value is greater than the critical t value, then we reject the null hypothesis. Note that this form of the independent samples t test statistic assumes equal variances. Because we assume equal population variances, it is OK to “pool” the sample variances (sp).
How do I 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 does unequal variance mean in 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.
What does it mean to assume equal variance?
homoscedasticity
What Is the Assumption of Equal Variance?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. Equal variances (homoscedasticity) is when the variances are approximately the same across the samples.
When population variance are equal the test statistic is?
F-test
An F-test (Snedecor and Cochran, 1983) is used to test if the variances of two populations are equal. This test can be a two-tailed test or a one-tailed test. The two-tailed version tests against the alternative that the variances are not equal.
When running a test of equal variance for normal data which test statistic is read when you are comparing several samples?
Levene’s test
Levene’s test ( Levene 1960) is used to test if k samples have equal variances. Equal variances across samples is called homogeneity of variance. Some statistical tests, for example the analysis of variance, assume that variances are equal across groups or samples. The Levene test can be used to verify that assumption.
What is meant by equal 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 know the variances are not the same.
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.
Should we assume the equality of population variance?
Chapter Review. In situations when we do not know the population variances but assume the variances are the same, the pooled sample variance will be smaller than the individual sample variances. This will give more precise estimates and reduce the probability of discarding a good null.
What does the t test for the difference between the means of 2 independent populations assume?
The t test for the difference between the means of two independent samples assumes that the respective:In testing for differences between the means of two independent populations the null hypothesis states that: the difference between the two population means is not significantly different from zero.
When testing for equal variances the null hypothesis is?
F-test of
In statistics, an F-test of equality of variances is a test for the null hypothesis that two normal populations have the same variance.
When Levene’s test for equality of variances is significant?
However, Levene’s test is statistically significant because its p < 0.05: we reject its null hypothesis of equal population variances.
Why is equality of variance important?
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 are the assumptions of 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.
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.
Which one is used to test the significance of the difference between the means of two random samples of size less than 30?
Please, use the t-test statistics to test for statistical significance for your sample.
How would you determine whether the difference between the two populations is statistically significant?
P-value: The primary output of statistical tests is the p-value (probability value). It indicates the probability of observing the difference if no difference exists.But because the difference is greater than 0%, we can conclude that the difference is statistically significant (not due to chance).
Which of the following conditions must be met to conduct a test for the difference in two sample means?
Which of the following conditions must be met to conduct a test for the difference in two sample means?Using two independent samples, two population means are compared to determine if a difference exists. The population standard deviations are equal.