When testing for differences between the means of two related populations, the null hypothesis states that: the population mean difference is not significantly different from zero.
The hypotheses for a difference in two population means are similar to those for a difference in two population proportions. The null hypothesis, H 0 , is again a statement of “no effect” or “no difference.”
When you test for a difference between two population means when should a pooled variance be computed?
When you test for a difference between two population means from small samples, when should a pooled variance be calculated? When the sample sizes are different . When a two-tail test is used.
What test is used for testing the difference between two population variances?
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 testing for the difference between two population means and the population variances are unknown at test is used?
The test comparing two independent population means with unknown and possibly unequal population standard deviations is called the Aspin-Welch t-test .
What is the null hypothesis for a 2 sample t-test?
The default null hypothesis for a 2-sample t-test is that the two groups are equal . You can see in the equation that when the two groups are equal, the difference (and the entire ratio) also equals zero.
How do you compare two means?
- Independent Samples T-Test. Use the independent samples t-test when you want to compare means for two data sets that are independent from each other. ...
- One sample T-Test. ...
- Paired Samples T-Test. ...
- One way Analysis of Variance (ANOVA).
How do you know if variance is equal or unequal?
- 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. ...
- Perform an F-test.
Which of the following distribution is used to compare two variances?
Explanation: F – Distribution is used when we require for comparing two variances. It uses a f-Test to compare two values of variances.
What is the null hypothesis for Levene’s test?
The null hypothesis for Levene’s test is that the groups we’re comparing all have equal population variances . If this is true, we’ll probably find slightly different variances in our samples from these populations. However, very different sample variances suggests that the population variances weren’t equal after all.
How do you compare two sample variances?
- The F-test: This test assumes the two samples come from populations that are normally distributed.
- Bonett’s test: this assumes only that the two samples are quantitative.
- Levene’s test: similar to Bonett’s in that the only assumption is that the data is quantitative.
What is F test used for?
ANOVA uses the F-test to determine whether the variability between group means is larger than the variability of the observations within the groups . If that ratio is sufficiently large, you can conclude that not all the means are equal.
How do you know if variance is correct?
A chi-square test ( Snedecor and Cochran, 1983) can be used to test if the variance of a population is equal to a specified value. This test can be either a two-sided test or a one-sided test.
How do you interpret a two-tailed test?
A two-tailed test will test both if the mean is significantly greater than x and if the mean significantly less than x. The mean is considered significantly different from x if the test statistic is in the top 2.5% or bottom 2.5% of its probability distribution, resulting in a p-value less than 0.05.
When should you use the z-test?
The z-test is best used for greater-than-30 samples because, under the central limit theorem, as the number of samples gets larger, the samples are considered to be approximately normally distributed. When conducting a z-test, the null and alternative hypotheses, alpha and z-score should be stated.
What is a two sample t test used for?
The two-sample t-test (also known as the independent samples t-test) is a method used to test whether the unknown population means of two groups are equal or not .
