Which of the following assumptions does not apply to the t test for independent means?

z test is used to test the difference between two means when the population standard deviations are known and the variables are normally or approximately normally distributed. In many situations, however, these conditions cannot be met—that is, the population standard deviations are not known. In these cases, a t test is used to test the difference between means.There are a number of different types of t-tests. The two that will be discussed here are:

• Independent-samples t-test,

Assumptions

For both of the t-tests that I discuss here, there are a number of assumptions that we will need to check before conducting these analyses. 

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• We are interested in studying the performance of students working in pairs or small groups. The behaviour of each member of the group influences all other group members, thereby violating the assumption of independence.
• Studying the TV-watching habits and preferences of children drawn from the same family. The behaviour of one child in the family (e.g. watching Program A) is likely to influence all children in that family; therefore, the observations are not independent. 

Normal distribution 
For parametric techniques, it is assumed that the populations from which the samples are taken are normally distributed. In a lot of research scores on the dependent variable are not normally distributed. Fortunately, most of the techniques are reasonably 'robust' or tolerant of violations of this assumption. With large enough sample sizes (e.g. 30+), the violation of this assumption should not cause any major problems. Normality of our variables can be checked using histograms, stem and leaf display, Box plot. WE can also check the value of Skewness  and mean, median, and mode of our variable (Mean=Median=mode).Homogeneity of variance 
Samples that are obtained from populations should have equal variances. This means that the variability of scores for each of the groups is similar. 

Independent Sample T-test

Purpose of Independent sample t-test

​—To compare differences between two (2) independent group means

Requirements

►​DV–Interval or ratio
►IV–Nominal or ordinal (k=2)

Example of research question: Is there a significant difference in the mean self esteem scores for males and females? What we need: Two variables: one categorical, independent variable (e.g. males/females) one continuous, dependent variable (e.g. self-esteem scores). What it does:An independent-samples t-test will tell us whether there is a statistically significant difference in the mean scores for the two groups (i.e. whether males and females differ significantly in terms of their self-esteem levels).   How to test the hypothesis for the independent sample t-test

Interpretation of output from independent-samples t-test

Step 1: Checking the information about the groups
Excel gives us the mean and standard deviation for each of our groups (in this case, Support/ Admin). It also gives us the number of people in each group (N). We should always check these values first. Are the N values for support and Admin correct? Or are there a lot of missing data? If so, we should find out why. Perhaps we have entered the wrong code for Support and females (0 and 1, rather than 1 and 2). We should check our codebook.

Step 2: Checking assumptions
The independent sample t-test assumes the variances of the two groups we are measuring are equal in the population. If our variances are unequal, this can affect the Type I error rate. We should run the F-test two sample for variances in Excel to check the equality of variances. This tests whether the variance (variation) of scores for the two groups (Support and Admin) is the same. If Sig-F is grater than the significance value (Sig-F ≥ œ), the T-test: two sample assuming equal variances can be used. If Sig-F is less than the level of significance (Sig-F≤ œ), the test for equality of variances is statistically significant. It indicates that the group variances are unequal in the population. We can correct this violation by using the T-test: two sample assuming unequal variances. 

In this case, Sig-F is larger than alpha value so we can use the T-test: two sample assuming equal variances.
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We should also check other assumptions such as level of measurement, random sampling, independence of observations, and normality of our data.

Step 3: Assessing differences between the groups

To find out whether there is a significant difference between our two groups, we should compare P-value ( Sign-t) with the level of significance.

• If the P value (Sig-t) is equal or less than .05 or 0.01 , we reject the null hypothesis. So, we can conclude that there is a significant difference in the mean scores on our dependent variable for the two groups.

• If the P value (Sig-t)  is above .05 or 0.01 , we fail to reject the null hypothesis. So, we can conclude that there is not a significant difference between the two groups.
  

In the example presented in the output above, the P value (Sig. t- 2-tailed) is .03. As this value is above the required cut-off of .01,  we conclude that there is not  ​a statistically significant difference in the mean Job stress scores for Support and Admin group. Calculating the effect size for independent-samples t-test 
One way that we can assess the importance of our finding is to calculate the effect size. Effect size statistics provide an indication of the magnitude of the differences between our groups (not just whether the difference could have occurred by chance). There are a number of different effect size statistics, the most commonly used are eta squared and Cohen’s d. Eta squared can range from 0 to 1 and represents the proportion of variance in the dependent variable that is explained by the independent (group) variable. 
We can use a formula to calculate the eta squared.

Presenting the results for independent-samples t-test
The results of the analysis can be presented as follows:

An independent-samples t-test was conducted to compare the job stress scores for Support and Admin groups. There was no significant difference in the mean Job stress scores for Support (M = 19.2, SD = 2.39) and Admin groups (M = 22, SD = 2.83) at 0.01 (t = -2.336, p = .03, two-tailed). Eta squared was 0.243 ( 24% of of variance in the Job stress is explained by the employee groups). The magnitude of the differences in the means (mean difference = 2.8,) was 1.07 .

What are the assumptions for an independent t

What three conditions are necessary for an independent measures t

What is the third assumption we make for a one independent sample t

In which condition we can apply independent sample t