To compare the population mean of X across two independent groups
Note:
The test variable X must be scale level and normally distributed in both groups.
The two groups must be independent.
H0: The two groups have the same population mean of X.
H1: The two groups have different population mean of X.
H0: Group 1 has the same population mean of X as Group 2.
H1: Group 1 has a larger population mean of X than Group 2.
Note : Strictly speaking, H0 for the one-tailed tests should be written as "The population mean of X for Group 1 is not greater than / smaller than that of Group 2", but since we don't care about the other side here, we would use the same H0 as the two-tailed test for simplicity.
Note: It doesn't matter which group is Group 1 and which is Group 2 as far as it is defined clearly in your writing.
Note : We conduct the above test only if the sample mean of Group 1 is already greater than the sample mean of Group 2.
You want to know if Male and Female respondents have the same answer in X.
H0: Male and female have the same population mean of X.
H1: Male and female have different population mean of X.
H0: Male has the same population mean of X as Female.
H1: Male has a larger population mean of X than Female.
Analyze -> Compare Means -> Independent-Samples T Test -> Select the Test Variables -> Select the Grouping Variable that splits the sample into two groups (e.g. Gender) -> Define the groups in the group variable by specifying the values corresponding to the two groups -> Click Options button to adjust the confidence interval percentage
Note the p-value (Sig.) under the Levene’s Test for Equality of Variances. Small enough p-value rejects the null hypothesis that the variances of the two populations are equal. In that case, one should look at the results in the second row of the table (i.e. Equal variances not assumed). Otherwise, look at the first row.
Hypotheses for the Levene’s Test for Equality of Variances:
H0: The two groups have equal population variance. -> Look at the first row of t-test results
H1: The two groups have different population variance. -> Look at the second row of t-test results
Analyses -> T-Tests -> Independent-Samples T Test -> Select the Dependent Variables -> Select the Grouping Variable that splits the sample into two groups (e.g. Gender).
Under Tests,
Select Student’s for t-test when variances are equal, or Welch’s for t-test when variances are unequal. (The equality of variance can be tested by using Homogeneity test under Assumption Checks. Or if you see a remark under the resulting table saying that the assumption of equal variances is violated, then you should choose Welch’s t-test.)
Select Mann-Whitney U for non-parametric test.
Hypotheses for the Homogeneity test (Levene’s Test for Equality of Variances):
H0: The two groups have equal population variance. -> Use Student’s t-test.
H1: The two groups have different population variance. -> Use Welch’s t-test.
Under Hypothesis, select the direction of the hypotheses.
Optionally, under Additional Statistics, select the descriptive statistics or confidence intervals to be shown. Also do the assumption checks if necessary.
Unless otherwise specified, the p-value given in the software is the two-tailed p-value. Divide it by two to get the one-tailed p-value in case of a one-tailed test.
If p<0.05 (or other significant levels), we take H1 as true, i.e., the population mean of X for Group 1 is not equal to that for Group 2 .
If p is not <0.05 (or other significant levels), we take H0 as true, i.e., the population mean of X for Group 1 is equal to that for Group 2.
If p<0.05 (or other significant levels), we take H1 as true, i.e., the population mean of X for Group 1 is larger than that for Group 2 .
If p is not <0.05 (or other significant levels), we take H0 as true, i.e., the population mean of X for Group 1 is equal to that for Group 2.
Name of the test being used (independent-samples t-test)
The test variable and the grouping variable (or the groups concerned)
The t statistic
The p-value
Your conclusion of the test
Elaboration of the result in your research context