Objective: independent samples from two populations, two population mean to infer whether there is a difference.
Conditions:
(1) total sample or from a subject to be approximately normally distributed;
(2) two independent samples, two samples of the sample can vary;
case analysis:
Case Description: evaluate the quality of teaching two teachers, taught trial to compare their respective A, B two classes (set up two classes A, B
Results similar to the original, there is no difference) after the results of the examination whether there is a difference? (Source: "Statistical analysis of the course" Zhang Wentong Chapter XI)
Topic Analysis: The problem involves two independent samples (teaching quality and class) overall, the overall mean test, while the overall approximate normal distribution, hence the two independent samples t-test.
Case steps:
The null hypothesis is proposed: the results after the A, B two classes exam there is no difference, as the quality of teaching two teachers.
Interface Procedure: input data - Analysis - output - Comparison of Mean - independent samples t test - Variable Settings
Screenshot key steps:
Test variables and variables distinguish packets (packets from variable Recognition)
Click defined group, fill in the name of their group
While some grouping variable is numeric when group definitions will be "cut point" (the relationship between cholesterol and smoked, 25 may be divided into smoked > = 25 and <25 groups, specific examples found in: "Analysis and Statistics SPSS applications "Xue Wei Chapter V)
Result analysis:
| Set of statistics |
|||||
|
|
class |
N |
Means |
Standard deviation |
The standard error of the mean |
| Achievement |
Armor |
20 |
83.30 |
6.906 |
1.544 |
| B |
20 |
75.45 |
9.179 |
2.053 |
|
SE:
;
| Independent sample test |
||||||||||
|
|
Variance equation Levene test |
Mean equation of the t test |
||||||||
| F |
Sig. |
t |
df |
Sig. ( Bilateral ) |
Mean difference |
The standard deviation |
The difference 95% confidence interval |
|||
| Lower limit |
Upper limit |
|||||||||
| Achievement |
Assume equal variances |
.733 |
.397 |
3.056 |
38 |
.004 |
7.850 |
2.569 |
2.650 |
13.050 |
| Assuming that the variances are unequal |
|
|
3.056 |
35.290 |
.004 |
7.850 |
2.569 |
2.637 |
13.063 |
|
analysis:
F : Levene F test method to determine whether the two population variances are equal?
Note: assume equal variances? Assuming that the variances are unequal? How do you decide t test t , df , Sig , the mean value of the difference ......?
Using the F test method determines whether two population variances are equal, comparator F test methods p and ɑ (generally the 0.05 ); if p> ɑ , is accepted the null hypothesis (two general methods no significant difference), at this time, select "assuming equal variances" the line of t data checking, if P < ɑ , and vice versa.
After the step, and the one-sample t test step as compared Sig ( bilateral ) i.e. p and ɑ (and generally 0.05 ).
In this problem: F. Test methods p = 0.397> 0.05, so the two methods generally no significant difference, select "assuming equal variance" line.
Reference books:
"Statistical Analysis with SPSS applications" (Fifth Edition) Xue Wei
" SPSS statistical analysis from scratch," Wu Jun
" SPSS statistical analysis based tutorial" Zhang Wentong