# Class_13 - The t-test Independent and Paired(Dependent...

• Notes
• 31

This preview shows pages 1–10. Sign up to view the full content.

The t-test: Independent and The t-test: Independent and Paired (Dependent) Samples Paired (Dependent) Samples

This preview has intentionally blurred sections. Sign up to view the full version.

Recapitulation Recapitulation 1. Still dealing with random samples . 2. However, they are partitioned into two subsamples . 3. Interest is in whether the means of some variable differ significantly between the two subsamples. 4. For large samples, the sampling distribution of mean differences is normally shaped . 5. For smaller samples, the sampling distribution takes the shape of one of the Student’s t distributions .
6. In either case, the significance tests involve a test of the null hypothesis (H 0 ) that in general (i.e., in the universe) the means do NOT differ. Symbolically, H 0 : μ 2 - μ 1 = 0.00 7. The alternate hypothesis (H 1 ) can either be nondirectional H 1 : μ 2 - μ 1 0.0 or directional , either H 1 : μ 2 - μ 1 > 0.0 or H 1 : μ 2 - μ 1 < 0.0

This preview has intentionally blurred sections. Sign up to view the full version.

Reject a null hypothesis (H 0 ) when either: 1. the value of the statistical test ( χ 2 , z, t , or F) exceeds the critical value at the chosen α -level; or, 2. the p-value for the statistical test is smaller than the chosen value of α .

This preview has intentionally blurred sections. Sign up to view the full version.

An Example of a T-Test PPD 404 The TTEST Procedure Statistics Lower CL Upper CL Lower CL Upper CL Variable Class N Mean Mean Mean Std Dev Std Dev Std Dev Std Err MANUFPCT Newer 38 22.928 26.526 30.125 8.9262 10.949 14.165 1.7761 MANUFPCT Older 25 20.1 23.92 27.74 7.2268 9.2553 12.875 1.8511 MANUFPCT Diff (1-2) -2.706 2.6063 7.9183 8.7659 10.316 12.536 2.6565 T-Tests Variable Method Variances DF t Value Pr > |t| MANUFPCT Pooled Equal 61 0.98 0.3304 MANUFPCT Satterthwaite Unequal 57.1 1.02 0.3139 Equality of Variances Variable Method Num DF Den DF F Value Pr > F MANUFPCT Folded F 37 24 1.40 0.3897
An Example of a T-Test PPD 404 The TTEST Procedure Statistics Lower CL Upper CL Lower CL Upper CL Variable Class N Mean Mean Mean Std Dev Std Dev Std Dev Std Err MANUFPCT Newer 38 22.928 26.526 30.125 8.9262 10.949 14.165 1.7761 MANUFPCT Older 25 20.1 23.92 27.74 7.2268 9.2553 12.875 1.8511 MANUFPCT Diff (1-2) -2.706 2.6063 7.9183 8.7659 10.316 12.536 2.6565 T-Tests Variable Method Variances DF t Value Pr > |t| MANUFPCT Pooled Equal 61 0.98 0.3304 MANUFPCT Satterthwaite Unequal 57.1 1.02 0.3139 Equality of Variances (null hypoth. Variances are equal) Variable Method Num DF Den DF F Value Pr > F MANUFPCT Folded F 37 24 1.40 0.0389

This preview has intentionally blurred sections. Sign up to view the full version.

The tests that we have performed thus all assumed that the “subuniverse” variances were equal. Remember, parameters (e.g., universe variances) are almost always unknown . Therefore, we let subsample variances be proxies for the unknown universe variances. If the two variances in the universe are greatly different —as indicated by statistically significant differences between the subsample variances —, then a different method must be used to estimate the standard error of the difference.
A hypothesis test exists to decide whether the two variances are significantly different. In this F' test , a ratio

This preview has intentionally blurred sections. Sign up to view the full version.

This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern