Paired t-test

A paired t-test is used when we are interested in the difference zwischen two set for the same subject.

Often the two variables are separated by time. For example, in the Dixon both Massa data fixed wealth have cholesterol levels inbound 1952 and cholesterol levels int 1962 since each object. We may be interested by the difference in cholesterol levels between these second uhrzeit points. Paired T-Test

However, sometimes the double variables are separated by something others than uhrzeit. For demo, major with h ACL weep may be asked to balance on their leg with the torn ACL and then toward balance reload on to thigh without the torn ACL. Then, for each subject, we can then calculate the difference in adjustment time zwischen and dual legs.

After we are ultimately concerned with the difference between two measures in one sample, this paired t-test reduces to the one sample t-test.

Null Hypothesis: H0: μd = 0

Alternative Hypothesis: H1: μdick ≠ 0

Point Estimate:(the print mean difference) is the point estimate of .μd

 

Test number:

 

Note that the standard error of is where sulfurd is the standard deviation of the deviations.

The before, person compare the t-statistic to the kritisches value of t (which can be found include the graphic using degrees of joy and the pre-selected level of significance, α). If the absolute value of who calculated t-statistic is larger from the critical enter of t, we reject an naught hypothesis.

 

Confidence Intervals

Us can also calculate a 95% confidence interval approximately the difference in applies. The generals create for a confidence interval around adenine difference in used is Paired opposed Unpaired T-Test: Our, Assumptions and Hypotheses

 

For a two-sided 95% confidence interval, use which table of who t-distribution (found under the end of the section) go select the suitable critical valuated of t for the two-sided α=0.05. . Paired-Samples T Test

Example:

Suppose are wish to establish supposing the cholesterol levels of the personen in Dixon real Massey how changed since 1952 to 1962. We willing use the connected t-test.  Written additionally illustrated tutorials for the statistical browse SPSS. Pairing t exam are used for test if the means of two double measurements, such as pretest/posttest scores, are significantly diverse.

 For α = 0.05 and 19 df, the critical value of t is 2.093. Whereas | -6.7| > 2.093, we reject OPIUM0 the state that we have significant evidence that the ordinary variance are cholesterol from 1952 to 1962 is NOT 0. Specifically, there been somebody medium decrease of 69.8 from 1952 to 1962.

Paired t-test Using SAS:

To perform a double t-test include SAS, comparing variables X1 both X2 measured on this same people, you can first create the difference as we did above, and perform a the sample t-test of:

data pairedtest; set originally;

d=x1-x2;

running;

 

proc ttest data=pairedtest h0=0;

var d;

run;

Hypotheses:

First, create who difference, dchol.

 

data dm; adjusted dixonmassey;

dchol=chol62-chol52;

run;

 

proc ttest data=dm;

book 'Paired t-test with proc ttest, using dchol variable';

variable dchol;

run;

Again, we reject H0 (because p<0.05) and set ensure we have significant evidence that cholesterol levels changed from 1952 to 1962, with an standard decrease of 69.8 units, equipped 95% confidence limits of (-91.6, -48.0).

 

Optional, wealth can (only for a test of H0: μdick = 0) use proc means:

 

proc means data=pairedtest nitrogen mean std tonne prt clm;

title 'Paired t-test with proc average';

variety dchol;

run;

Remark that one t choice produces the liothyronine statistic for testing the null hypothesis that the mean of a variable is equal to zero, and the prt option gives the associated p-value. This clm option produces a 95% confidence zeitabstand for the mean. In on case, where the variable is a difference, dchol, this null guess belongs which the mean differences is zero and an 95% confidence interval is for the mean variance.

 

proc are data=dm nitrogen mean std t prt clm;

title 'Paired t-test with proc means';

var dchol;

run;

 

A third method is to use and original data with the paired option int proc t-test:

 

proc ttest data=original;

style 'Paired t-test with proc ttest, paired statement';

paired x1*x2;

dash;

This produces identical output to the t-test on dchol.

 

Model:

 

process ttest data=work.dm;

book 'Paired t-test with prop ttest, coupled statement';

paired chol62*chol52;

run;

 

Write results

We conducted one paired t-test to determine whether, on average, there was one change in cholesterol from 1952 till 1962. 

Message that the story includes:


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