T Test for Two Dependent Sample Means

1 T test for Two Dependent Sample Means (Paired samples/Repeated Measures)

Online Course Pharmaceutical Biostatistics Chapter 4: Parametric Techniques

18/7/2017

2 Examples of Paired Data 1. Systolic blood pressure before administering a drug and again 6 hours after administering the drug.

2. Natural paired data: twin studies in schizophrenia.

3. Efficacy of two different hand cream, one on each arm.

4. Matched pairs (age, gender, and blood pressure) to a similar patient who had an angioplasty.

5. “Pairing� the data points of corn A and corn B between 7 different farms- similar to matched pairs.

Online Course Pharmaceutical Biostatistics Chapter 4: Parametric Techniques

18/7/2017

3 Case: An experiment was conducted to compare the performance of two varieties of corn, A and B. Seven farms were randomly chosen for the experiment and the yields in metric tons per hectare for each variety on each farm were as follows: Farm

Different (Corn ACorn B)

1

0.5

2

0.8

3

-0.3

4

0.6

4.6

5

-0.2

3.7

3.3

6

0.4

4.1

3.8

7

0.3

Farm

Corn A

Corn B

1

4.7

4.2

2

4.9

4.1

3

3.3

3.6

4

4.7

4.1

5

4.4

6 7

Online Course Pharmaceutical Biostatistics Chapter 4: Parametric Techniques

18/7/2017

4 Step 1. Hypothesis • H0 : µd =0; µA - µB = 0; µA =µB • HA: µd ≠ 0; µA - µB ≠ 0; µA ≠ µB

• Since the two columns of data collapse into one column of interest, we treat these data as a one sample experiment.

• There is no preliminary variance test and the only assumption is the di’s are approximately normally distributed.

• Analysis is analogous to one-sample T test.

Online Course Pharmaceutical Biostatistics Chapter 4: Parametric Techniques

18/7/2017

5 Step 2. Calculate the t Statistic

Online Course Pharmaceutical Biostatistics Chapter 4: Parametric Techniques

18/7/2017

6 Step 3. Formulate the Decision Rules: tcritical value • •

•

Degree of freedom is n – 1 = 7-1= 6 α= 0.05 for a two tailed test.

Reject H0 if the t statistic is > 2.447 or < -2.447.

Online Course Pharmaceutical Biostatistics Chapter 4: Parametric Techniques

18/7/2017

7 Step 4. Interpretation of Results â&#x20AC;˘ â&#x20AC;˘

Since t(6) = 1.94 is within the acceptance range, -2.447<1.94<2.447, we DO NOT reject the H0.

Thus, there is no significant difference between yields of varieties A and B.

Online Course Pharmaceutical Biostatistics Chapter 4: Parametric Techniques

18/7/2017