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