1 Variance Test for Two Independent Samples
Online Course Pharmaceutical Biostatistics Chapter 4: Parametric Techniques
18/7/2017
2 •
•
Table 1
Variance Test Case 2: The mass (in gram) of random samples of female penguin from location A and location B in the Philip Island, Melbourne, Australia are given in Table 1. Is the variability (variance) in mass different on the two locations?
Location A (g)
Location B (g)
510
690
322
235
435
610
790
505
590
460
765
650
440
815
660
773
780
455
836
Online Course Pharmaceutical Biostatistics Chapter 4: Parametric Techniques
570
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3 Step 1. Hypothesis •
Variance test (F test) is performed prior to independent t test. • H0 : σ2 A = σ2 B
•
Ha : σ2 A ≠ σ2 B
Online Course Pharmaceutical Biostatistics Chapter 4: Parametric Techniques
18/7/2017
4 Step 2. Calculate the F statistics • • =
Given SA2 Var=37.853 and SB2 = 15.037 Sa 2 F statistic, F= 2 Sb 37.853/15.037=2.52
Online Course Pharmaceutical Biostatistics Chapter 4: Parametric Techniques
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5
Step 3. Formulate the Decision Rules: Fcritical values • • • •
Given α = 0.05 (two tailed) and dfA (numerator) = 13-1 = 12; dfB (denominator) = 7-1 = 6, The Fcritical value is 5.37 on the right hand tail. (Refer to F distribution). While the left tail is reciprocal of the corresponding right-tail critical value with the degree of freedom reversed. F0.025(12,6) = 1/F0.975(6,12) = 1/3.73 = 0.27 (Refer F distribution)
Online Course Pharmaceutical Biostatistics Chapter 4: Parametric Techniques
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6 If the t statistic is < 0.27 or > 5.37, we reject H0
â&#x20AC;˘
Îą = 0.05/2= 0.025
Online Course Pharmaceutical Biostatistics Chapter 4: Parametric Techniques
18/7/2017
7 Fcritical values for the left hand tail
Online Course Pharmaceutical Biostatistics Chapter 4: Parametric Techniques
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8 Step 4. Interpret the Results • • •
Since 2.52 is within the acceptance region, 0.27<2.52<5.37, we DO NOT reject the H0 . There is no significant variability in mass of female penguin from location A and B with F(12,6) = 2.52 < 5.37. Equal variances assumed.
Online Course Pharmaceutical Biostatistics Chapter 4: Parametric Techniques
18/7/2017