1 T Test for Two Independent Sample Means with Equal Variances
Online Course Pharmaceutical Biostatistics Chapter 4: Parametric Techniques
18/7/2017
2
Location A (g)
Location B (g)
Average mass of the penguin
510
690
322
235
435
610
•
790
505
590
460
765
650
440
815
660
773
780
455
•
Does the average mass of the penguins differs between location A and location B? Equal population variances assumed.
836
Online Course Pharmaceutical Biostatistics Chapter 4: Parametric Techniques
570
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3 T Test for 2 Independent Sample Means
• • •
•
H0 : µA = µB or : µA -µB = 0 HA: µA ≠ µB or : µA -µB ≠ 0 The degree of freedom is: Descriptive Statistics
nA+ nB
– 2 = 13 + 7 – 2 = 18 Location A Location B
n
13
7
x̅
618
551
S2
37853
15037
Pooled sample variance (Sp2 ) is used as it is the best estimate of the overall variability. Online Course Pharmaceutical Biostatistics Chapter 4: Parametric Techniques
18/7/2017
4 Step 1. How to calculate the Pooled Sample Variance?
Online Course Pharmaceutical Biostatistics Chapter 4: Parametric Techniques
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5 Step 2. Calculate the t Statistic
• • •
The test statistic is t (18) =0.82 Subscript1 = location A Subscript2 = location B Online Course Pharmaceutical Biostatistics Chapter 4: Parametric Techniques
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6 Step 3. Formulate the Decision Rules: tcritical value • • •
Given: Degree of freedom is nA + nB – 2 = 13 + 7 – 2 = 18 α= 0.05 for a two tailed test. Reject H0 if the t statistic is > 2.101 or < -2.101.
Online Course Pharmaceutical Biostatistics Chapter 4: Parametric Techniques
18/7/2017
7 Step 4. Interpretation of Results â&#x20AC;˘
Since the test statistic, t (18) =0.82 is in the acceptance region, -2.101< 0.82< 2.101, we DO NOT reject H0.
â&#x20AC;˘
Conclusion: There is no significant difference for the mean masses of penguin from location A and location B with t (18) = 0.82 < 2.101.
Online Course Pharmaceutical Biostatistics Chapter 4: Parametric Techniques
18/7/2017