T Test for Two Independent Sample Means with Unequal Variances

1

T Test for Two Independent Sample Means with Unequal Variances

Online Course Pharmaceutical Biostatistics Chapter 4: Parametric Techniques

18/7/2017

2 • • •

Case 3: Amphetamine and Water Consumption When the preliminary variance test, H0 : σ2A = σ2B , is rejected, we don’t pool the sample variances because they are each estimating a different parameter.

Case 3: A pharmacologist injected 15 rats with amphetamine and 10 with saline solution as controls. Over the next 24 hours, she measured the amount of water consumed by each rat and expressed the results in ml/kg body weight.

Does the Amphetamine significantly suppress water consumption?

With α= 0.05 Descriptive Amphetamine Saline Statistics n

15

10

x̅

115

135

S2

40

15

HA= Amphetamine suppress water consumption thus it has lower mean value.

Online Course Pharmaceutical Biostatistics Chapter 4: Parametric Techniques

18/7/2017

3 Step 1. Calculate the t statistics

Online Course Pharmaceutical Biostatistics Chapter 4: Parametric Techniques

18/7/2017

4 Step 2: Calculate the Degree of Freedom

Online Course Pharmaceutical Biostatistics Chapter 4: Parametric Techniques

18/7/2017

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

Degree of freedom=19 α = 0.05 for one tailed test Reject H0 if the statistic is < -1.729

Online Course Pharmaceutical Biostatistics Chapter 4: Parametric Techniques

18/7/2017

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

Since the test statistic, t (19) =-1.759 , we reject H0.

Conclusion: The data support the claim that amphetamine significantly suppress water consumption.

Online Course Pharmaceutical Biostatistics Chapter 4: Parametric Techniques

18/7/2017