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Standard Deviations Sample Sizes Assume Equal Standard Deviations (Pooled) Do Not Assume Equal Standard Deviations (Not Pooled) Study T test statistic Degrees of Freedom P-value

Standard Deviations

Sample Sizes

Assume Equal Standard Deviations (Pooled)

Do Not Assume Equal Standard Deviations (Not Pooled)

Study

T test statistic

Degrees of Freedom

P-value

T test statistic

Degrees of Freedom

P-value

1

12

10

20

20

1.431

38

0.1605

1.431

36.80

0.1607

2

12

10

50

50

2.263

98

0.0258

2.263

94.91

0.0259

3

6

5

20

20

2.863

38

0.0068

2.863

36.80

0.0069

4

6

6

32

8

2.108

38

0.0417

2.108

10.79

0.0593

5

8

6

20

20

2.236

38

0.0313

2.236

35.24

0.0318

6

8

6

10

30

2.097

38

0.0427

1.814

12.55

0.0937

7

8

6

30

10

1.808

38

0.0785

2.088

20.58

0.0494

8

12

2

20

20

1.838

38

0.0739

1.838

20.05

0.0809

9

12

2

10

30

2.246

38

0.0306

1.312

9.17

0.2216

10

12

2

30

10

1.301

38

0.2012

2.193

33.29

0.0354

What do we learn from this? Answer the following questions.

  1. Compare Study 3 and Study 1: Based on your results, how (in general) does decreasing standard deviations decrease (holding the means and sample sizes constant) impact our three metrics (degrees of freedom, the test statistics and the p-values)?

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