Customizable tables of p values
for teaching the t, F, and chi-square distributions

Unpublished manuscript
by Paul T. von Hippel

Abstract

Many textbooks still use critical values to teach hypothesis tests, and use statistical tables that were designed with critical values in mind. We present statistical tables that allow students to look up p values directly, eliminating the need to teach the critical-value approach. The tables are generated using statistical functions in Microsoft Excel spreadsheets; by editing the spreadsheets, instructors can modify the tables to suit their tastes.

Key words: hypothesis test, critical value, significance level, p value

Many textbooks still teach a cumbersome and old-fashioned approach to hypothesis testing, in which the observed test statistic is compared to the critical value associated with a fixed significance level. Most applied researchers, however, simply report the p value, or indidate whether the p value is below the significance level.

Students find p values easily when analyzing data on a computer, but they have more difficulty when working problems by hand. The difficulty comes from the fact that many textbooks use old-fashioned statistical tables designed for the critical-value approach. In principle, textbook tables can be used to look up p values. In practice, though, p values obtained in this way can be rather coarse, since textbook tables often give just a handful of probabilities.

Table 1 summarizes the dimensions of t tables in a convenient sample of 27 textbooks and references published in the past decade or so. (This updates the summary in Dawson 1997.) Teachers who favor p values will find some books more hospitable than others. A teacher using Ritchey (2000), for example, may find it difficult to teach p values, since the t table in that book gives only 3 different probabilities. A teacher using Walpole., Myers,  Myers, & Ye (2002), however, will have an easier time, since that book's t table gives 14 different probabilities -- though none of these exceeds .40.

Tables 2 and 3 summarize the chi-square and F tables in the same books. Chi-square tables often give 10 or more probabilities, but F tables rarely give more than 4 traditional significance levels (e.g., .10, .05, .025, .01). Using textbook F tables, it is difficult to avoid discussing critical values, even if the topic has been successfully avoided in teaching the t and chi-square.

Table 1. Dimensions of t tables

Book

Probabilities

df values

Pages

Ritchey (2000)

3

34

1

Thorne & Giessen (2000)

4

42

1

Agresti & Finlay (1997)

5

30

1

Freund (2004)

5

30

1

Hogg & Craig (1995)

5

30

1

Bartz (1999)

6

38

2

Freedman, Pisani, & Purves (1998)

6

25

1

Levin & Fox (2004)

6

34

1

Frankfort-Nachmias & Leon-Guerrerro (2002)

6

34

2

Gravetter & Wallnau (2004)

6

34

1

Kendrick (2005)

6

34

2

Triola (2001)

6

30

1

Zwillinger & Kokoska (2000)

7

36

1

Sincich (1993)

7

34

1

Siegel & Morgan (1996)

7

35

2.5

Rice (1995)

8

34

1

Lunneborg (1994)

8

45

2

Rossman, Chance, & Lock (2001)

8

43

2

Dean & Voss (1999)

9

43

1

Kirk (1995)

9

34

1

Johnson & Wichern (1999)

9

34

1

Milton & Arnold (2003)

9

101

2

Spiegel & Liu (1999)

10

34

1

Moore & McCabe (2006)

12

37

1

Watkins, Scheaffer, & Cobb (2004)

12

37

1

Walpole, Myers, Myers, & Ye (2002)

14

34

2

Neter et al. (1996)

14

34

2

Minimum

3

25

1

Median

7

34

1

Maximum

14

101

2.5

Table 2. Dimensions of chi-square tables

Book

Probabilities

df values

Pages

Thorne & Giessen (2000)

2

30

0.5

Levin & Fox (2004)

2

30

1

Bartz (1999)

3

30

0.5

Ritchey (2000)

4

34

1

Siegel & Morgan (1996)

4

100

4

Gravetter & Wallnau (2004)

5

37

1

Lunneborg (1994)

5

44

2

Hogg & Craig (1995)

6

30

1

Agresti & Finlay (1997)

7

29

1

Freund (2004)

8

30

1

Freedman, Pisani, & Purves (1998)

9

20

1

Johnson & Wichern (1999)

9

37

1

Neter et al. (1996)

9

37

1

Rossman, Chance, & Lock (2001)

9

35

2

Rice (1995)

10

23

1

Triola (2001)

10

37

1

Dean & Voss (1999)

10

41

1

Sincich (1993)

10

42

2

Watkins, Scheaffer, & Cobb (2004)

11

35

1

Moore & McCabe (2006)

12

35

1

Spiegel & Liu (1999)

13

37

1

Milton & Arnold (2003)

13

30

2

Kirk (1995)

14

30

1

Frankfort-Nachmias & Leon-Guerrerro (2002)

14

30

1

Kendrick (2005)

14

30

2

Zwillinger & Kokoska (2000)

16

82

4

Walpole, Myers, Myers, & Ye (2002)

20

30

2

Minimum

2

20

0.5

Median

9

34

1

Maximum

20

100

4

Table 3. Dimensions of F tables

Book

Probabilities

df values

Pages

 

 

Numerator

Denominator

 

Levin & Fox (2004)

2

8

34

2

Ritchey (2000)

2

8

34

2

Thorne & Giessen (2000)

2

9

33

2

Kendrick (2005)

2

10

34

2

Frankfort-Nachmias & Leon-Guerrerro (2002)

2

11

34

2

Spiegel & Liu (1999)

2

16

40

2

Freund (2004)

2

19

30

2

Bartz (1999)

2

9

33

2.5

Gravetter & Wallnau (2004)

2

15

52

3

Walpole, Myers, Myers, & Ye (2002)

2

19

34

4

Lunneborg (1994)

2

19

34

4

Milton & Arnold (2003)

2

43

43

11

Hogg & Craig (1995)

3

12

12

2

Agresti & Finlay (1997)

3

11

34

3

Johnson & Wichern (1999)

3

17

34

6

Dean & Voss (1999)

3

19

30

6

Triola (2001)

3

19

35

6

Siegel & Morgan (1996)

4

8

24

4

Rice (1995)

4

19

34

4

Kirk (1995)

4

30

24

6

Sincich (1993)

4

19

34

8

Moore & McCabe (2006)

5

20

36

8

Zwillinger & Kokoska (2000)

6

13

25

6