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[waitarajo-blog]

Exploring Statistical Interactions

Table of TAB12MDX by USQUAN

TAB12MDX(Tobacco Dependence Past 12 Months)

USQUAN

Frequency   Percent   Row Pct   Col Pct

03

Total

0630  50.00  91.84  52.72

56  4.44  8.16  86.15

686  54.44      

1

565  44.84  98.43  47.28

9  0.71  1.57  13.85

574  45.56      

Total

1195  94.84

65  5.16

1260  100.00

  Statistics for Table of TAB12MDX by USQUAN

 Statistic

DF

Value

Prob

Chi-Square

1

27.7842

<.0001

Likelihood  Ratio Chi-Square

1

31.3968

<.0001

Continuity Adj. Chi-Square

1

26.4525

<.0001

Mantel-Haenszel Chi-Square

1

27.7621

<.0001

Phi Coefficient

 -0.1485

 Contingency  Coefficient

 0.1469

 Cramer's V

 -0.1485

   Fisher's Exact Test

Cell (1,1)  Frequency (F)

630

Left-sided  Pr <= F

<.0001

Right-sided  Pr >= F

1.0000

  Table  Probability (P)

<.0001

Two-sided Pr  <= P

<.0001

 Sample Size = 1260

Table of TAB12MDX by USQUAN

TAB12MDX(Tobacco Dependence Past 12 Months)

USQUAN

Frequency   Percent   Row Pct   Col Pct

03

Total

0110  24.66  88.71  25.70

14  3.14  11.29  77.78

124  27.80      

1

318  71.30  98.76  74.30

4  0.90  1.24  22.22

322  72.20      

Total

428  95.96

18  4.04

446  100.00

  Statistics for Table of TAB12MDX by USQUAN

 Statistic

DF

Value

Prob

Chi-Square

1

23.3380

<.0001

Likelihood  Ratio Chi-Square

1

20.3350

<.0001

Continuity Adj. Chi-Square

1

20.8157

<.0001

Mantel-Haenszel Chi-Square

1

23.2856

<.0001

Phi Coefficient

 -0.2288

 Contingency  Coefficient

 0.2230

 Cramer's V

 -0.2288

   Fisher's Exact Test

Cell (1,1)  Frequency (F)

110

Left-sided  Pr <= F

<.0001

Right-sided  Pr >= F

1.0000

  Table  Probability (P)

<.0001

Two-sided Pr  <= P

<.0001

 Sample Size = 446

2  Variables:

urbanrate       internetuserate

  Simple Statistics

Variable

N

Mean

Std Dev

Sum

Minimum

Maximum

Label

urbanrate

47

33.50553

12.83453

1575

10.40000

66.60000

urbanrate

internetuserate

45

8.22063

8.70764

369.92856

0.21007

40.12223

INTERNETUSERATE

  Pearson Correlation Coefficients   Prob > |r| under H0: Rho=0   Number of Observations

 urbanrate

internetuserate

urbanrate  urbanrate

1.00000    47

0.11558  0.4496  45

internetuserate  INTERNETUSERATE

0.11558  0.4496  45

1.00000    45

2  Variables:

urbanrate       internetuserate

  Simple Statistics

Variable

N

Mean

Std Dev

Sum

Minimum

Maximum

Label

urbanrate

94

56.58000

18.64588

5319

12.54000

93.32000

urbanrate

internetuserate

92

30.76527

19.76304

2830

1.28005

79.88978

INTERNETUSERATE

  Pearson Correlation Coefficients   Prob > |r| under H0: Rho=0   Number of Observations

 urbanrate

internetuserate

urbanrate  urbanrate

1.00000    94

0.32516  0.0017  91

internetuserate  INTERNETUSERATE

0.32516  0.0017  91

1.00000    92

2  Variables:

urbanrate       internetuserate

  Simple Statistics

Variable

N

Mean

Std Dev

Sum

Minimum

Maximum

Label

urbanrate

48

78.20417

19.82159

3754

13.22000

100.00000

urbanrate

internetuserate

46

70.58821

15.94746

3247

36.00033

95.63811

INTERNETUSERATE

  Pearson Correlation Coefficients   Prob > |r| under H0: Rho=0   Number of Observations

 urbanrate

internetuserate

urbanrate  urbanrate

1.00000    48

0.07514  0.6197  46

internetuserate  INTERNETUSERATE

0.07514  0.6197  46

1.00000    46

      Now, let's evaluate third variables as

potential moderators in the context of chi-squared test of independence. For this, we're gonna return to our

original SAS program using the NESARC data and asking the question, is smoking

associated with nicotine dependence? We're going to create another

smoking variable for this purpose, reflecting how many cigarettes each

young adult smoker smokes per day. 0 will indicate non-daily smokers. 3 indicates those smoking

1 to 5 cigarettes per day. 8 indicates 6 to 10 cigarettes per day. 13 indicates 11 to 15 cigarettes per day. 18 indicates 16 to 20 cigarettes per day,

and 37 indicates greater than

20 cigarettes per day.Categorical explanatory variable

USQUAN/discrete tells SAS that we want levels of our categorical explanatory

variable to be represented on the x-axis.

TAB12MDX to be displayed as a mean on the y-axis. And this gives us the graphic

representation of this positive linear relationship. As smoking quantity increases, so does the proportion of individuals

with nicotine dependence. This finding is accurate with regard

to the larger population of young adult smokers. Though might a third variable

moderate the relationship between smoking quantity and nicotine? Put another way,

might there be a statistical interaction between a third

variable in smoking behavior and predicting our response variable,

nicotine dependence? We're going to evaluate major depressive

disorder as the third variable. Our question will be, does Major

Depression affect either the strength or the direction of the relationship

between smoking and nicotine dependence? Put another way, might a third

variable moderate the relationship between smoking and nicotine dependence? Is smoking related to nicotine dependence

for each level of this third variable, that is, for those with major depression

and those without major depression? Similar to our anova example, syntax to be added to the PROC FREQ

code is circled here in red. We need to first sort the data, according

to the categorical third variable, then include a bistatement,

telling SAS to run a chi-square for each level of the third

variable separately. The specific syntax for this example is shown here, PROC SORT; BY MAJORDEPLIFE;

PROC FREQ; TABLES TAB12MDX*USQUAN/CHISQ; BY MAJORDEPLIFE;. When this syntax is added to the SAS

program, here are the results. You can see the cross tabs or

cross tabulation table, looking at usual quantity by tobacco

dependence in the past 12 months. First, for major depression equal to 0,

which is those without major depression, the chi-square value is large and

the P-value is quite small. In addition, the column percents

reveal what seems to be a positive linear relationship with percentages

of nicotine dependency increasing between lower levels of smoking and

higher levels of smoking. So we can say that this is a statistically

significant relationship for those without major depression. For those with major depression,

we find a large chi-square value and small P value,

which is statistically significant. These column percents also reveal what

seems to be a positive linear relationship with percentages of nicotine

dependence increasing between lower levels of smoking and

higher levels of smoking. Using a line graph to examine the rates of

nicotine dependence by different levels of smoking, it seems that

both the direction and size of the relationship is

similar between smoking and nicotine dependence for those with

major depression and for those without. Although, those with major depression show

higher rates of nicotine dependence at every level of smoking quantity. In this case, we would say a diagnosis

of major depression does not moderate the relationship between smoking and

nicotine dependence. For both young adult smokers with major

depression and those without, higher levels of smoking behavior is associated

with higher rates of nicotine dependence.

[waitarajo-blog]

3  Variables:

urbanrate       incomeperperson internetuserate

  Simple Statistics

Variable

N

Mean

Std Dev

Sum

Minimum

Maximum

Label

urbanrate

203

56.76936

23.84493

11524

10.40000

100.00000

urbanrate

incomeperperson

190

8741

14263

1660784

103.77586

105147

INCOMEPERPERSON

internetuserate

192

35.63272

27.78028

6841

0.21007

95.63811

INTERNETUSERATE

  Pearson Correlation Coefficients   Prob > |r| under H0: Rho=0   Number of Observations

 urbanrate

incomeperperson

internetuserate

urbanrate  urbanrate

1.00000    203

0.49009  <.0001  189

0.61395  <.0001  190

incomeperperson  INCOMEPERPERSON

0.49009  <.0001  189

1.00000    190

0.75094  <.0001  183

internetuserate  INTERNETUSERATE

0.61395  <.0001  190

0.75094  <.0001  183

1.00000    192

 We're going to be looking at two different correlations, that between Internet use and urban rate, and between Internet use and income per person. We can actually list these together.

To locate the correlation coefficients of interest and the associated p values, we need to examine the Pearson Correlation Coefficient table here, and find the row and column where our two variables of interest intersect.

For the association between urbanrate and internetuserate, the correlation coefficient is approximately 0.61 with a p-value of 0.0001. This tells us that the relationship is statistically significant.

For the association between incomeperperson and internetuserate, the correlation coefficient is approximately 0.75 and also has a significant p-value.Now we can actually interpret the scatter plots and the coefficients together.

The association between internetuserate and income is fairly strong and it's also positive, as the scatter plot had already shown us. The association between internetuserate and urbanrate is also positive but slightly more modest at 0.61. Both are statistically significant. That is, for both associations, it's highly unlikely that a relationship of this magnitude would be due to chance alone.

Here's some good news. Post hoc tests are not necessary when conducting Pearson correlation.Post hoc tests are needed only when your research question includes a categorical explanatory variable with more than two levels. Because our explanatory variable and the context of correlation coefficient is quantitative, there's never a need to perform a post hoc test.Another interesting and useful aspect of the correlation coefficient is if we square the correlation coefficient. That is, we multiply it by itself, we get a value that also helps our understanding of the association between the two quantitative variables.

Small r squared is the fraction of the variability of one variable that can be predicted by the other. For example, when looking at the relationship between urban rate and Internet use rate, if we square our correlation coefficient of 0.61, we get 0.37. This could be interpreted the following way. If we know the urban rate, we can predict 37% of the variability we will see in the rate of Internet use. Of course, that also means that 63% of the variability is unaccounted for.

If we square the correlation coefficient for income per person and Internet use rate we get a value of 0.56. This suggests, if we know income per person, we can predict 56% of the variability we'll see in the rate of Internet use.

This is a little bit more impressive, because we can predict over half the variability.

Again, correlation coefficients are commonly denoted with a lowercase r, and they're squared to determine the amount of variability that can be predicted. [MUSIC] You might be wondering how much variability in Internet use rates can be predicted if we consider both urban rate and income per person. A multivariate inferential tool called multiple regression can be used to answer this question and we'll discuss that in the future.

[waitarajo-blog]

Table of TAB12MDX by USFREQMO

TAB12MDX(Tobacco Dependence Past 12 Months)

USFREQMO

Frequency   Percent   Row Pct   Col Pct

1

2.5

5

14

22

30

Total

064  3.76  7.93  90.14

53  3.11  6.57  81.54

69  4.05  8.55  78.41

59  3.46  7.31  64.84

41  2.41  5.08  60.29

521  30.59  64.56  39.47

807  47.39      

1

7  0.41  0.78  9.86

12  0.70  1.34  18.46

19  1.12  2.12  21.59

32  1.88  3.57  35.16

27  1.59  3.01  39.71

799  46.92  89.17  60.53

896  52.61      

Total

71  4.17

65  3.82

88  5.17

91  5.34

68  3.99

1320  77.51

1703  100.00

Frequency Missing = 3

  Statistics for Table of TAB12MDX by USFREQMO

 Statistic

DF

Value

Prob

Chi-Square

5

165.2732

<.0001

Likelihood  Ratio Chi-Square

5

176.1834

<.0001

Mantel-Haenszel Chi-Square

1

162.8952

<.0001

Phi Coefficient

 0.3115

 Contingency  Coefficient

 0.2974

 Cramer's V

 0.3115

  Sample Size = 1703  Frequency Missing = 3

Table of TAB12MDX by USFREQMO

TAB12MDX(Tobacco Dependence Past 12 Months)

USFREQMO

Frequency   Percent   Row Pct   Col Pct

1

2.5

Total

064  47.06  54.70  90.14

53  38.97  45.30  81.54

117  86.03      

1

7  5.15  36.84  9.86

12  8.82  63.16  18.46

19  13.97      

Total

71  52.21

65  47.79

136  100.00

  Statistics for Table of TAB12MDX by USFREQMO

 Statistic

DF

Value

Prob

Chi-Square

1

2.0893

0.1483

Likelihood  Ratio Chi-Square

1

2.1023

0.1471

Continuity Adj. Chi-Square

1

1.4349

0.2310

Mantel-Haenszel Chi-Square

1

2.0740

0.1498

Phi Coefficient

 0.1239

 Contingency  Coefficient

 0.1230

 Cramer's V

 0.1239

   Fisher's Exact Test

Cell (1,1)  Frequency (F)

64

Left-sided  Pr <= F

0.9553

Right-sided  Pr >= F

0.1154

  Table  Probability (P)

0.0707

Two-sided Pr  <= P

0.2153

 Sample Size = 136

Table of TAB12MDX by USFREQMO

TAB12MDX(Tobacco Dependence Past 12 Months)

USFREQMO

Frequency   Percent   Row Pct   Col Pct

1

Total

064  90.14  100.00  90.14

64  90.14      

1

7  9.86  100.00  9.86

7  9.86      

Total

71  100.00

71  100.00

Table of TAB12MDX by USFREQMO

TAB12MDX(Tobacco Dependence Past 12 Months)

USFREQMO

Frequency   Percent   Row Pct   Col Pct

1

14

Total

064  39.51  52.03  90.14

59  36.42  47.97  64.84

123  75.93      

1

7  4.32  17.95  9.86

32  19.75  82.05  35.16

39  24.07      

Total

71  43.83

91  56.17

162  100.00

  Statistics for Table of TAB12MDX by USFREQMO

 Statistic

DF

Value

Prob

Chi-Square

1

13.9727

0.0002

Likelihood  Ratio Chi-Square

1

15.0854

0.0001

Continuity Adj. Chi-Square

1

12.6226

0.0004

Mantel-Haenszel Chi-Square

1

13.8865

0.0002

Phi Coefficient

 0.2937

 Contingency  Coefficient

 0.2818

 Cramer's V

 0.2937

   Fisher's Exact Test

Cell (1,1)  Frequency (F)

64

Left-sided  Pr <= F

1.0000

Right-sided  Pr >= F

0.0001

  Table  Probability (P)

<.0001

Two-sided Pr  <= P

0.0002

 Sample Size = 162

Table of TAB12MDX by USFREQMO

TAB12MDX(Tobacco Dependence Past 12 Months)

USFREQMO

Frequency   Percent   Row Pct   Col Pct

1

22

Total

064  46.04  60.95  90.14

41  29.50  39.05  60.29

105  75.54      

1

7  5.04  20.59  9.86

27  19.42  79.41  39.71

34  24.46      

Total

71  51.08

68  48.92

139  100.00

  Statistics for Table of TAB12MDX by USFREQMO

 Statistic

DF

Value

Prob

Chi-Square

1

16.7459

<.0001

Likelihood  Ratio Chi-Square

1

17.5739

<.0001

Continuity Adj. Chi-Square

1

15.1695

<.0001

Mantel-Haenszel Chi-Square

1

16.6254

<.0001

Phi Coefficient

 0.3471

 Contingency  Coefficient

 0.3279

 Cramer's V

 0.3471

   Fisher's Exact Test

Cell (1,1)  Frequency (F)

64

Left-sided  Pr <= F

1.0000

Right-sided  Pr >= F

<.0001

  Table  Probability (P)

<.0001

Two-sided Pr  <= P

<.0001

 Sample Size = 139

Table of TAB12MDX by USFREQMO

TAB12MDX(Tobacco Dependence Past 12 Months)

USFREQMO

Frequency   Percent   Row Pct   Col Pct

1

30

Total

064  4.60  10.94  90.14

521  37.46  89.06  39.47

585  42.06      

1

7  0.50  0.87  9.86

799  57.44  99.13  60.53

806  57.94      

Total

71  5.10

1320  94.90

1391  100.00

  Statistics for Table of TAB12MDX by USFREQMO

 Statistic

DF

Value

Prob

Chi-Square

1

70.9888

<.0001

Likelihood  Ratio Chi-Square

1

76.4339

<.0001

Continuity Adj. Chi-Square

1

68.9247

<.0001

Mantel-Haenszel Chi-Square

1

70.9378

<.0001

Phi Coefficient

 0.2259

 Contingency  Coefficient

 0.2204

 Cramer's V

 0.2259

   Fisher's Exact Test

Cell (1,1)  Frequency (F)

64

Left-sided  Pr <= F

1.0000

Right-sided  Pr >= F

<.0001

  Table  Probability (P)

<.0001

Two-sided Pr  <= P

<.0001

 Sample Size = 1391

Table of TAB12MDX by USFREQMO

TAB12MDX(Tobacco Dependence Past 12 Months)

USFREQMO

Frequency   Percent   Row Pct   Col Pct

2.5

Total

053  81.54  100.00  81.54

53  81.54      

1

12  18.46  100.00  18.46

12  18.46      

Total

65  100.00

65  100.00

Table of TAB12MDX by USFREQMO

TAB12MDX(Tobacco Dependence Past 12 Months)

USFREQMO

Frequency   Percent   Row Pct   Col Pct

2.5

14

Total

053  33.97  47.32  81.54

59  37.82  52.68  64.84

112  71.79      

1

12  7.69  27.27  18.46

32  20.51  72.73  35.16

44  28.21      

Total

65  41.67

91  58.33

156  100.00

  Statistics for Table of TAB12MDX by USFREQMO

 Statistic

DF

Value

Prob

Chi-Square

1

5.2241

0.0223

Likelihood  Ratio Chi-Square

1

5.4011

0.0201

Continuity Adj. Chi-Square

1

4.4318

0.0353

Mantel-Haenszel Chi-Square

1

5.1906

0.0227

Phi Coefficient

 0.1830

 Contingency  Coefficient

 0.1800

 Cramer's V

 0.1830

   Fisher's Exact Test

Cell (1,1)  Frequency (F)

53

Left-sided  Pr <= F

0.9939

Right-sided  Pr >= F

0.0166

  Table  Probability (P)

0.0105

Two-sided Pr  <= P

0.0299

 Sample Size = 156

Table of TAB12MDX by USFREQMO

TAB12MDX(Tobacco Dependence Past 12 Months)

USFREQMO

Frequency   Percent   Row Pct   Col Pct

2.5

22

Total

053  39.85  56.38  81.54

41  30.83  43.62  60.29

94  70.68      

1

12  9.02  30.77  18.46

27  20.30  69.23  39.71

39  29.32      

Total

65  48.87

68  51.13

133  100.00

  Statistics for Table of TAB12MDX by USFREQMO

 Statistic

DF

Value

Prob

Chi-Square

1

7.2372

0.0071

Likelihood  Ratio Chi-Square

1

7.3891

0.0066

Continuity Adj. Chi-Square

1

6.2484

0.0124

Mantel-Haenszel Chi-Square

1

7.1827

0.0074

Phi Coefficient

 0.2333

 Contingency  Coefficient

 0.2272

 Cramer's V

 0.2333

   Fisher's Exact Test

Cell (1,1)  Frequency (F)

53

Left-sided  Pr <= F

0.9982

Right-sided  Pr >= F

0.0059

  Table  Probability (P)

0.0041

Two-sided Pr  <= P

0.0080

 Sample Size = 133

Table of TAB12MDX by USFREQMO

TAB12MDX(Tobacco Dependence Past 12 Months)

USFREQMO

Frequency   Percent   Row Pct   Col Pct

2.5

30

Total

053  3.83  9.23  81.54

521  37.62  90.77  39.47

574  41.44      

1

12  0.87  1.48  18.46

799  57.69  98.52  60.53

811  58.56      

Total

65  4.69

1320  95.31

1385  100.00

  Statistics for Table of TAB12MDX by USFREQMO

 Statistic

DF

Value

Prob

Chi-Square

1

45.1777

<.0001

Likelihood  Ratio Chi-Square

1

46.1611

<.0001

Continuity Adj. Chi-Square

1

43.4608

<.0001

Mantel-Haenszel Chi-Square

1

45.1451

<.0001

Phi Coefficient

 0.1806

 Contingency  Coefficient

 0.1777

 Cramer's V

 0.1806

   Fisher's Exact Test

Cell (1,1)  Frequency (F)

53

Left-sided  Pr <= F

1.0000

Right-sided  Pr >= F

<.0001

  Table  Probability (P)

<.0001

Two-sided Pr  <= P

<.0001

 Sample Size = 1385

Table of TAB12MDX by USFREQMO

TAB12MDX(Tobacco Dependence Past 12 Months)

USFREQMO

Frequency   Percent   Row Pct   Col Pct

14

Total

059  64.84  100.00  64.84

59  64.84      

1

32  35.16  100.00  35.16

32  35.16      

Total

91  100.00

91  100.00

Table of TAB12MDX by USFREQMO

TAB12MDX(Tobacco Dependence Past 12 Months)

USFREQMO

Frequency   Percent   Row Pct   Col Pct

22

Total

041  60.29  100.00  60.29

41  60.29      

1

27  39.71  100.00  39.71

27  39.71      

Total

68  100.00

68  100.00

Table of TAB12MDX by USFREQMO

TAB12MDX(Tobacco Dependence Past 12 Months)

USFREQMO

Frequency   Percent   Row Pct   Col Pct

30

Total

0521  39.47  100.00  39.47

521  39.47      

1

799  60.53  100.00  60.53

799  60.53      

Total

1320  100.00

1320  100.00

Table of TAB12MDX by USFREQMO

TAB12MDX(Tobacco Dependence Past 12 Months)

USFREQMO

Frequency   Percent   Row Pct   Col Pct

14

22

Total

059  37.11  59.00  64.84

41  25.79  41.00  60.29

100  62.89      

1

32  20.13  54.24  35.16

27  16.98  45.76  39.71

59  37.11      

Total

91  57.23

68  42.77

159  100.00

  Statistics for Table of TAB12MDX by USFREQMO

 Statistic

DF

Value

Prob

Chi-Square

1

0.3439

0.5576

Likelihood  Ratio Chi-Square

1

0.3432

0.5580

Continuity Adj. Chi-Square

1

0.1768

0.6741

Mantel-Haenszel Chi-Square

1

0.3417

0.5588

Phi Coefficient

 0.0465

 Contingency  Coefficient

 0.0465

 Cramer's V

 0.0465

   Fisher's Exact Test

Cell (1,1)  Frequency (F)

59

Left-sided  Pr <= F

0.7743

Right-sided  Pr >= F

0.3365

  Table  Probability (P)

0.1108

Two-sided Pr  <= P

0.6198

 Sample Size = 159

Table of TAB12MDX by USFREQMO

TAB12MDX(Tobacco Dependence Past 12 Months)

USFREQMO

Frequency   Percent   Row Pct   Col Pct

14

30

Total

059  4.18  10.17  64.84

521  36.92  89.83  39.47

580  41.11      

1

32  2.27  3.85  35.16

799  56.63  96.15  60.53

831  58.89      

Total

91  6.45

1320  93.55

1411  100.00

  Statistics for Table of TAB12MDX by USFREQMO

 Statistic

DF

Value

Prob

Chi-Square

1

22.6255

<.0001

Likelihood  Ratio Chi-Square

1

22.2336

<.0001

Continuity Adj. Chi-Square

1

21.5899

<.0001

Mantel-Haenszel Chi-Square

1

22.6095

<.0001

Phi Coefficient

 0.1266

 Contingency  Coefficient

 0.1256

 Cramer's V

 0.1266

   Fisher's Exact Test

Cell (1,1)  Frequency (F)

59

Left-sided  Pr <= F

1.0000

Right-sided  Pr >= F

<.0001

  Table  Probability (P)

<.0001

Two-sided Pr  <= P

<.0001

 Sample Size = 1411

Table of TAB12MDX by USFREQMO

TAB12MDX(Tobacco Dependence Past 12 Months)

USFREQMO

Frequency   Percent   Row Pct   Col Pct

22

30

Total

041  2.95  7.30  60.29

521  37.54  92.70  39.47

562  40.49      

1

27  1.95  3.27  39.71

799  57.56  96.73  60.53

826  59.51      

Total

68  4.90

1320  95.10

1388  100.00

  Statistics for Table of TAB12MDX by USFREQMO

 Statistic

DF

Value

Prob

Chi-Square

1

11.6386

0.0006

Likelihood  Ratio Chi-Square

1

11.3718

0.0007

Continuity Adj. Chi-Square

1

10.7904

0.0010

Mantel-Haenszel Chi-Square

1

11.6302

0.0006

Phi Coefficient

 0.0916

 Contingency  Coefficient

 0.0912

 Cramer's V

 0.0916

   Fisher's Exact Test

Cell (1,1)  Frequency (F)

41

Left-sided  Pr <= F

0.9998

Right-sided  Pr >= F

0.0006

  Table  Probability (P)

0.0003

Two-sided Pr  <= P

0.0009

 Sample Size = 1388

  To determine which groups are different from the others, we will again, need to perform a post hoc test. By conducting post hoc comparisons between pairs of rates, in a way that avoids excessive type one error. In other words, avoids rejecting the null hypothesis, when the null hypothesis is true. We will be much better able to appropriately describe which population rates are different from the others.

If we reject the null hypothesis, we need to perform comparisons for each pair of nicotine dependent's rates across the six smoking frequency categories. In the case of 6 groups, we actually need to perform 15 pairwise comparisons.

The goal of using the Bonferroni Adjustment is to control a family-wise error rates, also known as the maximum overall type 1 error rate. So, that we can evaluate which pairs of nicotine dependents rate are different from one another.Briefly, the process would be to conduct each of the 15 paired comparisons. But rather than evaluating significance at the p .05 level, we would adjust the p value to make it more difficult to reject the null hypothesis. The adjusted p value is calculated by dividing p .05 by the number of comparisons that we plan to make. So, if we make 3 comparisons, we would only reject null hypothesis if the p value were .017 or less. For the 15 paired comparisons that we plan to make to better understand the association between smoking frequency and nicotine dependence, our adjusted p value is .003. Adjusting the p value is definitely the easy part of the process. Now, for the more challenging piece. For the actual post hoc testing, we need to run a Chi-Square test for each of the 15 paired comparisons. To do this, I can add syntax to my program at the end of the data step just before the PROC SORT statement. Where I choose two smoking frequency groups at a time. So, I'm going to start by comparing my usual smoking frequency per month group 1, and my usual smoking frequency per month group 2.5. If I save and run this program, I get a new Chi-Square table that includes only those two frequency groups by the presence or absence of nicotine dependence.

Again, I wanna focus here on the column percentages. 9.86 and 18.46, are these two rates significantly different from one another? If I look down at my Chi-Square value and probability, I can see that they aren't.

So, I want to accept the null hypothesis, since this probability value is not only not less than 0.05. It is definitely not less than my Bonferroni Adjusted p value of .003. This is just the first step at our post hoc analysis. Now, we need to run two by two Chi-Squares for each of the remaining 14 paired comparisons.To do this, we could continue one comparison at a time, choosing two frequency groups. By adding syntax to the program, at the end of the data step, and just before the PROC SORT statement. Use the syntax requesting a Chi-Square analysis, comparing those smoking one day per month and those smoking six days per month.

For our code, we can see that only smoking frequency groups equal to 1 and equal to 6 are included in the Chi-Square table and analysis.

The nicotine dependence rates are 9.86 and 21.59. The p value associated with the Chi-Square statistic is .0468. Initially, we might wanna say that this is a significant finding because it's less than a p value of .05. Remember though, that the adjusted p value for these comparison is .003. So, this is not significant.

Going back to the graph of nicotine dependence rates, we now know that frequency group equal to 1 and equal to 6, do not have significantly different rates of nicotine dependence.

This can get pretty tedious and of course, it would be very easy to get a big confused and to skip one or more paired comparisons. Let's look at how to use syntax that you already know to this systematically. And to get results for all of the paired comparisons simultaneously.

First, we'll get rid of the lines of syntax that subsets our data to specific smoking frequency groups. Now, we'll create a series of new data sets in associated Chi-Square tables that call in the original working data set. And select each of the various combination of smoking frequency groups. We've just added quite a bit of syntax to this program.

You'll see however, that it's repetitive, and that in each group of syntax, only the logic statements that select the specific frequency groups and the working data set name need to change.

 Following the data step and the request for output that we've been working with. We're going to add a new data step, and call it COMPARISON1.

We set the original working data set, which was called NEW, above. And then subset the data to the two smoking frequency categories. Smoking frequency category 1, and 2.5. We end this data step by sorting by the unique identifier, and requesting a Chi-Square analysis with a PROC FREQ procedure. Then we end this new syntax group with a RUN statement.

Next, we repeat those same lines of syntax for each of the remaining 14 paired comparisons. Changing only the name of the new working data set, and the selected smoking frequency groups.

Here, we call the DATA COMPARISON2, and select smoking frequency group 1, compared to smoking frequency group 6. Here, the data is COMPARISON3. And we're comparing smoking frequency group 1 to smoking group 14. COMPARISON4 is comparing smoking frequency group 1, and smoking frequency group 22. We see these lines of syntax repeated with new data names, and the additional paired comparisons for the smoking frequency groups. All the way down to COMPARISON15, smoking frequency group 22 versus smoking frequency group 30. Well, we run this program, the results include the overall Chi-Squared table. That is, the sixth level smoking frequency variable by the nicotine dependence response variable. And then Chi-Square tables for each of the paired comparisons. 1 versus 2.5, 1 versus 6, 1 versus 14, 1 versus 22, 1 versus 30, 2.5 versus 6, and so on.

The goal is to examine the p value for each of the paired comparisons. And to use the adjusted Bonferroni p value of .003 to evaluate significance. Here, we've created a table that shows the p values of each of the paired comparisons from the output. Obviously, there are several that are less that p is .05. Here are the p values that are less than .003. As we can see, smoking frequency group 30 that is, those who smoke 30 days in a usual month, is significantly different from each of the other smoke frequency levels. In addition, smoking frequency group 1 has significantly different nicotine dependence rates, than smoke frequency groups 14, and 22.

[waitarajo-blog]

Class Level Information

Class

Levels

Values

MAJORDEPLIFE

2

0 1

 Number of Observations Read

1706

Number of  Observations Used

1697

Source

DF

Sum of Squares

Mean Square

F Value

Pr > F

Model

1

266974.1

266974.1

3.55

0.0597

Error

1695

127468189.9

75202.5

 Corrected Total

1696

127735164.0

  R-Square

Coeff Var

Root MSE

NUMCIGMO_EST Mean

0.002090

85.61566

274.2307

320.3044

 Source

DF

Anova SS

Mean Square

F Value

Pr > F

MAJORDEPLIFE

1

266974.1235

266974.1235

3.55

0.0597

  Level of   MAJORDEPLIFE

N

NUMCIGMO_EST

Mean

Std Dev

01253

312.837989

269.002344

1

444

341.375000

288.495118

Class Level Information

Class

Levels

Values

ETHRACE2A

5

1 2 3 4 5

 Number of Observations Read

1706

Number of  Observations Used

1697

Source

DF

Sum of Squares

Mean Square

F Value

Pr > F

Model

4

6965167.9

1741292.0

24.40

<.0001

Error

1692

120769996.1

71377.1

 Corrected Total

1696

127735164.0

  R-Square

Coeff Var

Root MSE

NUMCIGMO_EST Mean

0.054528

83.40969

267.1649

320.3044

 Source

DF

Anova SS

Mean Square

F Value

Pr > F

ETHRACE2A

4

6965167.919

1741291.980

24.40

<.0001

 Note:

This test controls the Type I comparisonwise  error rate, not the experimentwise error rate.

 Alpha

0.05

Error  Degrees of Freedom

1692

Error Mean  Square

71377.07

Harmonic Mean of Cell Sizes

100.4731

Note:

Cell sizes are not equal.

 Number of Means

2

3

4

5

Critical  Range

73.93

77.84

80.46

82.39

 Class Level Information

Class

Levels

Values

MAJORDEPLIFE

2

0 1

 Number of Observations Read

1706

Number of  Observations Used

1697

Source

DF

Sum of Squares

Mean Square

F Value

Pr > F

Model

1

266974.1

266974.1

3.55

0.0597

Error

1695

127468189.9

75202.5

 Corrected Total

1696

127735164.0

  R-Square

Coeff Var

Root MSE

NUMCIGMO_EST Mean

0.002090

85.61566

274.2307

320.3044

 Source

DF

Anova SS

Mean Square

F Value

Pr > F

MAJORDEPLIFE

1

266974.1235

266974.1235

3.55

0.0597

  Level of   MAJORDEPLIFE

N

NUMCIGMO_EST

Mean

Std Dev

01253

312.837989

269.002344

1

444

341.375000

288.495118

 3:39: >> Proc ANOVA first displays a table that includes the following. The name of the variable in the class statement. The number of different values or levels of the class variable. The value of the class variable. And the number of observations in the data set and the number of observations excluded from the analysis because of missing data,

3:39: So here we see our categorical explanatory variable, MAJORDEPLIFE, as two levels.

3:47: And the values are 0 and 1. Of the 1706 observations, 1697 were included in the analysis.

Proc ANOVA then displays an analysis of variance table for the response variable, also known as the dependent variable from the MODEL statement. >> In this case, our response or dependent variable was NUMCIGMO_EST.

3.54: Our calculated F statistic, called the F Value in this output, is. The significance, probability, or P value associated with this F statistic, is labeled Pr > F. And as you can see, the P value is .0601, just over our P value .05 cut point. If we look at the means table, we see that young adult smokers without major depression, as indicated by a value of 0, smoke an average of 312 cigarettes per month. And that those with major depression, indicated by a value of one, smoke on average 341.5 cigarettes per month. Because the P value is greater than 0.05, actually 0.06, we must accept the null hypothesis and say that these means are statistically equal. And that there’s no association between the presence or absence of major depression in the number of cigarettes smoked per month among young adult smokers. >> If I chose to reject the null hypothesis, I would be wrong six out of 100 times. And again, by normal scientific standards, this is not adequate certainty to reject the null hypothesis and say that there is an association.

Play video starting at.

5:37: Instead, we’re going to accept the null hypothesis and say that there is no association. Had the P value been less than .05, I would know that there was a significant association and to interpret that as significant. I would look at the means table, if P would’ve been less than .05, I can see that individuals with major depression smoke more than individuals without. And again, with a significant P value, I could have said that young adult smokers with major depression smoke significantly more cigarettes per month than young adult smokers without major depression. >> So, we’ve shown you the ropes in terms of a categorical explanatory variable that has two levels, as it did here with depression. For this interpretation, all we need to know is the P value and the means for each of the two groups.