Coursera: Data analysis Tools
Week 2 assignment: Chi Square analysis
1.- Analysis Question:
Does money
really bring happiness? At least what I am willing to discover is whether
individuals from a richer or poorer household are more or less likely to suffer
from depression sympthoms.
For that
matter, we are going to take into account two variable.
·
A
numerical explanatory variable; “Household income per year”, which I have
turned into a categorical one by making Average Household Income Groups (From
now on, HHIG)
·
A
categorical response variable, S4AQ1, which tells us if the individual has had
a period of +2weeks of sadness, being:
o
1:
The individual HAS suffered from these sympthoms
o
2:
The individual HAS NOT suffered from these sypmthoms
2.- Code Used:
LIBNAME mydata "/courses/d1406ae5ba27fe300
" access=readonly;
DATA new; set mydata.nesarc_pds;
/*Names for the variables*/
LABEL S1Q12B="Average household income
group"
S4CQ1="Had a +2weeks low mood
period";
/*Set appropriate missing data as
needed*/
IF S4CQ1=9 THEN S4CQ1=.;
/*Creating the average household
income groups*/
IF S1Q12B=1 OR S1Q12B=2 OR S1Q12B=3 OR S1Q12B=4
OR S1Q12B=5 OR S1Q12B=6 OR S1Q12B=7 OR S1Q12B=8 THEN HHIG=1;
ELSE IF S1Q12B=9 OR S1Q12B=10 OR S1Q12B=11 OR
S1Q12B=12 OR S1Q12B=13 THEN HHIG=2;
ELSE IF S1Q12B=14 OR S1Q12B=15 OR S1Q12B=16
THEN HHIG=3;
ELSE IF S1Q12B=17 OR S1Q12B=18 OR S1Q12B=19 OR
S1Q12B=20 OR S1Q12B=21 THEN HHIG=4;
/* HHIG is the average household
income group
1.- 0 to 29.999$ - Low/ Mid-Low
2.- 30.000 to 69.999$ - Medium
3.- 70.000 to 99.999$ - High
4.- 100.000$ and more - Very High
*/
/*Starting the Chi Square
anlysis*/
PROC FREQ; TABLES S4CQ1*HHIG/CHISQ;
RUN;
3.- Results and interpretation:
Procedimiento FREQ
|
Frecuencia
Porcentaje
Pct fila
Pct col
|
|
|
Tabla de S4CQ1 por HHIG
|
|
S4CQ1(Had a
+2weeks low mood period)
|
HHIG
|
|
1
|
2
|
3
|
4
|
Total
|
|
1
|
1237
2.96
52.89
7.00
|
780
1.86
33.35
4.90
|
186
0.44
7.95
4.20
|
136
0.32
5.81
3.54
|
2339
5.59
|
|
2
|
16433
39.27
41.59
93.00
|
15132
36.16
38.30
95.10
|
4239
10.13
10.73
95.80
|
3706
8.86
9.38
96.46
|
39510
94.41
|
|
Total
|
17670
42.22
|
15912
38.02
|
4425
10.57
|
3842
9.18
|
41849
100.00
|
|
Frecuencia de ausentes = 1244
|
|
Estadísticos para la tabla de S4CQ1 por HHIG
|
Estadístico
|
DF
|
Valor
|
Prob
|
|
Chi-cuadrado
|
3
|
127.6301
|
<.0001
|
|
Chi-cuadrado de
ratio de verosimilitud
|
3
|
129.3039
|
<.0001
|
|
Chi-cuadrado
Mantel-Haenszel
|
1
|
113.1129
|
<.0001
|
|
Coeficiente Phi
|
|
0.0552
|
|
|
Coeficiente de
contingencia
|
|
0.0551
|
|
|
V de Cramer
|
|
0.0552
|
|
Tamaño efectivo de la muestra = 41849
Frecuencia de valores ausentes = 124
Interpretation: The P value of less
than 0.001 tells us that the differencces are statistically relevant, thus the conclusion
being that, the higher the income of a household, the less likely to suffer
from depression its dwellers are.
3.- Post HOC analyses:
We know
that there are representative differences between groups, but we still need to
learn which groups are really different.
As we have
6 possible impairments, the BONFERRONI ADJUSTMENT gives us an “Adjusted p value”
of 0,00833 to use as a
benchmark to compare against the p values for each individual comparison.
4.- Post HOC analyses code:
DATA
COMPARISON1; SET NEW;
IF HHIG=1
OR HHIG=2;
PROC SORT;
BY IDNUM;
PROC FREQ;
TABLES S4CQ1*HHIG/CHISQ;
RUN;
DATA
COMPARISON1; SET NEW;
IF HHIG=1
OR HHIG=3;
PROC SORT;
BY IDNUM;
PROC FREQ;
TABLES S4CQ1*HHIG/CHISQ;
RUN;
DATA
COMPARISON1; SET NEW;
IF HHIG=1
OR HHIG=4;
PROC SORT;
BY IDNUM;
PROC FREQ;
TABLES S4CQ1*HHIG/CHISQ;
RUN;
DATA
COMPARISON1; SET NEW;
IF HHIG=2
OR HHIG=3;
PROC SORT;
BY IDNUM;
PROC FREQ;
TABLES S4CQ1*HHIG/CHISQ;
RUN;
DATA
COMPARISON1; SET NEW;
IF HHIG=2
OR HHIG=4;
PROC SORT;
BY IDNUM;
PROC FREQ;
TABLES S4CQ1*HHIG/CHISQ;
RUN;
DATA
COMPARISON1; SET NEW;
IF HHIG=3
OR HHIG=4;
PROC SORT;
BY IDNUM;
PROC FREQ;
TABLES S4CQ1*HHIG/CHISQ;
RUN;
5.- Post HOC analyses results and
interpretation
Procedimiento FREQ
|
Frecuencia
Porcentaje
Pct fila
Pct col
|
|
|
Tabla de S4CQ1 por HHIG
|
|
S4CQ1(Had a
+2weeks low mood period)
|
HHIG
|
|
1
|
2
|
Total
|
|
1
|
1237
3.68
61.33
7.00
|
780
2.32
38.67
4.90
|
2017
6.01
|
|
2
|
16433
48.93
52.06
93.00
|
15132
45.06
47.94
95.10
|
31565
93.99
|
|
Total
|
17670
52.62
|
15912
47.38
|
33582
100.00
|
|
Frecuencia de ausentes = 1052
|
|
Estadísticos para la tabla de S4CQ1 por HHIG
|
Estadístico
|
DF
|
Valor
|
Prob
|
|
Chi-cuadrado
|
1
|
65.3157
|
<.0001
|
|
Chi-cuadrado de
ratio de verosimilitud
|
1
|
66.0145
|
<.0001
|
|
Chi-cuadrado adj. de
continuidad
|
1
|
64.9445
|
<.0001
|
|
Chi-cuadrado
Mantel-Haenszel
|
1
|
65.3138
|
<.0001
|
|
Coeficiente Phi
|
|
0.0441
|
|
|
Coeficiente de
contingencia
|
|
0.0441
|
|
|
V de Cramer
|
|
0.0441
|
|
|
Test exacto de Fisher
|
|
Celda (1,1)
Frecuencia (F)
|
1237
|
|
Alineado a la
izquierda Pr <= F
|
1.0000
|
|
Alineado a la
derecha Pr >= F
|
<.0001
|
|
|
|
|
Tabla de
probabilidad (P)
|
<.0001
|
|
De dos caras Pr
<= P
|
<.0001
|
Tamaño efectivo de la muestra = 33582
Frecuencia de valores ausentes = 1052
Procedimiento FREQ
|
Frecuencia
Porcentaje
Pct fila
Pct col
|
|
|
Tabla de S4CQ1 por HHIG
|
|
S4CQ1(Had a
+2weeks low mood period)
|
HHIG
|
|
1
|
3
|
Total
|
|
1
|
1237
5.60
86.93
7.00
|
186
0.84
13.07
4.20
|
1423
6.44
|
|
2
|
16433
74.37
79.49
93.00
|
4239
19.19
20.51
95.80
|
20672
93.56
|
|
Total
|
17670
79.97
|
4425
20.03
|
22095
100.00
|
|
Frecuencia de ausentes = 721
|
|
Estadísticos para la tabla de S4CQ1 por HHIG
|
Estadístico
|
DF
|
Valor
|
Prob
|
|
Chi-cuadrado
|
1
|
45.9511
|
<.0001
|
|
Chi-cuadrado de
ratio de verosimilitud
|
1
|
50.5550
|
<.0001
|
|
Chi-cuadrado adj. de
continuidad
|
1
|
45.4881
|
<.0001
|
|
Chi-cuadrado
Mantel-Haenszel
|
1
|
45.9490
|
<.0001
|
|
Coeficiente Phi
|
|
0.0456
|
|
|
Coeficiente de
contingencia
|
|
0.0456
|
|
|
V de Cramer
|
|
0.0456
|
|
|
Test exacto de Fisher
|
|
Celda (1,1)
Frecuencia (F)
|
1237
|
|
Alineado a la
izquierda Pr <= F
|
1.0000
|
|
Alineado a la
derecha Pr >= F
|
<.0001
|
|
|
|
|
Tabla de
probabilidad (P)
|
<.0001
|
|
De dos caras Pr
<= P
|
<.0001
|
Tamaño efectivo de la muestra = 22095
Frecuencia de valores ausentes = 721
Procedimiento FREQ
|
Frecuencia
Porcentaje
Pct fila
Pct col
|
|
|
Tabla de S4CQ1 por HHIG
|
|
S4CQ1(Had a
+2weeks low mood period)
|
HHIG
|
|
1
|
4
|
Total
|
|
1
|
1237
5.75
90.09
7.00
|
136
0.63
9.91
3.54
|
1373
6.38
|
|
2
|
16433
76.39
81.60
93.00
|
3706
17.23
18.40
96.46
|
20139
93.62
|
|
Total
|
17670
82.14
|
3842
17.86
|
21512
100.00
|
|
Frecuencia de ausentes = 713
|
|
Estadísticos para la tabla de S4CQ1 por HHIG
|
Estadístico
|
DF
|
Valor
|
Prob
|
|
Chi-cuadrado
|
1
|
63.2565
|
<.0001
|
|
Chi-cuadrado de
ratio de verosimilitud
|
1
|
72.3478
|
<.0001
|
|
Chi-cuadrado adj. de
continuidad
|
1
|
62.6786
|
<.0001
|
|
Chi-cuadrado
Mantel-Haenszel
|
1
|
63.2535
|
<.0001
|
|
Coeficiente Phi
|
|
0.0542
|
|
|
Coeficiente de
contingencia
|
|
0.0541
|
|
|
V de Cramer
|
|
0.0542
|
|
|
Test exacto de Fisher
|
|
Celda (1,1)
Frecuencia (F)
|
1237
|
|
Alineado a la
izquierda Pr <= F
|
1.0000
|
|
Alineado a la
derecha Pr >= F
|
<.0001
|
|
|
|
|
Tabla de
probabilidad (P)
|
<.0001
|
|
De dos caras Pr
<= P
|
<.0001
|
Tamaño efectivo de la muestra = 21512
Frecuencia de valores ausentes = 713
Procedimiento FREQ
|
Frecuencia
Porcentaje
Pct fila
Pct col
|
|
|
Tabla de S4CQ1 por HHIG
|
|
S4CQ1(Had a
+2weeks low mood period)
|
HHIG
|
|
2
|
3
|
Total
|
|
1
|
780
3.84
80.75
4.90
|
186
0.91
19.25
4.20
|
966
4.75
|
|
2
|
15132
74.41
78.12
95.10
|
4239
20.84
21.88
95.80
|
19371
95.25
|
|
Total
|
15912
78.24
|
4425
21.76
|
20337
100.00
|
|
Frecuencia de ausentes = 531
|
|
Estadísticos para la tabla de S4CQ1 por HHIG
|
Estadístico
|
DF
|
Valor
|
Prob
|
|
Chi-cuadrado
|
1
|
3.7344
|
0.0533
|
|
Chi-cuadrado de
ratio de verosimilitud
|
1
|
3.8393
|
0.0501
|
|
Chi-cuadrado adj. de
continuidad
|
1
|
3.5816
|
0.0584
|
|
Chi-cuadrado
Mantel-Haenszel
|
1
|
3.7342
|
0.0533
|
|
Coeficiente Phi
|
|
0.0136
|
|
|
Coeficiente de
contingencia
|
|
0.0135
|
|
|
V de Cramer
|
|
0.0136
|
|
|
Test exacto de Fisher
|
|
Celda (1,1)
Frecuencia (F)
|
780
|
|
Alineado a la
izquierda Pr <= F
|
0.9769
|
|
Alineado a la
derecha Pr >= F
|
0.0280
|
|
|
|
|
Tabla de
probabilidad (P)
|
0.0049
|
|
De dos caras Pr <=
P
|
0.0551
|
Tamaño efectivo de la muestra = 20337
Frecuencia de valores ausentes = 531
Procedimiento FREQ
|
Frecuencia
Porcentaje
Pct fila
Pct col
|
|
|
Tabla de S4CQ1 por HHIG
|
|
S4CQ1(Had a
+2weeks low mood period)
|
HHIG
|
|
2
|
4
|
Total
|
|
1
|
780
3.95
85.15
4.90
|
136
0.69
14.85
3.54
|
916
4.64
|
|
2
|
15132
76.60
80.33
95.10
|
3706
18.76
19.67
96.46
|
18838
95.36
|
|
Total
|
15912
80.55
|
3842
19.45
|
19754
100.00
|
|
Frecuencia de ausentes = 523
|
|
Estadísticos para la tabla de S4CQ1 por HHIG
|
Estadístico
|
DF
|
Valor
|
Prob
|
|
Chi-cuadrado
|
1
|
12.9852
|
0.0003
|
|
Chi-cuadrado de
ratio de verosimilitud
|
1
|
13.8344
|
0.0002
|
|
Chi-cuadrado adj. de
continuidad
|
1
|
12.6790
|
0.0004
|
|
Chi-cuadrado
Mantel-Haenszel
|
1
|
12.9846
|
0.0003
|
|
Coeficiente Phi
|
|
0.0256
|
|
|
Coeficiente de
contingencia
|
|
0.0256
|
|
|
V de Cramer
|
|
0.0256
|
|
|
Test exacto de Fisher
|
|
Celda (1,1)
Frecuencia (F)
|
780
|
|
Alineado a la
izquierda Pr <= F
|
0.9999
|
|
Alineado a la
derecha Pr >= F
|
0.0001
|
|
|
|
|
Tabla de
probabilidad (P)
|
<.0001
|
|
De dos caras Pr
<= P
|
0.0002
|
Tamaño efectivo de la muestra = 19754
Frecuencia de valores ausentes = 523
Procedimiento FREQ
|
Frecuencia
Porcentaje
Pct fila
Pct col
|
|
|
Tabla de S4CQ1 por HHIG
|
|
S4CQ1(Had a
+2weeks low mood period)
|
HHIG
|
|
3
|
4
|
Total
|
|
1
|
186
2.25
57.76
4.20
|
136
1.65
42.24
3.54
|
322
3.90
|
|
2
|
4239
51.28
53.35
95.80
|
3706
44.83
46.65
96.46
|
7945
96.10
|
|
Total
|
4425
53.53
|
3842
46.47
|
8267
100.00
|
|
Frecuencia de ausentes = 192
|
|
Estadísticos para la tabla de S4CQ1 por HHIG
|
Estadístico
|
DF
|
Valor
|
Prob
|
|
Chi-cuadrado
|
1
|
2.4190
|
0.1199
|
|
Chi-cuadrado de
ratio de verosimilitud
|
1
|
2.4312
|
0.1189
|
|
Chi-cuadrado adj. de
continuidad
|
1
|
2.2450
|
0.1340
|
|
Chi-cuadrado
Mantel-Haenszel
|
1
|
2.4187
|
0.1199
|
|
Coeficiente Phi
|
|
0.0171
|
|
|
Coeficiente de
contingencia
|
|
0.0171
|
|
|
V de Cramer
|
|
0.0171
|
|
|
Test exacto de Fisher
|
|
Celda (1,1)
Frecuencia (F)
|
186
|
|
Alineado a la
izquierda Pr <= F
|
0.9468
|
|
Alineado a la
derecha Pr >= F
|
0.0668
|
|
|
|
|
Tabla de
probabilidad (P)
|
0.0136
|
|
De dos caras Pr <=
P
|
0.1241
|
Tamaño efectivo de la muestra = 8267
Frecuencia de valores ausentes = 192
Interpretation: The groups that are actually
different are the following. Meaning people from households with an income of
less of 30.000$ are certainly more likely than the rest to suffer from
depression.
|
Pair
|
Meaning
|
Statistically
Different
|
|
1
vs 2
|
"Low/Mid-low" vs "Medium"
|
Yes
|
|
1
vs 3
|
"Low/Mid-low" vs "High"
|
Yes
|
|
1
vs 4
|
"Low/Mid-low" vs "Very High"
|
Yes
|
|
2
vs 3
|
"Medium"
vs " Very High"
|
No
|
|
2
vs 4
|
"Medium"
vs "High"
|
Yes
|
|
3
vs 4
|
"High"
vs " Very High"
|
No
|
