CAN MONEY BUY HAPPINESS?
Nicole Amy
Statistics
Prof. Dan Myers
December 7, 1998
Introduction
Even in today’s commercialized, profit-driven society, the old adage "Money can’t buy happiness" is often repeated. Is this actually true or is it simply something that those without money say to make themselves feel better? Sociological research seems to disagree on the answer to this question. One study found that income does have a significant effect on happiness far beyond the level of meeting subsistence needs (Diener 1993). Others found that happiness levels do not necessarily correspond with income but rather that the strongest indicator of happiness is the type of political system in one’s country (Veenhoven 1990) and one’s self-assessed health status (McKenzie 1987). As the gap between the rich and the poor gets increasingly wider, it is important to understand how one’s economic status affects other aspects of one’s life, including self-assessed happiness. Though the people at the lower end of the wage gap may not want to believe it, money may just buy happiness.
Hypotheses and Data
I hypothesize that there is a relationship between one’s income level and one’s level of happiness. I also hypothesize that there is a relationship between one’s socioeconomic class and the number of traumatic events one will have experienced. The source of my data is the General Social Survey from 1987-1991. My sample consisted of 1,400 randomly chosen respondents from the surveys administered in the above years. The data gathered by the GSS serves as a database for social scientists and consists of information on socially relevant attitudes, behaviors, and characteristics of a cross-section of American adults. The GSS is conducted by the National Opinion Research Center in Chicago each year and surveys a sample of 1,500 people from across the United States each year. The data collected is representative of non-institutionalized, English speaking Americans age 18 or older.
To test my first hypothesis that income level is related to happiness level, I used the GSS variable REALINC as my independent variable and HAPPY as my dependent variable. REALINC is the respondent’s self-reported family income in dollars. The question was open-ended and allowed the respondent to answer with any value. The variable HAPPY consisted of the respondents’ answers to the question, "Taken all together, how would you say things are these days--would you say that you are very happy, pretty happy, or not too happy?" Respondents had a choice of the three happiness levels listed above.
To test my second hypothesis that class level is related to number of traumatic events experienced, I used the GSS variable CLASS as my independent variable and TRAUMA5 as my dependent variable. The variable CLASS consisted of the respondent’s self-assessed social class level. The question was forced response, and the respondents could choose between lower class, working class, middle class, and upper class. The variable TRAUMA5 consisted of the respondents’ self-report of the number of traumatic events (deaths, divorces, unemployments, and hospitalizations/disabilities) that happened to them during the last five years. The respondents had a choice of reporting 0, 1, 2, 3, or 4 traumatic events.
Before testing my first hypothesis, the data for my first independent variable, REALINC, needed to be recoded. REALINC was a ratio variable, and the dependent variable, HAPPY, was an ordinal variable. Since we have not learned any statistical tests which can be run on this combination of variables, the independent variable needed to be recoded and treated as a categorical variable in order to run statistical tests. The independent variable, REALINC, was renamed MYINC and recoded into seven categories, each with a range of $10,000 beginning with the category of $0-10,000 and ending with the category of $60,001-maximum value. I also recoded the variable HAPPY because the way in which the answers were coded gave the smallest number (1) to those with the greatest level of happiness. This made the graphs which include HAPPY to be very visually misleading. I simply recoded HAPPY into MYHAPPY in which those with the greatest level of happiness were coded by the highest number (3) and those with the lowest level of happiness by the lowest value (1).
Results
MYINC had a mean value of 3.02, a value which falls in the third category, $20,001-30,000. This is quite consistent with the REALINC mean of $26,409.34. The median value is 3, and the mode is 2, a value which occurred 193 times. This indicates that the distribution may be slightly positively skewed, and this can also be seen in the skewness value of 0.71. The data has a standard deviation of 1.80, which in this case indicates that the data is quite dispersed and is not tightly clustered around the mean. The cumulative frequency distribution shows that 23.54% of the values fall into the first category, 48.63% fall into the second category or below, 64.89% in the third or below, 78.80% in the fourth or below, 87.65% in the fifth or below, 93.63% in the sixth or below, and, of course, 100% into the seventh category or below. (See figure 1 for the distribution of this variable.)
The variable MYHAPPY has a median value of 2, which corresponds to the category "pretty happy." It also has a mode of 2 with 824 people or 59.67% of people giving this response. The cumulative frequency distribution shows that 12.31% of people fall into the first category, "not so happy." 71.98% fall into the second category, "pretty happy," or below. And, of course, 100% fall into the third category, "very happy," or below. (See figure 2 for the distribution of this variable.)
By treating both variables as categorical, a chi-square test was run on the data in order to test my first hypothesis that income level is related to happiness level. The chi-square value of the table of MYHAPPY and MYINC is calculated to be 37.81. The probability of achieving this value by chance is less than .000 and so is significant even at the .001 level. The results of the chi-square test allow me to reject the null hypothesis that income and happiness level are unrelated. The results indicate that there is a relationship between income and happiness, supporting my first hypothesis, though the direction of the relationship can not be determined from chi-square.
Though the Cramer’s V value of .1581 shows a relationship between MYHAPPY and MYINC, it is not a very strong one. The seeming discrepancy between the results of the chi-square test and the results of the Cramer’s V test can be easily explained. Chi-square is sensitive to N. A very high N value can result in a very high chi-square value even if the relationship in the table is not strong. Since my table had an N value of 756, the chi-square value was correspondingly high. Cramer’s V takes into account the size of N, and in doing so can tell you the strength of the relationship. Since the Cramer’s V value falls between 0 and 1, it indicates that there is a relationship between income and happiness and that the null hypothesis can be rejected. However, the relationship is less strong than one is lead to believe by the high chi-square value. And as with chi-square, the direction of the relationship can not be determined from Cramer’s V.
However, by looking at histograms of happiness by income the direction of the relationship can be determined (see figure 3). In the lowest income level, the highest number of people (58%) fall into the middle category "pretty happy." Almost equal amounts of people at this income level fall into the "not too happy" category (22%) and the "very happy" category (19%). As income level goes up, the proportion of people responding "pretty happy" remains at almost the same high level with anywhere from 56-63% of people at each income level falling in this category. The difference between the income levels lies in the proportions of each level reporting they are "not too happy" or "very happy." As income increases, the proportion of respondents replying "not too happy" falls and the proportion of respondent replying "very happy" rises. In the lowest income level, almost equal numbers fall into each of these two categories. In the highest income level only one person reported being "not too happy," and 20 people or 41% reported being "very happy." The direction of the relationship can be determined by looking at the graph. The higher one’s income, the more likely that one will report being "very happy." The results go against the adage that money can not buy happiness, and suggest that money can buy happiness.
To test my second hypothesis that socio-economic class is related to the number of traumatic events experienced, I used CLASS as my independent variable and TRAUMA5 as my dependent variable. CLASS had a median value of 2, which corresponds with the category of "working class." This category was also the modal category with 658 of the 1387 respondents placing themselves in it. The cumulative frequency distribution shows that 7.21% of people fell into the first category "lower class," 54.65% fell into the second category "working class" or below, 97.04% fell into the third category "middle class" or below, and, of course, 100% fell into the fourth category "upper class" or below. (See figure 4 for the distribution of this variable.)
The mean number of traumas occurring to the respondents in the last five years was 1.04. The median value was 1, and the modal value was 1. The standard deviation was .9. This indicates that the data is relatively tightly clustered around the mean, and show only a small positive skew, measure to be .53. The cumulative frequency distribution shows that 31.69% of people experienced no traumatic events in the last five years, 70.58% experienced 1 or less, 94.14% experienced 2 or less, 99.49% experienced 3 or less, and, of course, 100% experienced 4 or less traumatic experiences in the last 5 years. (See figure 5 for the distribution of this variable.)
Since my independent variable, CLASS, is ordinal and my dependent variable, TRAUMA5, is ratio, I ran an Analysis of Variance (ANOVA) to test my second hypothesis that socio-economic class is related to number of traumatic events experienced. The ANOVA test produced an F value of 6.46. The probability of achieving an F value of this magnitude by chance is only .0002. This means that the results are significant to the .001 level and that the null hypothesis that there is no relationship between class and number of traumatic events experienced can be rejected. These results show that there is a significant relationship between socio-economic class and number of traumatic events experienced. However, the direction of the relationship can not be discerned from the results of the ANOVA.
This direction can be discerned by looking at the graph showing the mean number of traumatic events experienced by each class level (see figure 6). Looking at the graph, you can see that as socio-economic class level goes up, the mean number of traumas experienced goes down. The mean level of 1.40 traumatic experiences for the lowest class is almost double the mean of .77 for the highest class. The histograms of number of traumatic events broken down by class (see figure 7), also shows that the higher one’s class, the less traumatic events one experiences. In fact, everyone in the middle class experienced 3 or fewer traumatic events, and not a single person in the upper class experienced more than two traumatic events. The data also becomes more progressively clustered around the mean as class goes up, meaning that there is less variance in the data for the higher classes. The graphs illustrate that the direction of the significant relationship found by the ANOVA test is a negative one, as class goes up, the number of traumatic events experienced goes down. These results, like those of the chi-square test, give support to the idea that the adage "Money can’t buy happiness" is not correct.
Discussion
The results of my research suggest some other research avenues which should be explored. Because we have not learned any tests which can be run on a ratio independent variable and an ordinal dependent variable, I had to treat income as a categorical variable. This means that information was lost in testing my first hypothesis. Further research which can deal with income as a ratio variable would utilize all available information, and it would be interesting to see if a relationship is still found when the relationship is tested with the independent variable at the ratio level. It would also be interesting to attempt to explain the differences in happiness within an income level. Further research could test whether the differences in happiness within an income level can be attributed to another variable, such as age, race, sex, health-status, marital status, or to something else.
I am very confident that my second hypothesis, which states that class and number of traumatic events experienced by respondent are related, is supported by my data. The F value calculated in the ANOVA has the possibility of 1 in 5,000 of occurring by chance. This shows a strong relationship between class and the number of traumatic events experienced. I am less confident that the data supports my first hypothesis that income and happiness are related. The chi-square value of 37.81 seems to support the hypothesis, but this large chi-square value could be a function of the large N value for the table. Cramer’s V which takes N into account shows only a weak relationship between income and happiness. Based on these results, I have to conclude that although there is a relationship between income and happiness, it may not be a strong one.
Though folk wisdom would like to deny it, my results support the idea that money can buy happiness. Though people, especially those without much money, would rather believe that money can not buy happiness, it makes practical sense to say that it can. Those who make more money can supply not only the basic necessities of food, clothing, and shelter but can also supply their family with physical and financial security, high-quality education, the possibility of more leisure time, and luxuries that those who make less money can not afford. Though my results show that money does not guarantee happiness, it makes sense that money can provide for basic necessities and luxuries and lessen the pressure and stress people experience when they do not have these things. Though folk wisdom is to the contrary and many people may not want to admit it, my results support the idea that money can buy happiness.
WORKS CITED
Diener, Ed. 1993. "The Relationship Between Income and Subjective Well-Being." Social Indicators Research. 28:195-223.
Mckenzie, Brad. 1987. "Race, Socio-economic Status, and Subjective Well-being in Older Americans." International Journal of Aging and Human Development. 25: 43-61.
Veenhoven, Ruut. 1990. "Inequality and Happiness Across Countries." International Sociological Association Paper.
Figure 1
Figure 2
Figure 3
1 = not too happy
Figure 4
Figure 5
Figure 6
Figure 7
LOG FILE:
summ realinc
Variable | Obs Mean Std. Dev. Min Max
---------+-----------------------------------------------------
realinc | 769 26409.34 21817.33 464 91462
. tab realinc
FAMILY |
INCOME IN |
CONSTANT $ | Freq. Percent Cum.
------------+-----------------------------------
464 | 1 0.13 0.13
483 | 1 0.13 0.26
500 | 3 0.39 0.65
1855 | 1 0.13 0.78
1930 | 9 1.17 1.95
2000 | 8 1.04 2.99
3247 | 6 0.78 3.77
3378 | 6 0.78 4.55
3500 | 7 0.91 5.46
4175 | 14 1.82 7.28
4343 | 9 1.17 8.45
4500 | 11 1.43 9.88
5102 | 5 0.65 10.53
5308 | 14 1.82 12.35
5500 | 9 1.17 13.52
6030 | 2 0.26 13.78
6273 | 4 0.52 14.30
6500 | 9 1.17 15.47
6958 | 6 0.78 16.25
7238 | 5 0.65 16.91
7500 | 11 1.43 18.34
8349 | 12 1.56 19.90
8685 | 11 1.43 21.33
9000 | 17 2.21 23.54
10436 | 15 1.95 25.49
10857 | 13 1.69 27.18
11250 | 25 3.25 30.43
12756 | 12 1.56 31.99
13269 | 13 1.69 33.68
13750 | 19 2.47 36.15
15075 | 16 2.08 38.23
15682 | 16 2.08 40.31
16250 | 18 2.34 42.65
17394 | 13 1.69 44.34
18094 | 6 0.78 45.12
18750 | 15 1.95 47.07
19713 | 12 1.56 48.63
20507 | 7 0.91 49.54
21250 | 11 1.43 50.98
22032 | 11 1.43 52.41
22919 | 14 1.82 54.23
23750 | 14 1.82 56.05
25511 | 21 2.73 58.78
26538 | 19 2.47 61.25
27500 | 28 3.64 64.89
30150 | 19 2.47 67.36
31364 | 17 2.21 69.57
32500 | 19 2.47 72.04
34788 | 11 1.43 73.47
36189 | 16 2.08 75.55
37500 | 25 3.25 78.80
41746 | 20 2.60 81.40
43426 | 18 2.34 83.75
45000 | 30 3.90 87.65
51023 | 19 2.47 90.12
53077 | 9 1.17 91.29
55000 | 18 2.34 93.63
87994 | 18 2.34 95.97
90172 | 20 2.60 98.57
91462 | 11 1.43 100.00
------------+-----------------------------------
Total | 769 100.00
. summ realinc, detail
FAMILY INCOME IN CONSTANT $
-------------------------------------------------------------
Percentiles Smallest
1% 1930 464
5% 3500 483
10% 5102 500 Obs 769
25% 10436 500 Sum of Wgt. 769
50% 21250 Mean 26409.34
Largest Std. Dev. 21817.33
75% 36189 91462
90% 51023 91462 Variance 4.76e+08
95% 87994 91462 Skewness 1.457384
99% 91462 91462 Kurtosis 4.943241
. gen myinc = realinc
(631 missing values generated)
. recode myinc 0/10000=1 10001/20000=2 20001/30000=3 30001/40000=4 40001/50000=
> 5 50001/60000=6 60001/max=7
(769 changes made)
. summ myinc
Variable | Obs Mean Std. Dev. Min Max
---------+-----------------------------------------------------
myinc | 769 3.028609 1.801826 1 7
. tab myinc
myinc | Freq. Percent Cum.
------------+-----------------------------------
1 | 181 23.54 23.54
2 | 193 25.10 48.63
3 | 125 16.25 64.89
4 | 107 13.91 78.80
5 | 68 8.84 87.65
6 | 46 5.98 93.63
7 | 49 6.37 100.00
------------+-----------------------------------
Total | 769 100.00
. summ myinc,detail
myinc
-------------------------------------------------------------
Percentiles Smallest
1% 1 1
5% 1 1
10% 1 1 Obs 769
25% 2 1 Sum of Wgt. 769
50% 3 Mean 3.028609
Largest Std. Dev. 1.801826
75% 4 7
90% 6 7 Variance 3.246576
95% 7 7 Skewness .7069489
99% 7 7 Kurtosis 2.495988
. hist myinc, ylab
. hist myinc, ylab
. gen myhappy = happy
(19 missing values generated)
. recode myhappy 1=3 3=1
(557 changes made)
. summ myhappy
Variable | Obs Mean Std. Dev. Min Max
---------+-----------------------------------------------------
myhappy | 1381 2.157133 .6155605 1 3
. tab myhappy
myhappy | Freq. Percent Cum.
------------+-----------------------------------
1 | 170 12.31 12.31
2 | 824 59.67 71.98
3 | 387 28.02 100.00
------------+-----------------------------------
Total | 1381 100.00
. summ myhappy, detail
myhappy
-------------------------------------------------------------
Percentiles Smallest
1% 1 1
5% 1 1
10% 1 1 Obs 1381
25% 2 1 Sum of Wgt. 1381
50% 2 Mean 2.157133
Largest Std. Dev. .6155605
75% 3 3
90% 3 3 Variance .3789147
95% 3 3 Skewness -.1083185
99% 3 3 Kurtosis 2.528384
. hist myhappy, ylab
. sort myinc
. hist myhappy, by(myinc) b2title(myinc) ylab
. tab myhappy myinc, chi2 all
| myinc
myhappy | 1 2 3 4 5 | Total
-----------+-------------------------------------------------------+----------
1 | 40 26 14 8 6 | 97
2 | 104 119 72 64 38 | 451
3 | 34 43 35 35 23 | 208
-----------+-------------------------------------------------------+----------
Total | 178 188 121 107 67 | 756
| myinc
myhappy | 6 7 | Total
-----------+----------------------+----------
1 | 2 1 | 97
2 | 26 28 | 451
3 | 18 20 | 208
-----------+----------------------+----------
Total | 46 49 | 756
Pearson chi2(12) = 37.8081 Pr = 0.000
likelihood-ratio chi2(12) = 39.1115 Pr = 0.000
Cramer's V = 0.1581
gamma = 0.2632 ASE = 0.043
Kendall's tau-b = 0.1777 ASE = 0.030
. summ class
Variable | Obs Mean Std. Dev. Min Max
---------+-----------------------------------------------------
class | 1387 2.410959 .6676148 1 4
. tab class
SUBJECTIVE |
CLASS |
IDENTIFICATI|
ON | Freq. Percent Cum.
------------+-----------------------------------
1 | 100 7.21 7.21
2 | 658 47.44 54.65
3 | 588 42.39 97.04
4 | 41 2.96 100.00
------------+-----------------------------------
Total | 1387 100.00
. summ class, detail
SUBJECTIVE CLASS IDENTIFICATION
-------------------------------------------------------------
Percentiles Smallest
1% 1 1
5% 1 1
10% 2 1 Obs 1387
25% 2 1 Sum of Wgt. 1387
50% 2 Mean 2.410959
Largest Std. Dev. .6676148
75% 3 4
90% 3 4 Variance .4457095
95% 3 4 Skewness -.1015821
99% 4 4 Kurtosis 2.716063
. hist class, ylab
. summ trauma5
Variable | Obs Mean Std. Dev. Min Max
---------+-----------------------------------------------------
trauma5 | 972 1.041152 .9010544 0 4
. tab trauma5
TRAUMA |
SCALE, LAST |
5 YEARS | Freq. Percent Cum.
------------+-----------------------------------
0 | 308 31.69 31.69
1 | 378 38.89 70.58
2 | 229 23.56 94.14
3 | 52 5.35 99.49
4 | 5 0.51 100.00
------------+-----------------------------------
Total | 972 100.00
. summ trauma5, detail
TRAUMA SCALE, LAST 5 YEARS
-------------------------------------------------------------
Percentiles Smallest
1% 0 0
5% 0 0
10% 0 0 Obs 972
25% 0 0 Sum of Wgt. 972
50% 1 Mean 1.041152
Largest Std. Dev. .9010544
75% 2 4
90% 2 4 Variance .811899
95% 3 4 Skewness .5276239
99% 3 4 Kurtosis 2.665482
. hist trauma5, ylab
. sort class
. hist trauma5, by(class) b2title(class) ylab
. by class: summ trauma5
-> class=1
Variable | Obs Mean Std. Dev. Min Max
---------+-----------------------------------------------------
trauma5 | 72 1.402778 .9443639 0 4
-> class=2
Variable | Obs Mean Std. Dev. Min Max
---------+-----------------------------------------------------
trauma5 | 455 1.076923 .9483439 0 4
-> class=3
Variable | Obs Mean Std. Dev. Min Max
---------+-----------------------------------------------------
trauma5 | 407 .953317 .8246704 0 3
-> class=4
Variable | Obs Mean Std. Dev. Min Max
---------+-----------------------------------------------------
trauma5 | 31 .7741935 .6688137 0 2
-> class=.
Variable | Obs Mean Std. Dev. Min Max
---------+-----------------------------------------------------
trauma5 | 7 1.285714 1.380131 0 4
. oneway trauma5 class, tabulate
SUBJECTIVE | Summary of TRAUMA SCALE, LAST 5 YEARS
CLASS |
IDENTIFICATI|
ON | Mean Std. Dev. Freq.
------------+------------------------------------
1 | 1 1 72
2 | 1 1 455
3 | 1 1 407
4 | 1 1 31
------------+------------------------------------
Total | 1 1 965
Analysis of Variance
Source SS df MS F Prob > F
------------------------------------------------------------------------
Between groups 15.3441132 3 5.11470441 6.46 0.0002
Within groups 761.159514 961 .792049442
------------------------------------------------------------------------
Total 776.503627 964 .805501688
Bartlett's test for equal variances: chi2(3) = 12.8404 Prob>chi2 = 0.005
.