Data Analysis Examples Using SPSS OUTPUTS: Significance Tests

General guideline: the significance value (p or sig.) represent the percentage or the probability that the results are due to chance. If you have p = .10, this mean 10% of your results is due to chance. The convention used in mass communication research is that results must be equal or less than 5% due to chance. That is, p must be smaller than or equals to 0.05 in order to claim the relationship is truly significant.

All of these samples are based on the GSS data set.

  1. Chi-square test:

Example 1

Research Question: Do respondents of different races have different beliefs in life after death?




Analysis: The Chi-square statistics is most appropriate in this case because both the independent variable, race, and the dependent variable, belief in life after death, are nominal variables. From the chi-square statistic, it is clear that there is no relationship between race and the belief in life after death. That is, whites are not more likely than black or other race to believe in life after death. (chi-square= 1.079, df = 2, p = .583).

Note: In interpreting the tables, just focus on the chi-square test table, the row on Pearson Chi-square value, df (degree of freedom) and Asymp. Sig. (Asymptotic significance). The raw count table above it helps you to interpret the results. It would be particularly useful if the chi-square statistic is significant and you need to explain the relationships of the variables.

Example 2.

Research Question: Do black people more likely to vote for a black as a president?


Data Analysis: The chi-square statistics is used to examine the difference between respondents of difference race and their likelihood to vote for a black president. The significant chi-square value show that blacks are very likely to vote for black president than any other races (Chi-square=14.934, df=2, p = .001).






You can recreate a simpler table to demonstrate the difference in a report:

Comparison of Respondents' Race and Likelihood to Vote for a Black President
Race
Vote for a black president
White
Black
Other Race
Total
Yes
634
109
30
773
No
98
1
6
105
Total
732
110
36
878

Chi-square = 14.934, df = 2, p = 0.001.


2. t-test

Research Question: Do male and female differ in their view on sex before marriage?




Analysis: Because this research question ask for comparison between two groups, male and female, and the attitude toward sex before marriage is an interval data, t-test should be used to analyze the relationship between sex of the respondents and their attitudes toward sex before marriage. The GSS data show that male and female differ significantly in attitudes toward sex before marriage because the t-value is higher than the critical value of 1.96 at 0.05 significance level. Male respondents are more likely to accept sex before marriage than female respondents (t = 3.402, df=891, p = .001). Male respondents have a mean of 2.93 while female respondents have a lower mean score of 2.43 toward sex before marriage.

Note: In interpreting these tables, focus on the t, df , and significance value, and ignore other peripheral information such as Levene's Test of Equality of Variance, standard error difference etc.

You can recreate a simpler table as follows to illustrate your results clearly:

Attitudes toward sex before marriage
N
Mean
t
df
p
Male
393
2.93
3.402
.891
.001
Female
500
2.43

(1=premarital sex is always wrong, 4=premarital sex is not wrong at all)

3. ANOVA

Research Question: Do people of difference race have different attitudes toward sex before marriage?


Data Analysis: One-way ANOVA is used to analyze the difference in attitudes toward sex before marriage between the three race groups: 1) white, 2) black, 3) and other races because sex before marriage is interval data and there are three groups to be compared. The ANOVA test of the three groups' attitudes toward sex before marriage show that the three groups do not differ significantly in their attitudes toward sex before marriage (F (2,890) =. 766, p = .465). Therefore we can conclude the people of different race do not have different attitudes toward sex before marriage.

Note: the F(2, 890) is the convention of presenting between group degree of freedom first and then within group degree of freedom. The df of between group is 2, and the df of within groups is 890. In interpreting the tables, you should only focus on the N, Mean, F ratio value and the Sig. Level, and ignore other peripheral information such as standard deviation, standard error, sum of squares between and within groups.

You can recreate a simpler table that is similar to Ha and James (1997)'s table 3:

Attitudes toward sex before among Whites, Blacks and other race

N
Mean
F
p
Whites
751
2.76
.766
.465
Blacks
105
2.9
Other Race
37
2.65
Total
893
2.77

(1=premarital sex is always wrong, 4=premarital sex is not wrong at all)