Data Analysis Report 2
Ian Giesinger
Introduction:
In this report I am conducting a statistical analysis of household spending patterns and nonhousehold debt proportions. I am seeking to answer if there is a difference in the proportion of
households with non-mortgage household debt by debt group. I am also seeking to answer if
there are differences in the average annual food spending by region and city type. Household
spending patterns are important because they can help us understand economic security.
Data Set:
Table 1. Proportion of households with non-mortgage debt by debt group
$0
$1 - $10,000 $10,001 - $20,000 $20,001 - $30,000 $30,001 +
6
48
86
48
12
There are 200 total households and the proportion of households with non-mortgage debt by debt
group is as follows: 3% of households have $0 of non-mortgage debt, 24% of households have
$1-$10,000 of non-mortgage debt, 43% of households have $10,001-$20,000 of non-mortgage
debt, 24% of households have $20,001-$30,000 of non-mortgage debt, and 6% of households
have $30,001+ of non-mortgage debt.
Table 2. Contingency table for average annual food spending by region and city type
Northeast
Midwest
South
West
9853.60
9211.43
8053.55
10025.13
Urban
9443.07
7122.70
7181.50
9290.28
Suburban
8696.75
7556.20
7614.35
8853.44
Rural
As we can see from table 2 above, the average annual food spending seems to be highest in
urban cities in the West and Northeast and lowest in rural areas in the South and Midwest. For all
regions average annual food spending seems to increase by population density.
Analysis, Results, and Conclusion
Test 1: Are there differences in the proportion of households with non-mortgage household debt
by debt group, at the 5% significance level?
Hypotheses:
H0: P1 = P2
HA: P1 ≠ P2
T-test: 198.0076
P-value: 0.0000
For this test I used the chi squared goodness of fit test. The test statistic was 198.0076 and the Pvalue was 0. Since the p-value is less than 0.05 we reject the null hypothesis that P1 = P2. We can
conclude that P1 ≠ P2. Therefore, there is a difference in the proportion of households with nonmortgage household debt by debt group.
Test 2: Are there differences in the average annual food spending by region and city type at the
5% significance level?
Hypotheses:
H0: 𝜇1 = 𝜇 2 = 𝜇3 = 𝜇4
HA: Not all population means are equal
ANOVA
Source of
Variation
Between Groups
Within Groups
Total
SS
df
MS
F
P-value
F crit
7584408
4199596
3
8
2528136 4.815961 0.033538 4.066181
524949.5
11784004 11
For this test I used the single factor ANOVA test. The test statistic is 4.815961 The p-value is
0.033538. Since the p-value is less than 0.05 we reject the null hypothesis that 𝜇1 = 𝜇 2 = 𝜇3 = 𝜇4.
We can conclude that not all population means are equal. Therefore, there are differences in
the average annual food spending by region and city type.
Test 2B: if you conclude differences exist in test 2, run a second test to determine exactly how
the data differs, at the 5% significance level.
I am using the fisher’s LSD test in excel to determine exactly how the data differs.
Groups
Northeast and Midwest
Northeast and South
Northeast and West
Midwest and South
Midwest and West
South and West
Difference Statistically
between
Significant
1367.696
Yes
5144.02
Yes
-175.433
No
1040.933
Yes
-4278.52
Yes
-5319.45
Yes
I calculated a value of 1194.99 for the fisher’s LSD. When comparing two regions only one
comparison is not statistically significant. When comparing the Northeast and the West the
difference is only -175.4333333 the absolute value of this number is less than the fisher’s LSD
meaning we cannot reject the null hypothesis (𝜇1 = 𝜇 2 = 𝜇3 = 𝜇4) for these two groups. Every other
comparison between groups is statistically significant meaning there is a difference in the
average annual food spending by those regions.