Geography Reference
In-Depth Information
TABLE 14.1. Observed Frequencies
Yearly Snowfall
Medium
(20-60 cm)
Elevation
Low (0-20 cm)
High (60 + cm)
Totals
500-1000 m
41
19
10
70
1000-2000 m
22
15
6
43
2000 + m
2
8
10
20
65
42
26
133
of cases that fit into the combination of elevation and snow—for example, 10
observations at elevations over 2,000 m have, on average, more than 60 cm
of snow yearly. Looking over all the cells, one sees a marked tendency in the
observations that suggest higher elevations receive more snow than lower
elevations do. The chi-square statistic is used to test the relationship between
the two qualitative variables.
2. Formulate a Test Statement
Each distribution accounts for both independent and dependent variables.
The test statement expresses the relationship we think we see in the data in a
more specific manner. The established approach for creating this
null hypoth-
esis
is that it states that the variables are not associated. If the chi-square sta-
tistic disproves the null hypothesis, then the opposite is proven, namely, that
more snow falls at higher elevation. In statistical terminology, H
0
refers to
the null hypothesis; H
1
refers to the alternative hypothesis.
We use the chi-square statistic to determine the difference between the
actual observations and what we would expect if the observations followed
our null hypothesis. We need to create a second table based on the assump-
tion that the null hypothesis is correct and then compare the two tables. The
values for the second table, called the “expected frequencies,” are calculated
by using the row and column totals. First, calculate the expected probability
that the snowfall is low by dividing the total number of observations of low
snowfall by the total number of observations (round the results to three sig-
nificant digits):
TABLE 14.2. Expected Frequencies
Yearly Snowfall
Medium
(20-60 cm)
Elevation
Low (0-20 cm)
High (60+ cm)
Totals
500-1000 m
34.209
22.107
13.648
70
1000-2000 m
21.006
13.575
8.379
43
2000+ m
9.709
6.251
3.79
20
65
42
26
133
Search WWH ::
Custom Search