Download DATA ANALYSIS II

DATA ANALYSIS II
MKT 525
CROSS-TABULATIONS-1
Numbers of Cars
1 or none
2 or more
Income
Less than $37,500 48
= or > $37,500
27
Total
75
6
19
25
Total
54
46
100
CROSS-TABULATIONS-2
Numbers of Cars
1 or none
Income
Less than $37,500 89%
= or > $37,500
59%
2 or more
Total
11%
41%
100%
100%
CROSS-TABULATIONS-3
Numbers of Cars
Income
Less than $37,500
= or > $37,500
Total
1 or none
2 or more
64%
36
100%
24%
76
100%
CROSS-TABULATIONS-4
Family size
4 or less
5 or more
Numbers of Cars
1 or none
2 or more
Total
90%
23%
100%
100%
10%
77%
CROSS-TABULATIONS-5
Family:
4 members or less
No. Cars 1 or none 2 or more
Income:
Less than
$37,500
96%
4%
= or >
$37,500
81%
19%
5 or more
1 or none 2 or more
50%
50%
7%
93%
CROSS-TABULATIONS-6
Size of family:
4 or less 5 or more
Income:
Less than $37,500 4%
= or > $37,500
19%
Total
50% 11%
93% 41%
Chi Square Test
• Does an observed set of frequencies match an
expected pattern?
• Requirements:
– samples in cells must be independent
– Expected frequency must be 5 or more
• SPSS: Nonparametric- chisquare-test variableexpected value
Chi Square: Compare Two Classifications
Women
Men:
Freq. Obs.
Exp.
Obs.
Exp..
Total
M
W
0
13
16.5
20
16.5
33
33%
50%
1-3
12
12
12
12
24
30%
30%
4-7
15
11.5
8
11.5
23
37%
20%
Total
40
80
100%
100%
40
Compare means from two samples:
t-test
• Assume the 2 samples are independent
Is there a difference in number of years to pay back a home
improvement loan between S&Ls and other financial
institutions?
S&L
Other
Mean years 8.7
7.7
Variance
.5
.6
N
100
64
t = (8.7 - 7.7)/.1175 = 8.51
At p=.05, df = n1+n2-no. groups=100+64-2=162, critical t= 1.96
Compare proportions from two
samples: t-test
Do younger women use bubble baths less than older women?
Women under 35
Women 35-64
p(use bb)
.13
.23
Std. Dev.
.04
.04
N
144
169
Average p(use bb):weighted mean:=.184
Std. error of diff. of proportions=.0439
t = (.13 - .23) - 0 = -2.28
.0439
df = n - no. gps. = 144 + 169 - 2 = 311 Critical t = 1.96
SPSS
• Chi Square-compare two classifications:
– Analyze-Descriptive Statistics -Crosstabs Statistics-Chi square
• t-test -compare mean with expectation
– Analyze- Compare Means - One sample t-test test variable - test value
• t-test - compare independent samples
– Analyze-Compare means -Independent samplestest variable-grouping variable-levels of 2 groups
Correlation
• Is there an association between two variables?
• If so, how strong is it?
• What is the form of the association?
Correlation = measure of relationship between
two variables
Correlation-2
•
•
•
•
•
CORRELATION DOES NOT MEAN CAUSATION!
A measure of relationship; NOT a proportion!
Reflects a linear relationship.
Can range from -1.00 to +1.00
Correlation high if points close together when form a
line and low if points are far apart when form a line.
• Correlation coefficient is standardized and
dimensionless.
• Value of correlation = degree of relationship
• Sign of correlation = direction of relationship
SPSS for Correlation
• Both continuous:
– Analyze-correlation-bivariate-enter 2 variables
• One dichotomous and one continuous:
– Analyze-correlation-bivariate-enter 2 variables
• Both dichotomous:
– Analyze-crosstabs-statistics-phi &Cramer’s v
• Both ranks:
– Analyze-correlation-Spearman-enter 2 variables
Simple linear regression
• Want to predict value of one variable (DV) from
another variable (IV)
• Y = bX + a
• For each unit increase in X there is a b increase in Y
• r2 = coefficient of determination = proportion of
variance accounted for by regression model.
• Relation between correlation coefficient (r) and b:
b = r (s.d.y/s.d.x)
Simple regression: SPSS
• Analyze- regression - linear - dependent
variable name - independent (predictor)
variable name
Case
• A baking company found a correlation of .70 between
the number of persons in a HH and the consumption
of bread. They also found a correlation of -.35
between HH income and bread consumption.
• How would you interpret these findings?
• How much variance in HH bread consumption is
explain by a linear regression model using the
number of persons in the HH as the predictor
variable?