CHI Square
11
is used when we have categorical (nominal) rather than interval / ratio data can also be used for measurement data, is less powerful and than typical tests such as means CHI Square
description
is used when we have categorical (nominal) rather than interval / ratio data can also be used for measurement data, is less powerful and than typical tests such as means. CHI Square. CHI Square for a multicategory case. GoodBad MediumTotal Observed 26401581 Expected 27272781. - PowerPoint PPT Presentation
Transcript of CHI Square
is used when we have categorical (nominal) rather than interval / ratio data
can also be used for measurement data, is less powerful and than typical tests such as means
CHI Square
CHI Square for a multicategory case
Good Bad Medium TotalObserved 26 40 15 81Expected 27 27 27 81
CHI square or X2 =
X2 = 11.63
Expected
ExpectedObserved 2)(
27
)2715(
27
)2740(
27
)2726( 222
SPSS output
NPar TestsChi-Square TestFrequencies
PAGEQUAL
26 27.0 -1.0
40 27.0 13.0
15 27.0 -12.0
81
1.00
2.00
3.00
Total
Observed N Expected N Residual
Test Statistics
11.630
2
.003
Chi-Square a
df
Asymp. Sig.
PAGEQUAL
0 cells (.0%) have expected frequencies less than5. The minimum expected cell frequency is 27.0.
a.
CHI Square for a Contingency Table Analysis
(when there is more than one variable)
Good Bad Medium TotalFinance 26 (27) 40 (27) 15 (27) 81Newspaper 21 (30) 27 (30) 42 (30) 90
The table shows that webpages in the Finance category were more were more likely to be good than were webpages in the Newspaper condition. Thus, the column a webpage is in (Good, Bad, or Medium) graduate) is contingent upon (depends on) the row the webpage is in (Finance or newspaper category)
SPSS:using the Non Parametric toolNPar TestsChi-Square TestFrequencies
PAGEQUAL
47 57.3 -10.3
67 57.3 9.7
58 57.3 .7
172
1.00 good
2.00 bad
3.00 medium
Total
Observed N Expected N ResidualCATEGORY
81 86.0 -5.0
91 86.0 5.0
172
1.00 finance
2.00 newspapers
Total
Observed N Expected N Residual
Test Statistics
3.500 .581
2 1
.174 .446
Chi-Square a,b
df
Asymp. Sig.
PAGEQUAL CATEGORY
0 cells (.0%) have expected frequencies less than5. The minimum expected cell frequency is 57.3.
a.
0 cells (.0%) have expected frequencies less than5. The minimum expected cell frequency is 86.0.
b.
SPSS: using cross tabs
Mean = 393.2
CrosstabsCase Processing Summary
172 100.0% 0 .0% 172 100.0%PAGEQUAL * CATEGORYN Percent N Percent N Percent
Valid Missing Total
Cases
PAGEQUAL * CATEGORY Crosstabulation
Count
26 21 47
40 27 67
15 43 58
81 91 172
1.00 good
2.00 bad
3.00 medium
PAGEQUAL
Total
1.00 finance2.00
newspapers
CATEGORY
Total
Chi-Square Tests
16.044a 2 .000
16.588 2 .000
10.016 1 .002
172
Pearson Chi-Square
Likelihood Ratio
Linear-by-LinearAssociation
N of Valid Cases
Value dfAsymp. Sig.
(2-sided)
0 cells (.0%) have expected count less than 5. Theminimum expected count is 22.13.
a.
Confidence Limits on Mean• Sample mean is a point estimate (estimate is in
form of a single number)• We want interval estimate (a range of numbers),
and be able to specify with 95% confidence that estimate will lie in that range– Probability that interval computed this way includes
= 0.95
XstXCI 025.95.
For Darts Data
33.866.
8.35.4
94.198.15.4025.95.
.*95.
XstXCI
errorstdcriticaltmeanCI
Displaying Confidence IntervalsComparing Darts and Dow (Means with 95% confidence
intervals)
0
2
4
6
8
10
Darts Dow
What would 99% confidence intervals look like?
Margin of Error
Generally computed for 95% confidence Computed for Proportions
Simple Formula (for estimating sample size before starting study)
Margin = + 1/ sqrt(N)For sample size 100 = 1/sqrt(100) = .1 or 10%For sample size 400 = 1/sqrt(400) = .05 or 5%
Formula for calculating Margin of Errors after gathering data
Probability Yes = .55, No = .45N = 200
Margin = 1.96 * sqrt((p*(1-p))/N) = 1.96 * sqrt((.25)/200)
= 1.96 *.0012
