11 chapter 12 quantitative data analysis: hypothesis testing © 2009 john wiley & sons ltd
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11
Chapter 12
Quantitative Data Analysis: Hypothesis Testing
© 2009 John Wiley & Sons Ltd.www.wileyeurope.com/college/sekaran
Type I Errors, Type II Errors and Statistical Power
Type I error (): the probability of rejecting the null hypothesis when it is actually true.
Type II error (): the probability of failing to reject the null hypothesis given that the alternative hypothesis is actually true.
Statistical power (1 - ): the probability of correctly rejecting the null hypothesis.
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Choosing the Appropriate Statistical Technique
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Testing Hypotheses on a Single Mean
One sample t-test: statistical technique that is used to test the hypothesis that the mean of the population from which a sample is drawn is equal to a comparison standard.
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Testing Hypotheses about Two Related Means
Paired samples t-test: examines differences in same group before and after a treatment.
The Wilcoxon signed-rank test: a non-parametric test for examining significant differences between two related samples or repeated measurements on a single sample. Used as an alternative for a paired samples t-test when the population cannot be assumed to be normally distributed.
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Testing Hypotheses about Two Related Means - 2
McNemar's test: non-parametric method used on nominal data. It assesses the significance of the difference between two dependent samples when the variable of interest is dichotomous. It is used primarily in before-after studies to test for an experimental effect.
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Testing Hypotheses about Two Unrelated Means
Independent samples t-test: is done to see if there are any significant differences in the means for two groups in the variable of interest.
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Testing Hypotheses about Several Means
ANalysis Of VAriance (ANOVA) helps to examine the significant mean differences among more than two groups on an interval or ratio-scaled dependent variable.
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Regression Analysis
Simple regression analysis is used in a situation where one metric independent variable is hypothesized to affect one metric dependent variable.
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Scatter plot
10
30 40 50 60 70 80 90
PHYS_ATTR
20
40
60
80
100
LKLH
D_D
ATE
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Simple Linear Regression
11
Y
X
0̂0̂0̂0̂0̂0̂ `0
0̂
iii XY 10
1̂1
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Ordinary Least Squares Estimation
12
Yi
Xi
Yiei
n
1i
2i Minimize e
ˆ
© 2009 John Wiley & Sons Ltd.www.wileyeurope.com/college/sekaran
SPSS
Analyze Regression Linear
13
Model Summary
.841 .707 .704 5.919Model1
R R SquareAdjustedR Square
Std. Error ofthe Estimate
ANOVA
8195.319 1 8195.319 233.901 .000
3398.640 97 35.038
11593.960 98
Regression
Residual
Total
Model1
Sum ofSquares df Mean Square F Sig.
© 2009 John Wiley & Sons Ltd.www.wileyeurope.com/college/sekaran
SPSS cont’d
14
Coefficients
34.738 2.065 16.822 .000
.520 .034 .841 15.294 .000
(Constant)
PHYS_ATTR
Model1
B Std. Error
UnstandardizedCoefficients
Beta
StandardizedCoefficients
t Sig.
© 2009 John Wiley & Sons Ltd.www.wileyeurope.com/college/sekaran
Model validation
1. Face validity: signs and magnitudes make sense2. Statistical validity:
– Model fit: R2
– Model significance: F-test– Parameter significance: t-test– Strength of effects: beta-coefficients– Discussion of multicollinearity: correlation matrix
3. Predictive validity: how well the model predicts– Out-of-sample forecast errors
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SPSS
16
Model Summary
.841 .707 .704 5.919Model1
R R SquareAdjustedR Square
Std. Error ofthe Estimate
© 2009 John Wiley & Sons Ltd.www.wileyeurope.com/college/sekaran
Measure of Overall Fit: R2
R2 measures the proportion of the variation in y that is explained by the variation in x.
R2 = total variation – unexplained variation total variation
R2 takes on any value between zero and one:– R2 = 1: Perfect match between the line and the data points.– R2 = 0: There is no linear relationship between x and y.
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SPSS
18
Model Summary
.841 .707 .704 5.919Model1
R R SquareAdjustedR Square
Std. Error ofthe Estimate
= r(Likelihood to Date, Physical Attractiveness)
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Model Significance
H0: 0 = 1 = ... = m = 0 (all parameters are zero)
H1: Not H0
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Model Significance
H0: 0 = 1 = ... = m = 0 (all parameters are zero)
H1: Not H0
Test statistic (k = # of variables excl. intercept)
F = (SSReg/k) ~ Fk, n-1-k
(SSe/(n – 1 – k)
SSReg = explained variation by regression
SSe = unexplained variation by regression
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SPSS
21
ANOVA
8195.319 1 8195.319 233.901 .000
3398.640 97 35.038
11593.960 98
Regression
Residual
Total
Model1
Sum ofSquares df Mean Square F Sig.
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Parameter significance
Testing that a specific parameter is significant (i.e., j 0)
H0: j = 0
H1: j 0
Test-statistic: t = bj/SEj ~ tn-k-1
with bj = the estimated coefficient for j SEj = the standard error of bj
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SPSS cont’d
23
Coefficients
34.738 2.065 16.822 .000
.520 .034 .841 15.294 .000
(Constant)
PHYS_ATTR
Model1
B Std. Error
UnstandardizedCoefficients
Beta
StandardizedCoefficients
t Sig.
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Conceptual Model
24
Physical Attractiveness
Likelihood to Date
+
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Multiple Regression Analysis
We use more than one (metric or non-metric) independent variable to explain variance in a (metric) dependent variable.
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Conceptual Model
26
Perceived Intelligence
Physical Attractiveness
+
+Likelihood
to Date
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Model Summary
.844 .712 .706 5.895Model1
R R SquareAdjustedR Square
Std. Error ofthe Estimate
ANOVA
8257.731 2 4128.866 118.808 .000
3336.228 96 34.752
11593.960 98
Regression
Residual
Total
Model1
Sum ofSquares df Mean Square F Sig.
Coefficients
31.575 3.130 10.088 .000
.050 .037 .074 1.340 .183
.523 .034 .846 15.413 .000
(Constant)
PERC_INTGCE
PHYS_ATTR
Model1
B Std. Error
UnstandardizedCoefficients
Beta
StandardizedCoefficients
t Sig.
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27
Conceptual Model
28
Perceived Intelligence
Physical Attractiveness
Likelihood to Date
Gender
+ +
+
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Moderators Moderator is qualitative (e.g., gender, race, class) or quantitative (e.g., level
of reward) that affects the direction and/or strength of the relation between dependent and independent variable
Analytical representation
Y = ß0 + ß1X1 + ß2X2 + ß3X1X2
with Y = DVX1 = IVX2 = Moderator
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Model Summary
.910 .828 .821 4.601Model1
R R SquareAdjustedR Square
Std. Error ofthe Estimate
ANOVA
9603.938 4 2400.984 113.412 .000
1990.022 94 21.170
11593.960 98
Regression
Residual
Total
Model1
Sum ofSquares df Mean Square F Sig.
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30
Moderators
Coefficients
32.603 3.163 10.306 .000
.000 .043 .000 .004 .997
.496 .027 .802 18.540 .000
-.420 3.624 -.019 -.116 .908
.127 .058 .369 2.177 .032
(Constant)
PERC_INTGCE
PHYS_ATTR
GENDER
PI_GENDER
Model1
B Std. Error
UnstandardizedCoefficients
Beta
StandardizedCoefficients
t Sig.
interaction significant effect on dep. var.
© 2009 John Wiley & Sons Ltd.www.wileyeurope.com/college/sekaran
31
Moderators
Conceptual Model
32
Perceived Intelligence
Physical Attractiveness
Communality of Interests
Likelihood to Date
Gender
Perceived Fit
+ +
+
+
+
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Mediating/intervening variable Accounts for the relation between the independent and dependent variable
Analytical representation1. Y = ß0 + ß1X
=> ß1 is significant
2. M = ß2 + ß3X=> ß3 is significant
3. Y = ß4 + ß5X + ß6M => ß5 is not significant => ß6 is significant
33
With Y = DVX = IVM = mediator© 2009 John Wiley & Sons Ltd.
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Step 1
34
Mode l Summary
.963 .927 .923 3.020Model1
R R SquareAdjustedR Square
Std. Error ofthe Estimate
ANOVA
10745.603 5 2149.121 235.595 .000
848.357 93 9.122
11593.960 98
Regression
Residual
Total
Model1
Sum ofSquares df Mean Square F Sig.
© 2009 John Wiley & Sons Ltd.www.wileyeurope.com/college/sekaran
Step 1 cont’d
35
Coefficients
17.094 2.497 6.846 .000
.030 .029 .044 1.039 .301
.517 .018 .836 29.269 .000
-.783 2.379 -.036 -.329 .743
.122 .038 .356 3.201 .002
.212 .019 .319 11.187 .000
(Constant)
PERC_INTGCE
PHYS_ATTR
GENDER
PI_GENDER
COMM_INTER
Model1
B Std. Error
UnstandardizedCoefficients
Beta
StandardizedCoefficients
t Sig.
significant effect on dep. var.
© 2009 John Wiley & Sons Ltd.www.wileyeurope.com/college/sekaran
Step 2
36
Mode l Summary
.977 .955 .955 2.927Model1
R R SquareAdjustedR Square
Std. Error ofthe Estimate
ANOVA
17720.881 1 17720.881 2068.307 .000
831.079 97 8.568
18551.960 98
Regression
Residual
Total
Model1
Sum ofSquares df Mean Square F Sig.
© 2009 John Wiley & Sons Ltd.www.wileyeurope.com/college/sekaran
Step 2 cont’d
37
Coefficients
8.474 1.132 7.484 .000
.820 .018 .977 45.479 .000
(Constant)
COMM_INTER
Model1
B Std. Error
UnstandardizedCoefficients
Beta
StandardizedCoefficients
t Sig.
significant effect on mediator
© 2009 John Wiley & Sons Ltd.www.wileyeurope.com/college/sekaran
Step 3
38
Mode l Summary
.966 .934 .930 2.885Model1
R R SquareAdjustedR Square
Std. Error ofthe Estimate
ANOVA
10828.336 6 1804.723 216.862 .000
765.624 92 8.322
11593.960 98
Regression
Residual
Total
Model1
Sum ofSquares df Mean Square F Sig.
© 2009 John Wiley & Sons Ltd.www.wileyeurope.com/college/sekaran
Step 3 cont’d
39
Coefficients
14.969 2.478 6.041 .000
.019 .028 .028 .688 .493
.518 .017 .839 30.733 .000
-2.040 2.307 -.094 -.884 .379
.142 .037 .412 3.825 .000
-.051 .085 -.077 -.596 .553
.320 .102 .405 3.153 .002
(Constant)
PERC_INTGCE
PHYS_ATTR
GENDER
PI_GENDER
COMM_INTER
PERC_FIT
Model1
B Std. Error
UnstandardizedCoefficients
Beta
StandardizedCoefficients
t Sig.
significant effect of mediator on dep. var.insignificant effect of indep. var on dep. Var.
© 2009 John Wiley & Sons Ltd.www.wileyeurope.com/college/sekaran
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