11 Chapter 12 Quantitative Data Analysis: Hypothesis Testing © 2009 John Wiley & Sons Ltd. .

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.

2© 2009 John Wiley & Sons Ltd.www.wileyeurope.com/college/sekaran

Choosing the Appropriate Statistical Technique


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.


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.


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.


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.


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.


Regression Analysis

Simple regression analysis is used in a situation where one metric independent variable is hypothesized to affect one metric dependent variable.


Scatter plot

10

30 40 50 60 70 80 90

PHYS_ATTR

20

40

60

80

100

LKLH

D_D

ATE


Simple Linear Regression

11

Y

X

0̂0̂0̂0̂0̂0̂ `0

0̂

iii XY 10

1̂1


Ordinary Least Squares Estimation

12

Yi

Xi

Yiei

n

1i

2i Minimize e

ˆ


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.


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.


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


SPSS

16

Model Summary

.841 .707 .704 5.919Model1




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.


SPSS

18

Model Summary

.841 .707 .704 5.919Model1



= r(Likelihood to Date, Physical Attractiveness)


Model Significance

H0: 0 = 1 = ... = m = 0 (all parameters are zero)

H1: Not H0


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


SPSS

21

ANOVA

8195.319 1 8195.319 233.901 .000

3398.640 97 35.038

11593.960 98

Regression

Residual

Total

Model1



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


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


Beta


t Sig.


Conceptual Model

24

Physical Attractiveness

Likelihood to Date

+


Multiple Regression Analysis

We use more than one (metric or non-metric) independent variable to explain variance in a (metric) dependent variable.


Conceptual Model

26

Perceived Intelligence


+

+Likelihood

to Date


Model Summary

.844 .712 .706 5.895Model1



ANOVA

8257.731 2 4128.866 118.808 .000

3336.228 96 34.752

11593.960 98

Regression

Residual

Total

Model1


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


Beta


t Sig.


27

Conceptual Model

28



Likelihood to Date

Gender

+ +

+


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


Model Summary

.910 .828 .821 4.601Model1



ANOVA

9603.938 4 2400.984 113.412 .000

1990.022 94 21.170

11593.960 98

Regression

Residual

Total

Model1



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


Beta


t Sig.

interaction significant effect on dep. var.


31

Moderators

Conceptual Model

32



Communality of Interests

Likelihood to Date

Gender

Perceived Fit

+ +

+

+

+


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.

www.wileyeurope.com/college/sekaran

Step 1

34

Mode l Summary

.963 .927 .923 3.020Model1



ANOVA

10745.603 5 2149.121 235.595 .000

848.357 93 9.122

11593.960 98

Regression

Residual

Total

Model1



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


Beta


t Sig.

significant effect on dep. var.


Step 2

36

Mode l Summary

.977 .955 .955 2.927Model1



ANOVA

17720.881 1 17720.881 2068.307 .000

831.079 97 8.568

18551.960 98

Regression

Residual

Total

Model1



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


Beta


t Sig.

significant effect on mediator


Step 3

38

Mode l Summary

.966 .934 .930 2.885Model1



ANOVA

10828.336 6 1804.723 216.862 .000

765.624 92 8.322

11593.960 98

Regression

Residual

Total

Model1



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


Beta


t Sig.

significant effect of mediator on dep. var.insignificant effect of indep. var on dep. Var.


11 Chapter 12 Quantitative Data Analysis: Hypothesis Testing © 2009 John Wiley & Sons Ltd. .

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Transcript of 11 Chapter 12 Quantitative Data Analysis: Hypothesis Testing © 2009 John Wiley & Sons Ltd. .