Parametric non Parametric test hypothesistesting-120928132044-phpapp01.ppt

8/10/2019 Parametric non Parametric test hypothesistesting-120928132044-phpapp01.ppt

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18-1

Hypothesis Testing and the Research Process


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18-2

Types of Hypotheses

Null

H0: = 50 mpg

H0: < 50 mpg

H0: > 50 mpg

Alternate

HA: = 50 mpg

HA: > 50 mpg HA: < 50 mpg


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18-3

Two-Tailed Test of Significance


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18-4

One-Tailed Test of Significance


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18-5

Decision Rule

Take no corrective action if theanalysis shows that one cannot

reject the null hypothesis.


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18-6

Statistical Decisions


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18-7

Factors Affecting Probability ofCommitting a Error

True value of parameter

Alpha level selected

One or two-tailed test used

Sample standard deviation

Sample size


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18-8

Statistical TestingProcedures

Obtain criticaltest value

Interpret thetest

Stages

Choosestatistical test

State nullhypothesis

Select level ofsignificance

Computedifference

value


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18-9

Tests of Significance

NonparametricParametric


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18-10

Assumptions for UsingParametric Tests

Independent observations

Normal distribution

Equal variances

Interval or ratio scales


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18-13

Advantages of NonparametricTests

Easy to understand and use

Usable with nominal data

Appropriate for ordinal data

Appropriate for non-normalpopulation distributions

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18-14

How To Select A Test

How many samples are involved?

If two or more samples are involved,are the individual cases independent or related?

Is the measurement scalenominal, ordinal, interval, or ratio?

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18-15

Recommended StatisticalTechniques

Two-Sample Tests____________________________________________

k-Sample Tests____________________________________________

Measurement

Scale One-Sample Case Related Samples

Independent

Samples Related Samples

Independent

Samples

Nominal Binomial

x

2

one-sample test

McNemar Fisher exact test

x2

two-samplestest

Cochran Q x2for ksamples

Ordinal Kolmogorov-Smirnovone-sample test

Runs test

Sign test

Wilcoxonmatched-pairstest

Median test

Mann-Whitney U

Kolmogorov-Smirnov

Wald-Wolfowitz

Friedman two-way ANOVA

Medianextension

Kruskal-Wallisone-way ANOVA

Interval andRatio

t-test

Ztest

t-test for pairedsamples

t-test

Ztest

Repeated-measures ANOVA

One-wayANOVA

n-way ANOVA

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18-16

Questions Answered byOne-Sample Tests

Is there a difference between observedfrequencies and the frequencies we wouldexpect?

Is there a difference between observedand expected proportions?

Is there a significant difference betweensome measures of central tendency andthe population parameter?

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18-17

Parametric Tests

t-testZ-test


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18-19

One Sample Chi-SquareTest Example

Living Arrangement

Intend to

Join

Number

Interviewed

Percent

(no. interviewed/200)

Expected

Frequencies

(percent x 60)

Dorm/fraternity 16 90 45 27

Apartment/roominghouse, nearby

13 40 20 12

Apartment/roominghouse, distant

16 40 20 12

Live at home 15

_____

30

_____

15

_____

9

_____

Total 60 200 100 60

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18-20

One-Sample Chi-SquareExample

Null Ho: 0 = E

Statistical test One-sample chi-square

Significance level .05

Calculated value 9.89

Critical test value 7.82

(from Appendix C, Exhibit C-3)

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18-21

Two-SampleParametric Tests

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18-22

Two-Sample t-TestExample

A Group B Group

Average hourly sales X1= $1,500 X2= $1,300

Standard deviation s1= 225 s2= 251

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18-23

Two-Sample t-TestExample

Null Ho: A sales = B sales

Statistical test t-test

Significance level .05 (one-tailed)

Calculated value 1.97, d.f. = 20




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Two-Sample Chi-SquareExample

Null There is no difference indistribution channel for age

categories.Statistical test Chi-square


Calculated value 6.86, d.f. = 2Critical test value 5.99



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Sales Data for Paired-Samples t-Test

Company

Sales

Year 2

Sales

Year 1 Differenc e D D2

GM

GE

Exxon

IBMFord

AT&T

Mobil

DuPont

Sears

Amoco

Total

126932

54574

86656

6271096146

36112

50220

35099

53794

23966

123505

49662

78944

5951292300

35173

48111

32427

49975

20779

3427

4912

7712

31923846

939

2109

2632

3819

3187

D= 35781 .

11744329

24127744

59474944

1022720414971716

881721

4447881

6927424

14584761

10156969

D= 157364693 .

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Paired-Samples t-TestExample

Null Year 1 sales = Year 2 sales

Statistical test Paired sample t-test


Calculated value 6.28, d.f. = 9



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k-Independent-SamplesTests: ANOVA

Tests the null hypothesis that the meansof three or more populations are equal

One-way: Uses a single-factor, fixed-

effects model to compare the effects of atreatment or factor on a continuousdependent variable

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ANOVA Example

__________________________________________Model Summary_________________________________________

Source d.f. Sum of Squares Mean Square FValue p Value

Model (airline) 2 11644.033 5822.017 28.304 0.0001

Residual (error) 57 11724.550 205.694

Total 59 23368.583

_______________________Means Table________________________

Count Mean Std. Dev. Std. Error

Delta 20 38.950 14.006 3.132Lufthansa 20 58.900 15.089 3.374

KLM 20 72.900 13.902 3.108

All data are hypothetical

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ANOVA ExampleContinued

Null A1 = A2 = A3

Statistical test ANOVA and F ratio


Calculated value 28.304, d.f. = 2, 57



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k-Related-Samples Tests

More than two levels ingrouping factor

Observations are matched

Data are interval or ratio

Parametric non Parametric test hypothesistesting-120928132044-phpapp01.ppt

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