Frequency Distribution, Cross-Tabulation,

And Hypothesis TestingWeek 08

W. Rofianto, ST, MSi

Internet Usage Internet Usage Data (Table A) Data (Table A)

Respondent Sex Familiarity Internet Attitude Toward Usage of InternetNumber Usage Internet Technology Shopping Banking

1 1.00 7.00 14.00 7.00 6.00 1.00 1.002 2.00 2.00 2.00 3.00 3.00 2.00 2.003 2.00 3.00 3.00 4.00 3.00 1.00 2.004 2.00 3.00 3.00 7.00 5.00 1.00 2.00 5 1.00 7.00 13.00 7.00 7.00 1.00 1.006 2.00 4.00 6.00 5.00 4.00 1.00 2.007 2.00 2.00 2.00 4.00 5.00 2.00 2.008 2.00 3.00 6.00 5.00 4.00 2.00 2.009 2.00 3.00 6.00 6.00 4.00 1.00 2.0010 1.00 9.00 15.00 7.00 6.00 1.00 2.0011 2.00 4.00 3.00 4.00 3.00 2.00 2.0012 2.00 5.00 4.00 6.00 4.00 2.00 2.0012 2.00 5.00 4.00 6.00 4.00 2.00 2.0013 1.00 6.00 9.00 6.00 5.00 2.00 1.0014 1.00 6.00 8.00 3.00 2.00 2.00 2.0015 1.00 6.00 5.00 5.00 4.00 1.00 2.0016 2.00 4.00 3.00 4.00 3.00 2.00 2.0017 1.00 6.00 9.00 5.00 3.00 1.00 1.0018 1.00 4.00 4.00 5.00 4.00 1.00 2.0019 1.00 7.00 14.00 6.00 6.00 1.00 1.0020 2.00 6.00 6.00 6.00 4.00 2.00 2.0021 1.00 6.00 9.00 4.00 2.00 2.00 2.0022 1.00 5.00 5.00 5.00 4.00 2.00 1.0023 2.00 3.00 2.00 4.00 2.00 2.00 2.0024 1.00 7.00 15.00 6.00 6.00 1.00 1.0025 2.00 6.00 6.00 5.00 3.00 1.00 2.0026 1.00 6.00 13.00 6.00 6.00 1.00 1.0027 2.00 5.00 4.00 5.00 5.00 1.00 1.0028 2.00 4.00 2.00 3.00 2.00 2.00 2.00 29 1.00 4.00 4.00 5.00 3.00 1.00 2.0030 1.00 3.00 3.00 7.00 5.00 1.00 2.00

Frequency Bar GraphFrequency Bar Graph

7

6

5

Fre

quency

8

2 3 4 5 6 70

4

3

2

1

Fre

quency

Familiarity

Frequency Distribution & Measures of Location

Mean

Median

Mode

Range

interquartile rangeinterquartile range

Variance

standard deviation

coefficient of variation

Steps Involved in Hypothesis TestingSteps Involved in Hypothesis Testing

Formulate H0 and H1

Select Appropriate Test

Choose Level of Significance

Collect Data and Calculate Test Statistic

Draw Marketing Research Conclusion

Determine Probability Associated with Test

Statistic

Determine Critical Value of Test Statistic TSCR

Determine if TSCR falls into (Non) Rejection

Region

Compare with Level of Significance, α

Reject or Do not Reject H0

A Broad Classification of Hypothesis TestsA Broad Classification of Hypothesis Tests

Tests of Tests of

Hypothesis Tests

Median/ RankingsDistributions ProportionsMeans

Tests of Association

Tests of Differences

CrossCross--Tabulation Gender Tabulation Gender and Internet Usageand Internet Usage

Gender

Row

Internet Usage Male Female Total

Light (1) 5 10 15Light (1) 5 10 15

Heavy (2) 10 5 15

Column Total 15 1 5

Statistics Associated with Cross-Tabulation Phi Coefficient

� The phi coefficient is used as a measure of the strength ofassociation in the special case of a table with two rows andtwo columns (a 2 x 2 table).

� While the phi coefficient is specific to a 2 x 2 table, thecontingency coefficient (C) can be used to assess thestrength of association in a table of any size.

Cramer's V is a modified version of the phi correlation� Cramer's V is a modified version of the phi correlationcoefficient, and is used in tables larger than 2 x 2.

Cross-Tabulation

Hypothesis Testing Related to Differences

� Parametric tests assume that the variables of interest are measured on at least an interval scale.

� Nonparametric tests assume that the variables are measured on a nominal or ordinal scale.

� These tests can be further classified based on whether one or� These tests can be further classified based on whether one ortwo or more samples are involved.

� The samples are independent if they are drawn randomly fromdifferent populations. For the purpose of analysis, datapertaining to different groups of respondents, e.g., males andfemales, are generally treated as independent samples.

� The samples are paired when the data for the two samples relate to the same group of respondents.

A Classification of Univariate Techniques

Metric Data Non-metric Data

Univariate Techniques

One Sample Two or More Samples

One Sample Two or More Samples

Independent RelatedIndependent Related

* Two- Group test* Z test * One-Way ANOVA

* Paired t test* Chi-Square* Mann-Whitney* Median* K-S* K-W ANOVA

* Sign* Wilcoxon* McNemar* Chi-Square

Samples Samples

* t test* Z test

* Frequency* Chi-Square* K-S* Runs* Binomial

Parametric TestsParametric Tests

� The t statistic assumes that the variable is normallydistributed and the mean is known (or assumed to beknown) and the population variance is estimated fromthe sample.

� Assume that the random variable X is normallydistributed, with mean and unknown population variancethat is estimated by the sample variance s 2.that is estimated by the sample variance s 2.

� Then, is t distributed with n - 1 degreesof freedom.

� The t distribution is similar to the normal distribution inappearance. Both distributions are bell-shaped andsymmetric. As the number of degrees of freedomincreases, the t distribution approaches the normaldistribution.

t = ( X - µ)/sX

One Sample : t TestOne Sample : t Test

For the data in Table A, suppose we wanted to test the hypothesis thatthe mean familiarity rating exceeds 4.0, the neutral value on a 7 pointscale. A significance level of α = 0.05 is selected. The hypotheses maybe formulated as:

< 4.0H0:

µ > 4.0

µ

H1:

Two IndependentTwo Independent--Samples Samples tt TestsTests

In the case of means for two independent samples, the hypotheses take the following form.

µµ210

: =H

µµ211

: ≠H

-

PairedPaired--Samples Samples tt TestTest

H0: µ

D= 0

H1: µ

D≠ 0

KK--S OneS One--Sample Test Sample Test for Normality for Normality of Internet Usageof Internet Usage