Research Proposal

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Week10DataAnalysisHypothesisTesting2andReportWritingstudentcopy.pdf

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MARK977: Research for Marketing Decisions

Dr. Thomas Lee Trimester 1, 2018

Data Analysis: Data Preparation and Basic Concepts

WEEK 10 READINGS: CHAPTERS 12 AND 13

Recap: Hypothesis testing techniques

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Hypothesis Testing

Test of association

Chi-square test Correlation

Regression

Test of differences

One-sample t-test

Independent- samples t-test

Paired-samples t-test

One-way ANOVA

Recap: Probability values in hypothesis testing

• p-value is the largest level of significance (typically 0.05 or 5%) at which we would not reject H0 (i.e., making Type I error)

• In general, the smaller the p-value, the greater the confidence in sample findings

– E.g., p-value of 0.78 vs. 0.02

• If the computed probability estimate or p-value is smaller than the significance level (usually 5% or 0.05), reject H0. If the probability estimate or p-value is larger than the significance level, do not reject H0.

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Definitions

Correlation analysis • Assesses the strength of the

relationship between two variables

Correlation coefficient • Provides a measure of the degree

to which there is an association between two variables (X and Y)

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Correlation analysis

Pearson correlation coefficient • Measures the degree to which there is a straight-line or linear

association between two interval-scaled (or ratio-scaled) variables, say X and Y.

• Originally proposed by Karl Pearson, it is also known as the Pearson correlation coefficient. It is also referred to as simple correlation, bivariate correlation, correlation coefficient or merely correlation.

• A positive correlation reflects a tendency for a high value in one variable to be associated with a high value in the second

• A negative correlation reflects an association between a high value in one variable and a low value in the second variable

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Scatter plots

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Scatter plots (cont.)

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Testing significance of correlation coefficient

• Null hypothesis: Ho : r = 0 Ho : no relationship

• Alternative hypothesis: Ha : r ≠ 0 Ha : relationship exists

• If the correlation coefficient is statistically significant (i.e., p < .05), the null hypothesis should be rejected and we assess the alternative hypo.

• If it is not significant, then it has no meaning.

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Correlation example

• Suppose a researcher wants to assess the relationship between attitudes toward motorcycles (attitude) and the number of years the respondent has owned a motorcycle (duration).

• Attitude – 1=do not like motorcycles – 11=very much like motorcycles

• Duration – (Raw) Number of years respondent has owned one or

more motorcycles

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Correlation example (cont.)

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Correlation example (cont.)

• Given p < .05, H0 should be rejected. • The value of r, 0.936, is close to 1.0, which means the number of years a

respondent has owned a motorcycle is strongly associated with the respondent’s attitude towards motorcycles.

• Positive sign of r implies a positive relationship – the longer the duration of motorcycle ownership, the more favourable the attitude, and vice versa.

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Correlation: Key considerations

• Even though the correlation coefficient (r) provides a measure of association between two variables, it does not imply any causal relationship between the variables.

• It can only measure the strength of association (or covariation) between variables – it cannot imply causation.

• It does not tell us anything about the nature of the relationship – hence, regression analysis.

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Regression analysis

• Statistical technique that is used to relate two or more variables

• Objective is to build a regression model or a prediction equation relating the dependent variable to one or more independent variables

• The model can then be used to describe, predict, and control the variable of interest on the basis of the independent variables

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Types of regression analysis

Bivariate regression analysis – Regression analysis that involves a single metric dependent variable and a single metric independent variable. E.g., • DV = market share • IV = size of sales force Multiple regression analysis - Regression analysis that involves more than one independent variable. E.g., • DV = market share • IVs = size of sales force, advertising expenditure and sales

promotion budget

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Regression analysis Simple Linear Regression Model

Yi = βo + β1xi + εi Where • Y = Dependent variable (e.g., no. of people entering store) • X =Independent variable (e.g., advertising expenditure the day before) • β0 = Model parameter that represents mean value of dependent variable (Y)

when the independent variable (X) is zero (i.e., intercept) • β1 = Model parameter that represents the slope that measures change in

mean value of dependent variable associated with a one-unit increase in the independent variable (e.g., slope – negative vs. positive, steep vs. flat)

• εi = Error term that describes the effects on Yi of all factors other than value of Xi (e.g., variables other than advertising expenditures – store location, weather, etc.)

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Multiple regression

• A linear combination of predictor factors is used to predict the outcome or response factors

• The general form of the multiple regression model is explained as:

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where β1 , β2, . . . , βk are regression coefficients associated with the independent variables X1, X2, . . . , Xk and ε is the error or residual.

Bivariate vs. multiple regression

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Size of sales force

Market share

Size of sales force

Advertising expenditure

Promotion budget

Predicting the DV – R square

• The measure of the regression model’s ability to predict is called the coefficient of determination (r2) – percentage of explained variation – E.g., if r2 = .74, it means 74% of the total variation of Y (DV) is

explained or accounted for by X (IV) – Hence, r2 values range from 0 to 1 – The larger the r2 value, the more variation in the DV is being

explained by the IV • Adjusted R Square – adjusted for the number of independent

variables and sample size • F test – used to test the null hypothesis that the coefficient of

determination in the population is zero. If rejected, one or more partial regression coefficients have a value different from zero.

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Testing the significance of IVs

Null Hypothesis • There is no linear relationship between the independent &

dependent variables • E.g., there is no linear relationship between advertising expenditure

(IV) and sales (DV)

Alternative Hypothesis • There is a linear relationship between the independent & dependent

variables • E.g., there is a linear relationship between advertising expenditure

(IV) and sales (DV)

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H0: β1 = 0

H0: β1 ≠ 0

Evaluating the importance of IVs

• Beta coefficients (β) – represents the slope that measures change in mean value of dependent variable associated with a one-unit increase in the independent variable

• Beta coefficients can be positive or negative, and have a p-value associated with it

• If the beta coefficient is not statistically significant (p > .05), then it implies no relationship between that predictor and the DV

• Examine significance, direction and strength – E.g., if the β is .70 and statistically significant (p < .05), it means for

each unit increase in the IV, the DV will increase by .70 units • Use (standardized) beta coefficients when independent variables

are in different units of measurement. E.g., – Advertising expenditure (thousands) – Frequency/intensity of promotion (1=not frequent/intense at all,

7=very frequent/intense)

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So …

Significance testing in regression involves: 1. Testing the significance of the overall regression

equation or model – reject or accept H0 of no relationship between IV(s) and DV?

2. If significant, check percentage of variation explained (R2) – but what kind of variation?

3. Then, check individual path coefficients to determine effect on DV (β) – whether negative or positive, strong or weak, etc.

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Regression example

Suppose a researcher wishes to determine whether attitude towards motorcycles can be explained by duration of motorcycle ownership and importance attached to performance

Step 1: Identify variables of interest • DV = attitude • IVs = duration and importance

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Regression example (cont.)

Step 2: Develop hypotheses • Null: there is no relationship • Alternative: there is a relationship

Step 3: Choose relevant test • Given more than one IV, multiple regression is

preferred

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Regression example (cont.)

Step 4: Perform test

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Regression example (cont.)

Step 5: Compare test statistic and critical value

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Variables Entered/Removed a

Model Variables Entered Variables Removed Method

1 Importance,

Duration b

. Enter

a. Dependent Variable: Attitude

b. All requested variables entered.

Model Summary

Model R R Square Adjusted R Square

Std. Error of the

Estimate

1 .972 a .945 .933 .860

a. Predictors: (Constant), Importance, Duration

ANOVA a

Model Sum of Squares df Mean Square F Sig.

1 Regression 114.264 2 57.132 77.294 .000 b

Residual 6.652 9 .739

Total 120.917 11

a. Dependent Variable: Attitude

b. Predictors: (Constant), Importance, Duration

Coefficients a

Model

Unstandardized Coefficients

Standardized

Coefficients

t Sig. B Std. Error Beta

1 (Constant) .337 .567 .595 .567

Duration .481 .059 .764 8.160 .000

Importance .289 .086 .314 3.353 .008

a. Dependent Variable: Attitude

Regression example (cont.)

Step 6: Determine whether to reject null and draw marketing research conclusion • There is a relationship (p < .05) • Predictors significantly explain variation in DV (R Square = 0.945;

Adjusted R Square = 0.933) – Both duration and importance contribute to explaining the

variation in attitude • Coefficients for both duration (β = .764, p < .05) and importance

(β = .314, p < .05) are positive and significant – Therefore, both duration and importance are important in

explaining attitude

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How to report

Variables Model: Attitude

Duration .764***

Importance .314**

Lifestyle … …

Personality … …

R2 .945

Adjusted R2 .933

F-value 77.294***

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Notes: NS not significant; *p < .05; **p < .01; ***p < .001; standardised regression coefficients are reported.

SPSS Exercise

Today’s activities: • Correlation • Regression

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Correlation demo

• Suppose a research wants to examine the relationship between attitudes towards motorcycles (attitude) and the number of years the respondent has owned a motorcycle (duration). Answer the following questions: – What are the null and alternative hypotheses? – Are attitude and duration related positively or negatively?

• Open the “Motorcycle” dataset • Follow your tutor’s instructions • Refer to the “Correlation” guide on Moodle

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Regression demo

• Suppose a researcher wants to know whether attitude towards motorcycles can be explained by duration of motorcycle ownership and importance attached to performance. Address the following issues: – Determine whether the IVs explain a significant variation in

the DV: • Does a relationship exist?

– How much variation in the DV can be explained? • What is the strength of the relationship? • What is the direction of the relationship?

– What are the implications for practice? • Follow your tutor’s instructions • Refer to the “Regression” guide on Moodle

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Practice

• Open the “Internet Usage” dataset • Answer the following questions:

1. Find simple correlations between the following sets of variables: a. Internet usage and attitude towards the Internet b. Internet usage and attitude towards technology c. Attitude towards the Internet and attitude towards

technology 2. Run a bivariate regression, with Internet usage as the DV

and attitude towards the Internet as the IV. Interpret the results.

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Practice (cont.)

• Open the “Internet Usage” dataset • Answer the following questions:

3. Run a bivariate regression, with Internet usage as the DV and attitude towards technology as the IV. Interpret the results.

4. Run a multiple regression, with Internet usage as the DV, and attitude towards the Internet and attitude towards technology as the IVs. Interpret the results.

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Practice for Tutorial/Lab Task 3

• Re-run all the demos from Week 8 to Week 10: – Variable recoding – Variable re-specification – Frequency distribution – Chi-square test – One-sample t-test – Independent-samples t-test – Paired-samples t-test – Correlation – Regression

• Attempt all the practice questions from Week 8 to Week 10 • Seek help if stuck

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