Copyright © 2008 by Nelson, a division of Thomson Canada Limited Chapter 17 Part 5 Analysis and Interpretation of Data BASIC DATA ANALYSIS

LEARNING OBJECTIVES 1.To understand that analysis consists of summarizing, rearranging, ordering, or manipulating data 2.To compute and explain the purposes of simple tabulations and cross-tabulations 3.To use cross-tabulation procedures to discuss the relationship between two variables 4.To discuss the nature of data transformations 5.To explain how to summarize rank-order data 6.To describe some computer software designed for descriptive analysis What you will learn in this chapter Copyright © 2008 by Nelson, a division of Thomson Canada Limited 17–1

LEARNING OBJECTIVES (cont’d) 7.To define hypothesis, null hypothesis, alternative hypothesis, and significance level 8.To discuss the steps in the hypothesis-testing procedure 9.To describe the factors that influence the choice of statistical method to use for analysis What you will learn in this chapter Copyright © 2008 by Nelson, a division of Thomson Canada Limited 17–2

Descriptive AnalysisDescriptive Analysis  The transformation of raw data into a form that will make them easy to understand and interpret; rearranging, ordering, and manipulating data to generate descriptive information The Nature of Descriptive Analysis Copyright © 2008 by Nelson, a division of Thomson Canada Limited 17–3

TabulationTabulation  The orderly arrangement of data in a table or other summary format  Frequency table  The arrangement of statistical data in a row-and-column format that exhibits the count of responses or observations for each category assigned to a variable PercentagesPercentages  Whether data are tabulated by computer or by hand, percentages, cumulative percentages, and frequency distributions are useful TabulationTabulation Copyright © 2008 by Nelson, a division of Thomson Canada Limited 17–4

Measures of Central TendencyMeasures of Central Tendency  Describing central tendencies of the distribution with the mean, median, or mode is another basic form of descriptive analysis  These measures are most useful when the purpose is to identify typical values of a variable or the most common characteristic of a group Tabulation (cont’d) Copyright © 2008 by Nelson, a division of Thomson Canada Limited 17–5

Cross-TabulationCross-Tabulation  Organizing data by groups, categories, or classes to facilitate comparisons; a joint frequency distribution of observations on two or more sets of variables Two-Way (Contingency) TablesTwo-Way (Contingency) Tables  The results of a cross-tabulation of two variables, such as answers to two survey questions Percentage Cross-TabulationsPercentage Cross-Tabulations  Base  The number of respondents or observations (in a row or column) used as a basis for computing percentages Cross-TabulationCross-Tabulation Copyright © 2008 by Nelson, a division of Thomson Canada Limited 17–6

Elaboration and RefinementElaboration and Refinement  Elaboration analysis  An analysis of the basic cross-tabulation for each level of a variable not previously considered, such as subgroups of the sample  Moderator variable  A third variable that, when introduced into an analysis, alters or has a contingent effect on the relationship between an independent variable and a dependent variable  Spurious relationship  An apparent relationship between two variables that is not authentic Cross-Tabulation (cont’d) Copyright © 2008 by Nelson, a division of Thomson Canada Limited 17–7

How Many Cross-Tabulations?How Many Cross-Tabulations?  The number of cross-tabulations should be determined early, when research objectives are stated Cross-Tabulation (cont’d) Copyright © 2008 by Nelson, a division of Thomson Canada Limited 17–8

Data Transformation (Data Conversion)Data Transformation (Data Conversion)  The process of changing the original form of data to a format suitable to achieve the research objective Data Transformation Copyright © 2008 by Nelson, a division of Thomson Canada Limited 17–9

Rank OrderRank Order  Respondents often rank order brand preferences or other variables of interest to researchers. To summarize these data for all respondents, the analyst performs a data transformation by multiplying the frequency by the rank (score) to develop a new scale that represents the summarized rank orders Calculating Rank Order Copyright © 2008 by Nelson, a division of Thomson Canada Limited 17–10

TablesTables  Tables are most useful for presenting numerical information, especially when several pieces of information have been gathered about each item discussed  The purpose of each table is to facilitate the summarization and communication of the data’s meaning Tabular and Graphic Methods of Displaying Data Copyright © 2008 by Nelson, a division of Thomson Canada Limited 17–12

Charts and GraphsCharts and Graphs  Charts translate numerical information into visual form so that relationships may be easily grasped Pie ChartsPie Charts  Pie charts shows the composition of some total quantity at a particular time Line GraphsLine Graphs  Line graphs are useful for showing the relationship of one variable to another Tabular and Graphic Methods of Displaying Data (cont’d) Copyright © 2008 by Nelson, a division of Thomson Canada Limited 17–13

Bar ChartsBar Charts  Bar charts show changes in the value of a dependent variable (plotted on the vertical axis) at discrete intervals of the independent variable (on the horizontal axis) Tabular and Graphic Methods of Displaying Data (cont’d) Copyright © 2008 by Nelson, a division of Thomson Canada Limited 17–14

 SAS  Statistical Package for the Social Sciences (SPSS)  STATA  MINITAB Computer Programs for Analysis Copyright © 2008 by Nelson, a division of Thomson Canada Limited 17–15

What is a Hypothesis?What is a Hypothesis?  Hypothesis  An unproven proposition or supposition that tentatively explains certain facts or phenomena; a proposition that is empirically testable Null and Alternative HypothesisNull and Alternative Hypothesis  Null Hypothesis  A statement about a status quo asserting that any change from what has been thought to be true will be due entirely to random sampling error  Alternative Hypothesis  A statement indicating the opposite of the null hypothesis Univariate Statistics: Stating a Hypothesis Copyright © 2008 by Nelson, a division of Thomson Canada Limited 17–16

The Hypothesis-Testing ProcedureThe Hypothesis-Testing Procedure  The specifically stated hypothesis is derived from the research objectives  A sample is obtained and the relevant variable is measured  The measured sample value is compared to the value either stated explicitly or implied in the hypothesis  Significance level  The critical probability in choosing between the null and alternative hypotheses; the probability level that is too low to warrant support of the null hypothesis Hypothesis Testing Copyright © 2008 by Nelson, a division of Thomson Canada Limited 17–17

An Example of Hypothesis TestingAn Example of Hypothesis Testing  Critical values  The values that lie exactly on the boundary of the region of rejection  Example of hypothesis testing The null hypothesis: the mean is equal to 3.0:  H o : μ = 3.0 The alternative hypothesis: the mean is not equal to 3.0:  H 1 : μ ≠ 3.0 Hypothesis Testing (cont’d) Copyright © 2008 by Nelson, a division of Thomson Canada Limited 17–18

An Example of Hypothesis Testing (cont’d)An Example of Hypothesis Testing (cont’d) Hypothesis Testing (cont’d) Copyright © 2008 by Nelson, a division of Thomson Canada Limited 17–19

Chi-Square ( χ 2 ) TestChi-Square ( χ 2 ) Test  A hypothesis test that allows for investigation of statistical significance in the analysis of a frequency distribution  Example of chi-square test where χ² = chi-square statistics O i = observed frequency in the ith cell E i = expected frequency on the ith cell The Chi-Square Test for Goodness of Fit Copyright © 2008 by Nelson, a division of Thomson Canada Limited 17–20

Chi-Square ( χ 2 ) Test (cont’d)Chi-Square ( χ 2 ) Test (cont’d)  Example of chi-square test (cont’d) The Chi-Square Test for Goodness of Fit (cont’d) Copyright © 2008 by Nelson, a division of Thomson Canada Limited 17–21 Awareness of Tire Manufacturer’s Brand Aware Unaware Frequency Brand Awareness Aware Unaware Total

Number of VariablesNumber of Variables  The researcher conducts univariate statistical analysis when attempting to generalize from a sample about one variable at a time  Statistically describing the relationship between two variables at one time requires bivariate statistical analysis Choosing the Appropriate Technique Copyright © 2008 by Nelson, a division of Thomson Canada Limited 17–22

Scale of MeasurementScale of Measurement  The scale of measurement on which the data are based or the type of measurement reflected in the data determines the permissible statistical techniques and appropriate empirical operations to perform Choosing the Appropriate Technique (cont’d) Copyright © 2008 by Nelson, a division of Thomson Canada Limited 17–23

Type of Question to be AnsweredType of Question to be Answered  The type of question the researcher is attempting to answer is a consideration in the choice of statistical technique  Marketing researchers frequently question whether a mean, a proportion, or a distribution differs from what was expected  Two other frequently asked questions are:  Are there differences between two (or more) groups, and  Is there a relationship between two or more variables? Choosing the Appropriate Technique (cont’d) Copyright © 2008 by Nelson, a division of Thomson Canada Limited 17–24