BUS 115 - Chapter 12 _ 13 and 14 _ 15.pdf

Descriptive Analysis - Used by marketing researchers to describe the sample dataset in such a way as to portray the “typical” respondent and to reveal the general pattern of responses Inference Analysis - Used when marketing researchers use statistical procedures to generalize the results of the sam...

Descriptive Analysis - Used by marketing researchers to describe the sample dataset in such a way as to portray the “typical” respondent and to reveal the general pattern of responses Inference Analysis - Used when marketing researchers use statistical procedures to generalize the results of the sample to the target population it represents. Difference Analysis - Used to determine the degree to which real and generalizable differences exist in the population to help the manager make an enlightened decision on which advertising theme to use. Association Analysis - Investigates if and how two variables are related Relationship Analysis - Statistical procedures and models to help allow insight into multiple relationships among variables Understanding Data via Descriptive Analysis Two sets of measures are used extensively to describe the information obtained in a sample. –Measures of central tendency or measures that describe the “typical” respondent or response –Measures of variability or measures that describe how similar (dissimilar) respondents or responses are to (from) “typical” respondents or responses Summarizing the “Typical” Respondent Measures of central tendency: –Mode: a descriptive analysis measure defined as that value in a string of numbers that occurs most often. –Median: expresses that value whose occurrence lies in the middle of an ordered set of values. –Mean (or average): Measures of Variability: Visualizing the Diversity of Respondents - All measures of variability are concerned with depicting the “typical” difference between the values in a set of values. - There are three measures of variability: – Frequency distribution –Range –Standard deviation A frequency distribution is a tabulation of the number of times that each different value appears in a particular set of values. The frequency for each value divided by the total number of observations for all values, resulting in a percent, called a percentage distribution. Range: identifies the distance between lowest value (minimum) and the highest value (maximum) in an ordered set of values. Standard deviation: indicates the degree of variation or diversity in the values in such a way as to be translatable into a normal or bell-shaped curve distribution. Chapter 13 Market segmentation is based on differences between groups of consumers. One commonly used basis for market segmentation is the discovery of differences that are the following: –Statistically significant –Meaningful –Stable –Actionable differences Segmentation is geographic, psychographic, demographic, behavioral Why Differences Are Important Market Segmentation - Differences must be statistically significant: the differences found in the sample(s) truly exist in the population(s) from which the random samples are drawn. - Differences must be meaningful: one that the marketing manager can potentially use as a basis for marketing decisions - Differences should be stable: one that will be in place for the foreseeable future. - Differences must be actionable: the marketer can focus various marketing strategies and tactics, such as product design or advertising, on the market segments to accentuate the differences between segments. Testing for Significant Differences Between Two Groups - Statistical tests are used when researchers wants to compare the means or percentages of two different groups or samples. The Use of a t Test or a z Test - t Test: statistical inference test to be used with small sample sizes z Test: statistical inference test to be used when the sample size is 30 or greater (n≤30) - z Test: statistical inference test to be used when the sample size is 30 or greater Differences Between Percentages with Two Groups (Independent Samples) - Independent samples are treated as representing two potentially different populations. Null hypothesis: the hypothesis that the difference in the population parameters is equal to zero With a differences test, the null hypothesis states that there is no difference between the percentages (or means) being compared Significance of differences between two percentages: alternative to the null hypothesis is that there is a true difference between the population parameters. How Do You Know When the Results Are Significant? - If the null hypothesis is true, we would expect there to be no differences between the two percentages. Yet we know that, in any given study, differences may be expected due to sampling error If the null hypothesis were true, we would expect 95% of the z scores computed from 100 samples to fall between +1.96 and -1.96 standard errors. If the computed z value is greater than +1.96 or -1.96 it is not likely that the null hypothesis of no difference is true. Rather, it is likely that there is a real statistical difference between the two percentages. Testing the Difference Between Means - Differences between two means from independent samples - Differences between three or more means from independent samples Differences Between Means with Two Groups (Independent Samples) - The procedure for testing the significance of difference between two means from two different groups is identical to the procedure for testing two percentages. - Equations differ due to the use of a metric (interval or ratio) scale. Analysis of Variance - Analysis of variance (ANOVA): used when comparing the means of three or more groups - ANOVA is an investigation of the differences between the group means to ascertain whether sampling errors or true population differences explain their failure to be equal Basics of Analysis of Variance ANOVA will “signal” when at least one pair of means has a statistically significant difference, but it does not tell which pair. Green light procedure: If at least one pair of means has a statistically significant difference, ANOVA will signal this by indicating significance. ANOVA Advantages - A N O V A has two distinct advantages over performing multiple t tests of the significance of the difference between means. - Immediately notifies researcher if there is any significant difference - Arranges the means so the significant differences can be located and interpreted easily P-Value A p-value is the probability of obtaining the observed difference (or a larger one) in the outcome measure, given that no difference exists between treatments in the population. If the result is statistically significant (or difference), then that means your results did not happen by chance. They can be generalizable to the larger population. Chapter 14 Associative Analyses - Associative analyses: determine where stable relationships exist between two variables Relationships between Two Variables - Relationship: a consistent, systematic linkage between the levels or labels for two variables “Levels” refers to the characteristics of description for interval or ratio scales. “Labels” refers to the characteristics of description for nominal or ordinal scales. A causal linkage is one in which you are certain one variable affected or caused the other one, but with a statistical linkage you cannot make causal assertions because some other variable(s) might have some influence. Linear and Curvilinear Relationships - A linear relationship means the two variables have a “straight-line’ relationship. - A curvilinear relationship means that some smooth pattern describes the relationship. Relationships between Two Variables Linear relationship: “straight-line association” between two variables Formula for a straight line y= a+bx where y = the dependent variable being estimated or predicted a = the intercept b = the slope x = the independent variable used to predict the dependent variable Monotonic relationship: the general direction of a relationship between two variables is known - Increasing relationship - Decreasing relationship Relationships between Two Variables Non Monotonic relationship: two variables are associated, but only in a very general sense. The presence (or absence) of one variable is associated with the presence (or absence) of another. Characterizing Relationships between Variables - Presence: whether any systematic (statistical) relationship exists between two variables Pattern: the general nature of the relationship, which may take the form of a direction - Strength of association: whether the relationship is consistent-Strong associations are those in which there is a high probability that the two variables will exhibit a dependable relationship, regardless of the type of relationship being analyzed. - A low degree of association, on the other hand, is one in which there is a low probability that the two variables will exhibit a dependable relationship. Correlation and Covariation - The correlation coefficient: is an index number, constrained to fall between the range of and - The correlation coefficient communicates both the strength and the direction of the linear relationship between two metric variables. Covariation: the amount of change in one variable systematically associated with a change in another variable. The amount of linear relationship between two variables is communicated by the absolute size of the correlation coefficient. The direction of the association is communicated by the sign of the correlation coefficient. Regardless of its absolute value, the correlation coefficient must be tested for statistical significance. Chapter 15 Bivariate Linear Regression Analysis - Regression analysis is a predictive analysis technique in which one or more variables are used to predict the level of another by use of the straight-line formula. - Bivariate regression means only two variables are being analyzed, and researchers sometimes refer to this case as “simple regression”. Basic Regression Analysis Concepts - Independent variable: used to predict the dependent variable (x in the regression straight-line equation) - Dependent variable: that which is predicted (y in the regression straight-line equation) Computing the Slope and the Intercept - Least squares criterion: used in regression analysis; guarantees that the “best” straight-line slope and intercept will be calculated Improving Regression Analysis - Identify any outlier -- a data point that is substantially outside the normal range of the data points being analyzed. Multiple Regression Analysis - Multiple regression analysis uses the same concepts as bivariate regression analysis, but uses more than one independent variable. - A general conceptual model identifies independent and dependent variables and shows their basic relationships to one another. Multiple Regression Analysis Described - Multiple regression means that you have more than one independent variable to predict a single dependent variable. - The addition of independent variables changes the conceptualization by adding more dimensions, or axes, to the regression graph. - Instead of being 2-dimensional (bivariate), the graph becomes multi-dimensional (multiple). - With multiple regression, the regression plane is the shape of the dependent variables.