Slide 1:Basic Marketing Research: Using Microsoft Excel Data Analysis, 2nd Edition Alvin C. Burns Louisiana State University Ronald F. Bush University of West Florida Prentice Hall Publishers


Slide 2:2 Generalizing Your Sample Findings to the Population


Slide 3:As long as we take a representative sample (probability), we have the tools to generalize the findings in the sample data to the total population. For example, researchers at MRI’s sample data estimates shows customers have a mean preference for a new service of 3.7 on a 5 point scale. This sample finding is an estimate yet, with the right tools, MRI researchers can generalize the sample finding to the total customer population. The Concept of Generalization


Slide 4:A sampling finding: is a computed value based on sample data. These values may be either a percentage, average, or other analysis value. Sample Finding


Slide 5:A population fact: is defined as the true value when a census of the population is taken and the “true” value is determined using all members of the population. It is rare that the population fact is ever known. Sample findings, however, are used to estimate population facts. Sample findings are our best estimates of population facts though they always contain sample error. Population Fact


Slide 6:Generalization: is the act of estimating a population fact from a sample finding. Generalization


Slide 7:Generalization is a form of logic in which you make an inference about an entire group based on some evidence about that group. The stronger the evidence, the more confident are your generalizations about the population. The strength of the evidence is based upon the sample size (the larger the sample size, the greater the evidence. the variance within the sample data (the less the variance in the sample data, the stronger the evidence.) Generalization


Slide 8:When we use a sample finding to estimate population values, we know the sample finding contains sampling error. Therefore, we translate our sample findings into ranges: For example, “33% ± x%” Generalizing Sample Data to the Total Population


Slide 9:Statisticians refer to population values as parameters. Parameter estimation: is defined as the process of generalizing a sample’s finding to the population. Generalizing a Sample’s Findings: Estimating the Population Value


Slide 10:Population parameters are designated by Greek letters. p = percent µ = mean or average Sample findings are designated by lowercase Roman letters. p = percent = mean or average Symbols Used in Generalizing Sample Findings to the Population


Slide 11:Calculating a confidence interval: which is a range (lower and upper boundary) into which the researcher believes the population parameter falls with an associated degree of confidence (typically 95% or 99%). How to Estimate a Population Percentage When We Have Categorical Data


Slide 12:The research objective measures the percentage of respondents who ordered Egg McMuffins for breakfast at McDonald’s. Data are categorical (“yes,” ordered Egg McMuffin; “no,” did not order Egg McMuffin) It is proper to calculate percentages when summarizing categorical variables. Let’s assume 60% of respondents ordered Egg McMuffin. How to Estimate a Population Percentage When We Have Categorical Data cont.


Slide 13:Formula to Estimate a Population Percentage Using a Confidence Interval


Slide 14:14 How to Estimate the Population Value for a Percentage


Slide 15:How to Estimate the Population Value for a Percentage cont.


Slide 16:The size of the standard error depends on two factors: Variability, denoted as p x q Sample size, denoted as n The Standard Error of the Percentage


Slide 17:If you took many, many samples, and plotted the sample percentage, p, for all these samples as a frequency distribution, it would approximate a bell-shaped curve called the sampling distribution. The Sampling Distribution


Slide 18:The standard error: is a measure of the variability in the sampling distribution based on what is theoretically believed to occur were we to take a multitude of independent samples from the same population. The shape of the sampling distribution is a function of variability and sample size. The Sampling Distribution cont.


Slide 19:The Sampling Distribution cont.


Slide 20:Theoretically if you took many, many samples and plotted your p, or percentage, your frequency distribution would look like a bell-shaped curve. 95% of your percentages would fall between ± 1.96 times the standard error of the percentage. This is what allows us to say that we are 95% confident that the population percentage falls in the range we have calculated by our confidence interval. Understanding Level of Confidence


Slide 21:Variability and Sampling Distribution


Slide 22:How to Obtain a 95% Confidence Interval for a Percentage Using XL Data Analyst


Slide 23:How to Obtain a 95% Confidence Interval for a Percentage Using XL Data Analyst cont.


Slide 24:The research objective: to determine the average number of minutes readers spend reading the New York Times. With metric data, the appropriate summarization statistic would be the average. How to Estimate a Population Average When Using Metric Data


Slide 25:Formula for a Population Average Estimation


Slide 26:The same logic is used here as with the standard error of the percentage, that is, the standard error is larger with more variability (higher standard deviation) and smaller with large samples (n). Standard Error of the Average


Slide 27:How to Estimate the Population Value for an Average


Slide 28:How to Estimate the Population Value for an Average cont.


Slide 29:If we conducted the survey many, many times and plotted the average number of minutes of reading the New York Times for each sample in a frequency distribution, it would look like a bell-shaped curve. 95% of the sample averages would fall in the confidence interval defined by the population average ± 1.96 times the standard error of the average. This allows us to state that we are 95% confident that the true population average falls within the range calculated by our confidence interval. Interpreting a Confidence Interval for an Average


Slide 30:How to Obtain a 95% Confidence Interval for an Average with XL Data Analyst


Slide 31:How to Obtain a 95% Confidence Interval for an Average with XL Data Analyst cont.


Slide 32:The Six Step Approach to Data Analysis for Generalization: Confidence Intervals


Slide 33:The Six Step Approach to Data Analysis for Generalization: Confidence Intervals cont.


Slide 34:The Six Step Approach to Data Analysis for Generalization: Confidence Intervals cont.


Slide 35:Sometimes the marketing researcher or manager – client makes a statement about the population parameter based on prior knowledge, assumptions, or intuition. This statement, called a hypothesis, most commonly takes the form of an exact specification as to what the population value is. Hypothesis testing: is a statistical procedure used to “support” (accept) or “not support” (reject) the hypothesis based on sample information. Testing Hypotheses about Percents or Averages


Slide 36:Hypothesis testing uses sample data as the only source of current information about the population. Hypothesis testing is appropriate when the sample is a probability sample and is therefore representative of the population. Sample results are used to determine whether or not the hypothesis about the population parameter has been supported. Hypothesis Testing


Slide 37:Testing a Hypothesis about a Percentage


Slide 38:In the formula, the sample percent (p) is compared to the hypothesized population percent (pH). p is compared to (pH) because in a hypothesis test, one tests the null hypothesis. The null hypothesis: is a formal statement that there is no (or null) difference between the hypothesized p value and the p value found in the sample. This difference is divided by the standard error to determine how many standard errors away from the hypothesized parameter the sample percentage falls. Testing a Hypothesis about a Percentage cont.


Slide 39:IF the hypothesized value is equal to the population value we would expect 95% of our sample percentages to fall between ± 1.96 standard errors. In other words, to support the hypothesis, we would expect z to fall between ± 1.96. Testing a Hypothesis about a Percentage cont.


Slide 40:Acceptance and Rejection regions for Hypothesis Tests


Slide 41:A directional hypothesis: is one that indicates the direction in which you believe the population parameter falls relative to some hypothesized average or percentage. To test these hypotheses, the sample percent or average must be in the right direction The critical z value is 1.64 (for the 95% level of confidence. 1.64 is used instead of 1.96 because we are using only one side of the bell-shaped curve in what is known as a one-tailed test. Testing a Directional Hypothesis


Slide 42:How to Test a Hypothesis about a Percentage with XL Data Analyst


Slide 43:How to Test a Hypothesis about a Percentage with XL Data Analyst cont.


Slide 44:If your variable is metric, the average is the appropriate summarization statistic. If we have a hypothesis about an average, we use the following formula: Testing a Hypothesis about an Average


Slide 45:Example: Testing a Hypothesis about an Average cont.


Slide 46:Testing a Hypothesis about an Average cont.


Slide 47:How to Test a Hypothesis about an Average with XL Data Analyst


Slide 48:How to Test a Hypothesis about an Average with XL Data Analyst cont.


Slide 49:The Six Step Approach to Data Analysis for Generalization Objectives: Hypothesis Test


Slide 50:The Six Step Approach to Data Analysis for Generalization Objectives: Hypothesis Test cont.


Homework :Homework Page 381 Questions 4-7, 13,15-18.