 Marketing Research Glossary Analysis of Variance (ANOVA) ANOVA shows whether a variable is related to one or two group membership variables. ANOVA also shows if multiple measures of numeric variables differ from each other more than could be expected due to chance. There are two types of ANOVA: One-way ANOVA shows how a group membership variable affects the values of another variable. The variable whose variation is to be analyzed is called the dependent variable (to what extent do its answers depend on the group membership variable). It must be a numeric variable (the kind in which a number is the actual answer). Ratings, dollar amounts, and quantities are some examples. Two-way ANOVA shows how group membership variables affect the values of another variable. The two-way method examines the interaction effects. These are the effects that two group variables may have in combination, apart from any effects each may have separately. The interaction effect can sometimes uncover important aspects of the relationships between variables. Central Limit Theorem As the sample size (number of observations in each sample) gets large enough, the sampling distribution of the mean can be approximated by the normal distribution. This is true regardless of the shape of the distribution of the individual values in the population.

 What sample is large enough? A great deal of statistical research has gone into this issue. As a general rule, statisticians have found that for many population distributions, once the sample size is at least 30, the sampling distribution of the mean will be approximately normal. However, we may be able to apply the central limited theorem for even smaller sample sizes if a great deal of information is already known about the target population. Cluster Analysis Cluster analysis is used for classifying objects or cases, and sometimes variables, into relatively homogeneous groups. The groups of clusters are suggested by the data and are not defined a priori. Researches at Penn and Associates select variables for cluster analysis based on hypothesis testing. Data Collection Methods There are several data collection methods and each have various advantages. Speed: Email and web page surveys are the fastest methods, followed by telephone interviewing. Interviewing by mail is the slowest. Cost: Personal interviews are the most expensive followed by telephone and then mail. Email and web page surveys are the least expensive for large samples. Internet: Web surveys offer fantastic advantages - cost, speed, and detail. Sensitive Questions: People are more likely to answer sensitive questions when interviewed directly. Factor Analysis Factor analysis is a class of procedures used for reducing and summarizing data. Each variable is expressed as a linear combination of the underlying factors. Likewise, the factors themselves can be expressed as linear combinations of the observed variables. The number of factors that should be extracted can be determined a priori. A rotation (varimax) transforms the factor matrix making it simpler and easier to interpret.

 The Normal Distribution The normal distribution is bell-shaped and symmetrical in appearance. The normal distribution's measures of central tendency (mean, median, and mode) are all identical. Numerous continuous phenomena seem to follow or can approximate the normal distribution. The normal distribution provides the basis for classical statistical inference because of its relationship to the central limit theorem. The normal distribution's middle spread is equal to 1.33 standard deviations. This means that the inter-quartile range is contained within an interval of two-thirds of a standard deviation below the mean to two-thirds of a standard deviation above the mean. The normal distribution is defined by the population mean (m) and the population standard deviation (s). Any normal random variable x can be converted to a standardized normal random variable z by the formula: z = X - m          s The random variable is always normally distributed with a mean of 0 and a standard deviation of 1. Regression The correlation coefficient, r, measures the linear association between two metric (interval or ratio scales) variables. Its square measures the proportion of variation in one variable explained by the other. The partial correlation coefficient measures additional variables. The order of a partial correlation indicates how many variables are being controlled. Research Goals The following are examples of survey questionnaires that can be accessed by all devices (desktops, laptops, tablets, and smartphones). Consumer Shopping Questionnaire Business Buying Questionnaire Advertising Concept Questionnaire Industry Research Questionnaire Business Opportunity Questionnaire Leadership Questionnaire    Pricing  Questionnaire