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?
Once the sample size is at least 30, the sampling distribution of the mean will be approximately normal. If a great deal of information is already known about the target population, then smaller sample may apply.

Data Collection
Email-to-online is the fastest method of data collection offered by Penn and Associates; mail is the slowest.
Personal interviews are the most expensive data collection offered by Penn and Associates; email-to-online is the least expensive.
People are more likely to answer sensitive questions when interviewed directly.

The Normal Distribution
The Normal Distribution (bell-shaped and symmetrical in appearance) measures of central tendency (mean, median, and mode) are all identical. Numerous continuous phenomena 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 and the population standard deviation. The random variable is always normally distributed with a mean of 0 and a standard deviation of 1. Any normal random variable x can be converted to a standardized normal random variable z by the formula:
z = X - m
         s

Research Goals
The following are examples of survey questionnaires that can be accessed by all devices (phones, tablets, laptops, desktops).



Consumer Shopping Questionnaire
Consumer Shopping Instant Report

Business Buying Questionnaire
Business Buying Instant Report

Advertising Concept Questionnaire
Advertising Concept Instant Report

Industry Research Questionnaire
Industry Research Instant Report

Business Opportunity Questionnaire
Business Opportunity Instant Report

Leadership Questionnaire   
Leadership Instant Report

Pricing Questionnaire
Pricing Instant Report