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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).
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