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SELECTING AND INTERPRETING INFERENTIAL STATISTICS
Selecting and Interpreting Inferential Statistics
Karli Bryant
BUSI 820 Quantitative Research Methods
November 18th, 2023
Discussion Board 4
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SELECTING AND INTERPRETING INFERENTIAL STATISTICS
Selecting and Interpreting Inferential Statistics
D4.5.1 – Compare and contrast a between-groups design and a within-subjects design.
When comparing and contrasting a between-groups design and a within-subjects design,
it is important to define each term. Between-groups designs have each participant in only one
condition or group and are independent of those in all other groups whereas within-subjects
designs each participant is connected to those in other conditions or levels of the independent
variable (Morgan, Leech, Gleckner, Barrett, 2020). When comparing the two designs, they are
both made up of participants and groups however, they are complete opposites in nature. As an
example, a between-groups design for a math achievement test would have three different groups
take three different tests whereas a within-subject design would have participants take a pretest
and a posttest to measure performance before and after interference (Morgan, Leech, Gleckner,
Barrett, 2020). As highlighted in their definitions, a between-groups design has independent
participant groups whereas a within-subject design has connected participant groups.
D4.5.2 – What information about variables, levels, and design should you keep in mind in
order to choose an appropriate statistic?
There are many variables, levels, and aspects of design that should be taken into
consideration in order to choose an appropriate statistic however, the process can be broken
down into several key pieces of information. First, decide how many variables are within the
research question or hypothesis as the number of variables will help determine which pieces of
information should be highlighted (Morgan, Leech, Gleckner, Barrett, 2020). For basic two-
variable statistics, the research should be looking for nominal independent variables, examples of
when both variables have many ordered levels, or examples of when both variables are normal or
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SELECTING AND INTERPRETING INFERENTIAL STATISTICS
dichotomous (Morgan, Leech, Gleckner, Barrett, 2020). For complex questions and statistics
with three or more variables, researchers should be looking for one normally distributed
dependent variable and two independent nominal variables, cases where multiple regression is
applicable or when the dependent variable is dichotomous or nominal a discriminant analysis or
logistic regression can be implemented (Morgan, Leech, Gleckner, Barrett, 2020). The primary
pieces of information would be how many variables are being taken into consideration, how
many ordered levels there are and what are the key characteristics such as nominal, ordinal, or
independent.
D4.5.3 – Provide an example of a study, including the variables, level of measurement, and
hypotheses, for which a researcher could appropriately choose two different statics to
examine the relations between the same variables. Explain your answer.
An example of a study for which a researcher could appropriately choose two different
statistics to examine the relations between the same variables would be to review which
individuals out of a group of employees that have been top performers in sales for an electronics
store would be more likely to help less successful employees increase their numbers. The
hypothesis would assume that employees who have the highest number of sales should be able to
assist less successful employees in improving sales. The independent variable would be the type
of products the employee is selling on an ordered scale based on the number of sales and the
price of those items whereas the dependent variable would be the number of sales the employee
is making in total. ANOVA could be utilized to compare the study on five different levels with
each level being made up of various products such as level one being small items like accessories
that are easy to sell and level five being big ticket items such as cellphones and gaming systems
that are more difficult to sell. In addition, the post hoc test could aid in determining how each
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SELECTING AND INTERPRETING INFERENTIAL STATISTICS
level differs in the employee’s likely ability to provide assistance to other employees as those at a
higher level of sales would be more likely to increase success than those at a lower level.
D4.5.6 – What statistic would you use if you wanted to see if there was a difference between
three ethnic groups on math achievement? Why?
The statistic you would use if you wanted to see if there was a difference between three
ethnic groups on math achievement would be ANOVA or Analysis of Variance. ANOVA is a
parametric test designed for data that have certain characteristics and approximately normal
distributions (Morgan, Leech, Gleckner, Barrett, 2020). The ANOVA test would allow multiple
means to be compared therefore, all three ethnic groups and the mean scores from the math
achievement could be easily taken into consideration.
D4.5.8– What statistic would you use if you had one independent variable, geographic
location (North, South, East, West), and one dependent variable (satisfaction with living
environment, Yes or No)?
The statistic you would use if you had one independent variable, geographic location, and
one dependent variable would be the chi-square test for independence. The chi-square test
provides information on whether the relationship is statistically significant and determines
whether two categorical variables are likely to be related (Morgan, Leech, Gleckner, Barrett,
2020). Since the two variables provided are categorical and one is independent while the other is
dependent, the chi-square test would be the best selection as it is an independent test.
D4.5.9– What statistic would you used if you had three normally distributed (scale)
independent variables (weight of participants, age of participants, and height of
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SELECTING AND INTERPRETING INFERENTIAL STATISTICS
participants), plus one dichotomous independent variable (academic track) and one
dependent variable (positive self-image), which is normally distributed?
The statistic you would use if you had three normally distributed independent variables,
plus one dichotomous independent variable and one dependent variable is multiple regression.
Multiple regression is primarily utilized to predict a scale or normal dependent variable from two
or more independent variables and since the example provided has three normally distributed
independent variables, it would be the best selection (Morgan, Leech, Gleckner, Barrett, 2020).
Multiple regression will allow for the relationship between the independent variables,
dichotomous variables, and dependent variables to be reviewed and analyzed appropriately.
