Inferential Statistics Week 2 Solution
Inferential Statistics
2. What are degrees of freedom? How are they calculated?
Answer: The degree of freedoms is equal to the number of independent observation or the number of
subjects in the data, minus the parameters estimated. A parameter to be estimated is related to the
value of an independent variable and included in a statistical equation. A researcher may estimate
parameters using different amounts or pieces of information and the number of independent pieces of
information he or she used to estimate statistic or a parameter is called the degree of freedom.
Calculation:
Step 1
Determine what type of statistical test I need to run. Both t-tests and chi-squared tests use
degrees of freedom and have distinct degrees of freedom tables. T-tests are used when the
population or sample has distinct variables. Chi-squared tests are used when the population or
sample has continuous variables. Both tests assume normal population or sample distribution.
Step 2
Identify how many independent variables I have in my population or sample. If I have a sample
population of N random values then the equation has N degrees of freedom. If my data set
required me to subtract the mean from each data point--as in a chi-squared test--then I will have
N-1 degrees of freedom.
Step 3
Look up the critical values for my equation using a critical value table. Knowing the degrees of
freedom for a population or sample does not give me much insight in of itself. Rather, the correct
degrees of freedom and my chosen alpha together give me a critical value. This value allows me
to determine the statistical significance of my results.
3. What do inferential statistics allow you to infer?
Answer: Inferential statistics is concerned with making predictions or inferences about a
population from observations and analyses of a sample. That is, we can take the results of an
analysis using a sample and can generalize it to the larger population that the sample represents.
In order to do this, however, it is imperative that the sample is representative of the group to
which it is being generalized.
To address this issue of generalization, we have tests of significance. A Chi-square or T-test, for
example, can tell us the probability that the results of our analysis on the sample are
representative of the population that the sample represents. In other words, these tests of

significance tell us the probability that the results of the analysis could have occurred by chance
when there is no relationship at all between the variables we studied in the population we
studied.
4. What is the General Linear Model (GLM)? Why does it matter?
Answer:
The General Linear Model (GLM) underlies most of the statistical analyses that are used in applied and
social research. It is the foundation for the t-test, Analysis of Variance (ANOVA), Analysis of Covariance
(ANCOVA), regression analysis, and many of the multivariate methods including factor analysis, cluster
analysis, multidimensional scaling, discriminant function analysis, canonical correlation, and others.
Because of its generality, the model is important for students of social research. Although a deep
understanding of the GLM requires some advanced statistics training, I will attempt here to introduce
the concept and provide a non-statistical description.
When there is a relationship among the variables and then they can expressed by the general linear
models.
5. Compare and contrast parametric and nonparametric statistics. Why and in what types of cases would
you use one over the other?
Answer: Nonparametric statistics (also called “distribution free statistics”) are those that can describe
some attribute of a population, test hypotheses about that attribute, its relationship with some other
attribute, or differences on that attribute across populations, across time or across related constructs,
that require no assumptions about the form of the population data distribution(s) nor require interval
level measurement.
In the literal meaning of the terms, a parametric statistical test is one that makes assumptions about the
parameters (defining properties) of the population distribution(s) from which one's data are drawn,
while a non-parametric test is one that makes no such assumptions. In this strict sense, "non-
parametric" is essentially a null category, since virtually all statistical tests assume one thing or another
about the properties of the source population(s).
We will use parametric statistics and non-parametric statistics in the following situation:

Inferential Statistics Week 2 Solution

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