Week 4
Topic 1 Describe/explain in your own words: What are the “Facts about Correlation” (see
section 4.6) for interpreting correlation coefficients and scatterplots.
Are 4 Facts:
The first one establishes that the correlation does not distinguish between explanatory
variables and response variables, and this means that it does not matter which variable you
place on the x-axis or the y-axis. The calculation of r is independent of the position of the
variables on the axes.
The second Facts, the correlation r does not change when the units of measures of the
variables are changed, and this is because r uses standardized measures and is
dimensionless
The third Facts refers to the possibility that r can have positive and negative values. In the
case of positive values, it indicates a positive association between the variables and in the
case of being negative, it indicates a negative association between the variables.
The fourth Facts indicates that the value of r can oscillate between -1 and 1. If the value of r
is zero or close, it indicates that the association between the variables is very weak. And the
association between the variables strengthens as r approaches 1 or -1. For there to be a
perfect linear relationship between the variables, the value of r=1 or -1.
Topic 2: Why is it necessary to declare variables as independent (explanatory) and
dependent (response) for regression modeling, but not needed for correlation analysis?
Because the linear regression model allows obtaining a relationship function between two
variables, and if it influences which variable is taken as independent (explanatory, x-axis)
and which as dependent (response, y-axis). While the correlation allows obtaining a
dimensionless number that accounts for the degree of strength of the association of two
variables without taking into account if one is the independent variable (explanatory) and
the other dependent (response).
Topic 3: Explain what does “correlation does not imply causation” mean regarding
“lurking” or “confounding” variables. Variable lurking pag 293, respuesta pag 296
Correlation does not imply causation because a controlled experiment has not been carried
out that eliminates possible lurking or confounding variables that may influence the results
of the response variable (Moore et al., 2018, pp. 293-296).
Topic 4. Read the article entitled “Exams and Grandmas” (see Start Here Folder). Do you
agree or disagree with the author? Please explain in terms of statistical reasoning.
I do not agree with the author, even when he dedicated himself to collecting data and
performed statistical procedures to search for possible relationships, some type of
experimental control was not observed to avoid lurking or confounding variables, such as
possible diseases, age, or risk situations that could influence the results (Moore et al., 2018,
pp. 293-296).
Topic 5:
a. Create an SPSS data set with the data in Table 6.1.
b. Run the crosstabs procedure and summarize the results.
c. Attach your SPSS output and rely on (paraphrase) the book presentation to guide your
statements/conclusions. Please paraphrase in your own words, which means do not simply
“copy” sentences from the book (with or without a reference). In your summary, make sure
to describe/explain what is meant by marginal and conditional distributions.
In the crosstab above, it can see two main variables make up the table, sex and
Degrees_Conferred. The gender variable occupies the position of the rows (2 rows) and the
variable Degrees_Conferred occupies the position of the columns (4 columns). By
intercepting rows and columns, it is possible to identify the number of women and men
who have been awarded a certain degree. And finally, the totals for the columns and rows
appear in the lower margin and in the right margin, and the global total located in the lower
right part must match for both.
The marginal distribution gives information about the values at the margins of the two-way
table (Moore et al., 2018, p. 326). While the conditional distribution gives information
about a condition that involves both variables (Moore et al., 2018, p. 329).
References
Moore, D, S.; Notz, W. I., & Fligner, M. (2018). The basic practice of statistics (8th
Edition). Macmillan Learning.