SACR 3080 FINAL EXAM QUESTIONS WITH
COMPLETE ANSWERS
In the formula for r, what is one function of the SDs in the denominator? - ANSWER The
SDs in the denominator is there to ensure that r stays in the range from minus to plus
one.
Why is the numerator of Pearson's r referred to as the "Covariance"? - ANSWER In its
form, the Covariance resembles a Variance, and it shows how the two variables move
together
In the formula for r, how is evidence of a positive association tallied up? Of a negative
association? - ANSWER Cases in which two variables score above their mean suggest a
positive association, as opposed to cases which lie below their mean. In either case, the
product of the two scores will be positive.
Cases in which two variables are on opposite sides of their means suggest a negative
association, and the products of their scores will be negative.
Starting from a formula for r that does not use algebraic notation, show what happens
when the variables are standardized. - ANSWER r = Cov(x,y)/(SD(x)SD(y)
when standardized it turns into:
∑ zₓzᵧ /N
,in words, this is the mean of the products of the standardized variables
What are two ways to interpret Pearson's r? - ANSWER Pearson's measure tells us how
much of an SD of change we get in one variable for an SD of change in the other. If we
square r, we obtain a PRE measure which tells us the proportion of Variance in one
variable that can be predicted from the other.
What is the difference between Spearman's ρ and Pearson's r? - ANSWER Spearman's
measure is calculated using the ranks of cases rather than their scores.
Spearman - for ordinal - understand the strength of 2 relationship between 2 variables
Pearson - interval scales - strength of the correlation- most widely used
What do we do before calculating rho if more than one case lies in a category? -
ANSWER If several scores lie in the same category, we suppose that, with finer
measurement, they could be distinguished, and we take the median rank that would
then be found for the set.
We assign each case in the category the median rank for the category.
Why might we find entries only in the lower triangle of a correlation matrix? - ANSWER
,The entries in the upper triangle will be the same as corresponding entries in the lower
triangle, and so are unnecessary. The entries on the diagonal represent rs between
variables and themselves, which are of course 1.00, so they are also unnecessary.
What is a scatterplot? What are some alternatives? - ANSWER A scatterplot is a graph in
which cases are placed at points corresponding to the scores on two variables, one
plotted on each axis. An alternative would be a boxplot.
What is a moving average? - ANSWER A moving average is an average of the values for
two or more points in time. The points used shift as we move forward in time, or across a
graph.
What are the two advantages of a bar chart over a line graph? Two disadvantages? -
ANSWER In a bar chart, the level top of the bar can make it easier to estimate a value on
the y-axis, and, particularly if coloured, a bar chart can have greater visual impact. On the
other hand, bars can break up the flow of a line, and require us to use more ink to
express the same information as in a line graph.
what is a mosaic plot? Why are the rectangles in the plot different sizes? Why do we care
about the "Pearson's residuals"? - ANSWER each cell is represented by a rectangle whose
area is proportional to the number of cases in the cell.
pearson's residuals tells us whether the observed cell value is greater or smaller than the
expected value
, Why are some cells shaded or patterned differently? Why might we be interested in a
cell that is particularly heavy (dark) or particularly light? - ANSWER the shading and
patterns represent the standardized residuals, whereas dark/heavy cells represent a
larger difference between the observed and expected value.
If we wanted to percentage the table showing vote by region, discussed above, in which
direction direction would we do this? How would we then interpret the differences in
percentages? - ANSWER We percentage down the columns rather than across the rows.
If we have percentages down the columns, we can see how the figures change as we
move across, from one category of the IV to another.
What measure do we typically use to identify heavy cells? How is it related to chi-square?
What values of the measure are we typically interested in? - ANSWER - we typically use
the standardized residual.
-it is the signed square root of the cells contribution for chi-square.
-we typically look for the values of at least +2 or -2, but for tables based on large
samples, which may lead to many values greater than this, we tend to look only at the
largest residuals
What is an association plot? What is the difference between rectangles above a line and
those below? - ANSWER an association plot shows us which cells in a table are heavy
and which are light, and thus informs us of the key aspects of how two variables are
related.
rectangles above a line represent heavy cells, and a rectangle below represents light cells
COMPLETE ANSWERS
In the formula for r, what is one function of the SDs in the denominator? - ANSWER The
SDs in the denominator is there to ensure that r stays in the range from minus to plus
one.
Why is the numerator of Pearson's r referred to as the "Covariance"? - ANSWER In its
form, the Covariance resembles a Variance, and it shows how the two variables move
together
In the formula for r, how is evidence of a positive association tallied up? Of a negative
association? - ANSWER Cases in which two variables score above their mean suggest a
positive association, as opposed to cases which lie below their mean. In either case, the
product of the two scores will be positive.
Cases in which two variables are on opposite sides of their means suggest a negative
association, and the products of their scores will be negative.
Starting from a formula for r that does not use algebraic notation, show what happens
when the variables are standardized. - ANSWER r = Cov(x,y)/(SD(x)SD(y)
when standardized it turns into:
∑ zₓzᵧ /N
,in words, this is the mean of the products of the standardized variables
What are two ways to interpret Pearson's r? - ANSWER Pearson's measure tells us how
much of an SD of change we get in one variable for an SD of change in the other. If we
square r, we obtain a PRE measure which tells us the proportion of Variance in one
variable that can be predicted from the other.
What is the difference between Spearman's ρ and Pearson's r? - ANSWER Spearman's
measure is calculated using the ranks of cases rather than their scores.
Spearman - for ordinal - understand the strength of 2 relationship between 2 variables
Pearson - interval scales - strength of the correlation- most widely used
What do we do before calculating rho if more than one case lies in a category? -
ANSWER If several scores lie in the same category, we suppose that, with finer
measurement, they could be distinguished, and we take the median rank that would
then be found for the set.
We assign each case in the category the median rank for the category.
Why might we find entries only in the lower triangle of a correlation matrix? - ANSWER
,The entries in the upper triangle will be the same as corresponding entries in the lower
triangle, and so are unnecessary. The entries on the diagonal represent rs between
variables and themselves, which are of course 1.00, so they are also unnecessary.
What is a scatterplot? What are some alternatives? - ANSWER A scatterplot is a graph in
which cases are placed at points corresponding to the scores on two variables, one
plotted on each axis. An alternative would be a boxplot.
What is a moving average? - ANSWER A moving average is an average of the values for
two or more points in time. The points used shift as we move forward in time, or across a
graph.
What are the two advantages of a bar chart over a line graph? Two disadvantages? -
ANSWER In a bar chart, the level top of the bar can make it easier to estimate a value on
the y-axis, and, particularly if coloured, a bar chart can have greater visual impact. On the
other hand, bars can break up the flow of a line, and require us to use more ink to
express the same information as in a line graph.
what is a mosaic plot? Why are the rectangles in the plot different sizes? Why do we care
about the "Pearson's residuals"? - ANSWER each cell is represented by a rectangle whose
area is proportional to the number of cases in the cell.
pearson's residuals tells us whether the observed cell value is greater or smaller than the
expected value
, Why are some cells shaded or patterned differently? Why might we be interested in a
cell that is particularly heavy (dark) or particularly light? - ANSWER the shading and
patterns represent the standardized residuals, whereas dark/heavy cells represent a
larger difference between the observed and expected value.
If we wanted to percentage the table showing vote by region, discussed above, in which
direction direction would we do this? How would we then interpret the differences in
percentages? - ANSWER We percentage down the columns rather than across the rows.
If we have percentages down the columns, we can see how the figures change as we
move across, from one category of the IV to another.
What measure do we typically use to identify heavy cells? How is it related to chi-square?
What values of the measure are we typically interested in? - ANSWER - we typically use
the standardized residual.
-it is the signed square root of the cells contribution for chi-square.
-we typically look for the values of at least +2 or -2, but for tables based on large
samples, which may lead to many values greater than this, we tend to look only at the
largest residuals
What is an association plot? What is the difference between rectangles above a line and
those below? - ANSWER an association plot shows us which cells in a table are heavy
and which are light, and thus informs us of the key aspects of how two variables are
related.
rectangles above a line represent heavy cells, and a rectangle below represents light cells
