Relationships Between Variables

Question 1

What is a better way to show data in tables and why?

Answer 1

In percentages because you can see clearly the relationship between variables.

Question 2

How do you use tables with two continuous variables?

Answer 2

Break data down into bands so that information can be shown more clearly and compact.

Question 3

How do you use tables with one continuous and one nominal variable?

Answer 3

A simple can be used, but the mean and other descriptive statistics for the continuous variable are normally given.

Question 4

Using diagrams: Two nominal variables

Answer 4

You can use either a compound or a stacked bar chart. May need to collapse some categories.

Question 5

What is a bad stacked bar chart?

Answer 5

One with too many bars, doesn’t clearly show the relationships. Looks too busy.

Question 6

Using diagrams: Two continuous variables

Answer 6

Use a scatter plot and then add a line of best fit to help visualise the relationship between the two.

Question 7

What can a line of best fit show?

Answer 7

It shows whether a relationship is positive/negative. If it is steep then there is a strong relationship and the variables have a great affect on each other and if it is flat then they don’t.

Question 8

What direction is a positive line of best fit?

Answer 8

Bottom left to top right.

Question 9

What direction is a negative line of best fit?

Answer 9

Top left to bottom right

Question 10

How do we quantitatively estimate how the two variables covary?

Answer 10

By using the covariance formula

Question 11

What is the covariance?

Answer 11

It is like variance but with two variables.

Question 12

How do you use tables with two nominal variables?

Answer 12

A cross-tabulation is usually appropriate.

May need to collapse categories if there are too many (e.g. gender and smoker/non-smoker)

Question 13

How does covariance work?

Answer 13

Like in variance where we find how much one data point deviates from the mean and then sum all the deviations and divide them by the number of points, we do this but with two variables which we times together then sum all the deviations before dividing by the number of data points.

Question 14

If the deviations have the same sign, what is the product?

Answer 14

Always positive

Question 15

If the deviations are of opposite sign, what is the product?

Answer 15

Product is negative

Question 16

What does covariance show us?

Answer 16

If the number is low then there is little covariance, and if it is high then there is high covariance.

Question 17

Is there a difference between covariance and correlation?

Answer 17

Yes. Covariance is used to calculate the correlation but there is more to correlations and they both produce different numbers. Correlations have two different characteristics.