L3 - Associations

Question 1

What kind of analysis is used to assess association between continuous variables?

Answer 1

Correlation

Question 2

What kind of analysis is used to assess association between categorical variables?

Answer 2

Odds Ratios (and contingency tables)

Question 3

What is covariance?

Answer 3

This is a measure of the degree of concurrent variation in people’s scores on two variables. This is a measure of strength and direction of linear association between two variables.Can be pop parameter or sample statistic

Question 4

What are similar features of variance and covariance?

Answer 4

• Similar formula!!- their size depends on the metric of the variables used to calculate it.. so they need to be standardised.. we need to know whether something is a big or small covariance—>PEARSON’S CORRELATION COEFFICIENT!

Question 5

What is pearson’s correlation coefficient?

Answer 5

This is basically the standardised version of covariance!This is where the deviation scores are replaced with z scores in the process of calculating covariance. denoted with an “r”

Question 6

What are some properties of the t distribution?

Answer 6

• bell shaped - Variability defined by its df- as df increases, the t dist converges to a standard normal dist

Question 7

Which distribution does the sampling distribution of a population correlation coefficient of zero correspond to?

Answer 7

dont know right now!!

Question 8

What are degrees of freedom?

Answer 8

It basically means you have certain constraints operating, and you only have a certain number (df) of options until the solution is known.

Question 9

how do you calculate the degrees of freedom for a correlation?

Answer 9

df = n-2basically, because there are 2 variables

Question 10

How does the the regions of rejection for a normal distribution differ from a t distribution?

Answer 10

The region of rejection is further out from zero in the t distribution

As df increases, it pushes the region close to 1.96 which is the normal distribution.

Question 11

How is the observed test statistic found for sample correlation?

Answer 11

Tobs = (r - null hypoth value) / standard error.

whereby, standard error is:

square root of: (1- r^2)/(n-2)

Question 12

When will a larger value of Tobs occur?

Answer 12

When:

• There is a bigger correlation (r), because then the numerator is larger and standard error is smaller
• There is a smaller standard error

Question 13

Why is pearson correlation coefficient an attractive statistic for research?

Answer 13

Because it is a natural effect size measure. there is no need to transform the value to know the size of the effect.

Question 14

When would we use fisher’s r to z transformation?

Answer 14

When there is a large sample, for confidence interval estimates on XECI

Question 15

What are the underlying assumptions of Pearson Correlations?

Answer 15

That the scores on both variables are..

• linearly related to each other.
• continuous
• independently observed of each other
• normally distributed
• measured without error
• unrestricted in their range

formula to calculate pearson correlation is biased, but consistent.
Violation of the assumptions causes further bias.

Question 16

What is a cross-classified contingency table?

Answer 16

A table in which each cell uniquely identifies the number of people (frequency) with joint membership in two variables.

Question 17

When is there a dependency between two categorical variables?

Answer 17

When the relative frequency of people in the categories of one variable covary with the categories of another variable.

Question 18

What test do we use to determine whether two categorical variables or independent or dependent?

Answer 18

CHI SQUARED TEST!

Question 19

How do you perform a Chi Squared NHST?

Answer 19

1. Calculate Tobs:
   = sum of all ((observed cell freq - expected freq) / observed cell freq)
2. Calculate the df:
   df = (rows - 1 ) x (columns -1)
3. Find the critical value for the alpha value, with the corresponding df.
4. Reject null if Tobs is LARGER. than critical value.

Question 20

How do you calculate expected frequencies?

Answer 20

(row marginal freq x column marginal freq) / n

Question 21

What can analysis of expected frequencies show?

Answer 21

Greater discrepancy between obs and expected cell frequencies indicates greater degree of dependency.

greater dependency reflects stronger association between the two variables.

stronger association corresponds to larger observed chi square statistic.

Question 22

What does the chi square distribution look like?

Answer 22

It is positively skewed, due to squared features (all values on positive side of x axis).

So critical region only in upper tail.
What does the chi square distribution look like?
Shape of this distribution is only affected by df.

Question 23

What can a chi squared test tell you in the end?

Answer 23

Whether there is an association or not.

No metric.

Question 24

What is an odds ratio?

Answer 24

An odds ratio indicates the odds of one category occurring in one variable, relative to the odds of a second and different category occurring in another variable.

Question 25

How is an odds ratio calculated?

Answer 25

For a contingency table: (A x D) / (B x C)

Question 26

How are odds calculated?

Answer 26

Probability of the event occuring / (1- Prob.)

Question 27

What are the properties of an odds ratio?

Answer 27

If OR = 1 then the two variables are independent and have no association.

OR can never be negative.

Stronger association is indicated by an estimated value further from 1.

Odds ratio is undefined if any observed cell freq is zero.

OR is a symmetric relationship between variables, so it doesn’t matter which row or column has what variable.

It is both a sample statistic and a population parameter.

Question 28

What does it mean when we have a 95% CI for an odds ratio that captures 1?

Answer 28

It provides no evidence for rejecting the null hypothesis.

Question 29

What happens when the odds ratio is below 1?

Answer 29

It is harder to interpret, so we take the reciprocal of the estimated value (1/x).

If it’s in a CI, we will swap the lower bound to become the upper bound and vice versa.

only done when BOTH values of a CI are