W4 - Analysis of Count and Proportion Data

Question 1

What are the two types of Chi-Squared Tests?

Answer 1

Goodness of fit or “one-way” (1-independent variable)

Conteingency table/cross-tab or 2-way analyses (2 indepedent variables)

Question 2

What is does a “goodness of fit” test measure?

Answer 2

How well an observed distribution of scores matches a distribution expected by chance.

hence the name “goodness of fit”

Question 3

How would you conduct a “goodness of fit” test?

Answer 3

Obtain observed frequences for each level of the IV

Compare it to what a chance outcome would be.

Question 4

What shape does a distribution based on chance look like?

Answer 4

Rectangle

Question 5

These tests are an example of what type of test?

Answer 5

Goodness of Fit

Question 6

If we are conducting a goodness of fit test on 3 vending machines and we observe 120 people, how many people should go each vending machine if the distribution was chance?

Answer 6

40 each

120/3

Question 7

What is distributional similarity

Answer 7

How similar one distribution is to another

e.g. in a Goodness of Fit test, how well does the observe data match the chance data

Question 8

What is the forumla for a Chi-Squared Test?

Answer 8

χ² = Σ ( O – E )² / E

Sum of [observed - expected frequency per level] / expected frequency

0 = Observed count per level

E = Expected count per level

Question 9

What is the symbol that we use for the “obtained test value” in a Chi-Squared Test?

Answer 9

X²

Question 10

How do we know if a Chi-Squared obtained test value is significant?

Answer 10

Compare the attained value with the critical value

If attained is greater than critical then it is significant

Critical value has something to do with DOF @ 20 mins in lecture if want to rewatch but doesn’t seem important

Question 11

What is the degrees of freedom in a Goodness of Fit test?

Answer 11

The number of variables minus 1

Question 12

How should you interpret a Goodness of Fit (or one-way) test?

Answer 12

Look for if the observed distribution of scores differs significantly from what would be expected by chance.

Are there any frequences which occur more than others?

Question 13

What does a 2-way chi-squared test aim to accomplish?

Answer 13

To determine whether there is an ASSOCIATION between 2 categorical / ordinal variables.

It is a test of independence

Question 14

What is meant by “a 2-way chi-squared test is a test of independence”?

Answer 14

Are the variables independent (no effect) or interdependent (related/ an effect)

Question 15

Which test do we use to compare whether 2 variables are independent of one another (a familiar test)?

Answer 15

2-way chi-squared test

Question 16

To test these hypothesis, what test should you conduct?

Answer 16

2-way chi-squared test

“familiar” or “independence” test

Question 17

What is the formula for calculating expected frequencies for a 2-way chi-squared test?

Answer 17

[Row-total / Total N] * column total

In the example

For “Men Mach 1” = (180 /290) * 90 = expected frequency at40 square

For “Women Mach 2” = (110 / 290) * 80 = expected frequency at 20 square

Question 18

What is the critical value for a 2-way chi-squared test?

Answer 18

The (number of rows minus 1) times the (number of columns take 1)

i.e. The observed chi-sq value is compared
with the critical value for

Df = (r – 1). (c-1) = 1.2 = 2

Critical value = 5.99

Your value is 18.69

The two variables are associated or
NOT independent

Question 19

How do you interpret if the chi-squared value (X²) is significant?

Answer 19

If the critical value is lower than the observed value

example

Critical value = 5.99

Your value is 18.69

The two variables are associated or
NOT independent

Question 20

What is the minimum expected frequency (MEF) that is allowed in order to have use a chi-squared test?

minimum expected frequency (MEF) assumption

Answer 20

No more than 25% of cells can have a minimum expected frequency of <5

SPSS will give you an error if you try to compute with more than 25% with less than 5 expected frequency

Question 21

What test should you use if the minimum expected frequency (MEF) assumption for a chi-squared test is violated?

Answer 21

Kolmogorov-Smirnov Test

Question 22

For a chi-squared test, what effect size measure do we use?

Answer 22

Effect size is given by: Kramer’s V

With the exception of a 2x2 chi-squared

Question 23

What are “standardised residules” in chi-squared tests and what are they used for?

Answer 23

A standardised measure of the difference between the observed frequency and the expected frequency

They can see how big the difference between the two groups are in chi-squared tests

Values of 2+ are large

Question 24

When should you use a Fisher Exact Test?

Answer 24

When 2 x 2 chi-sq is invalid due to violation of minimum expected frequencies (MEF) assumption

When you have really small frequencies

Question 25

How do you report a **Fisher Exact Test?**

Answer 25

Reported as: "Fisher Exact, p \< .05" *Interpretation same as Chi-sq*

Question 26

What are **binomial tests** used for?

Answer 26

To test for the probability of binary outcomes. e. g. left vs right turns, good vs. bad in a batch, left v right handers etc. * Does the probability obtained for one event (e.g., Right) differ from what is expected by chance?*

Question 27

What symbol do we usually use in a binomial test?

Answer 27

**Z-approximation** or **Z-test**

Question 28

What is the calculation for a **Z-test**?

Answer 28

**Z = X – Mean / SE** X = observations of binary outcome M = Number expected by chance SE = standard error = √n.p.(1-p), where p = probability of the event *(n = number of trials)*

Question 29

What *type* of test is a **proportion difference** test?

Answer 29

Parametric Test

Question 30

Describe what a **Proportion Difference** test examines?

Answer 30

Examines whether **two samples are drawn from populations with the same proportions of a given characteristic** *like a t-test for proportions*

Question 31

These questions should be investigated using what type of test?

Answer 31

Proportion Difference (PD) test

Question 32

Why would you use a PD test instead of a Chi-sq test?

Answer 32

1) Easier to interpret: you get a Z score and the test statistic (difference between proportion is clear) 2) Can calculate a confidence interval

Question 33

How do you calculate a **proportion difference (PD)** test?

Answer 33

*Following from image* P’ = the overall probability of the event or quality (e.g., smoking in the whole sample) If E1 = instances in sample 1 (n1) and E 2 = instances in sample 2 (n2) **Then p’ = [E1+E2] / [n1 + n2]**

Question 34

What is a **Kappa test** used for?

Answer 34

Used to examine inter-rater reliability in situations involving 2 independent raters

Question 35

Which test should you use to test these two examples? Example 1: 2 clinical psychologists are asked to assess 50 clients as having or not having clinical depression Example 2: 30 job applicants are rated for suitability by 2 different interviewers

Answer 35

Kappa test

Question 36

What is the formula for calculating **Kappa** tests?

Answer 36

Question 37

What symbol do we use when reporting a **Kappa** test? What value is considered very good, good, fair and then not good?

Answer 37

K Very good =\> 70 Good = 50 Fair = 30 Not good = Less than 30

Question 38

What tests can we use for **Repeated Measure in Catageorical Data Analysis**

Answer 38

**McNemar Test:** *examines whether the probability of a given event is more or less likely in the same sample over time*

Question 39

What does **Cochran's Q** measure?