Textbook Notes (280,000)

CA (170,000)

McMaster (10,000)

PNB (70)

PNB 3XE3 (6)

Rutherford (2)

Chapter 13-15

# PNB 3XE3 Chapter Notes - Chapter 13-15: Likelihood Ratios In Diagnostic Testing, Categorical Variable, Effect Size

by OC2033465

School

McMaster UniversityDepartment

Psychology, Neuroscience & BehaviourCourse Code

PNB 3XE3Professor

RutherfordChapter

13-15This

**preview**shows pages 1-3. to view the full**11 pages of the document.** CHAPTER 13: RELATIONSHIPS

THINGS TO KNOW

• Chi-square test: Finding relationships in categorical data

o How to do it

▪ Calculate expected values

▪ Calculate Chi-square (this is your test statistic)

• Assumptions

• Fisher’s exact test

• The likelihood ratio

• Standardized residuals

• Effect size

DEGREES OF FREEDOM

• The degrees of freedom are calculated as (r-1)(c-1), in which r is the number of rows and

c is the number of columns

*There is a practice example in the chapter 13 slides!

ASSUMPTIONS

• Independent errors

o Each case (entity) contributes to only one cell

• Sample size

o If 2x2, no expected frequency less than 5

o If larger

▪ No more than 20% of cells less than 5

▪ All expected frequencies greater than 1

• Else use Fisher’s exact

Only pages 1-3 are available for preview. Some parts have been intentionally blurred.

FISHER’S EXACT

• Computes the probability of your X2 value

o Each case (entity) contributes to only one cell

• Use it with a 2x2 table

• Usually just with a small sample size

YATES’S CORRECTION

• Shaves 0.5 off of each cell difference before you sum together to find X2.

o Each case (entity) contributes to only one cell

• Makes X2 smaller and p bigger

• More conservative

THE LIKELIHOOD RATIO (G-TEST)

• The test statistic has a chi-square distribution

• It is preferred when samples are small

• It will be the same as X2 when samples are large

STANDARDIZED RESIDUAL

• Tells you what is contributing to the X2 value that you calculated

•

• They are z-scores

o Z-score with a value outside of +/- 1.96 will be significant at p < 0.05

o Z-scores with a value outside of +/- 2.58 is significant at p <0.01

Only pages 1-3 are available for preview. Some parts have been intentionally blurred.

- Pearson’s correlation coefficient is a special case of the linear model

COVARIANCE

• If two variables are related, then if an observation is far from the mean on one

variable, it should be far from the mean on the other variable

• Multiply the deviation for one variable by the corresponding deviation for the other

• This captures the positive or negative nature of the relationship

• Sum of cross-product deviations

PEARSON’S CORRELATION COEFFICIENT

TEST THE HYPOTHESIS THAT R IS NOT ZERO

• Pearson’s r does not have a normal sampling distribution, but it can be transformed so

that it does

o Use a z score zr. it is normally distributed, it has a known standard error

o Or use a t statistic tr.

▪ Changes shape with the sample size

▪ Look it up in a t-table or use SPSS

EFFECT SIZE

• R is an effect size

• R2 is a measure of the amount of variability in one variable that is shared by the other

###### You're Reading a Preview

Unlock to view full version