week 1 SCM (chi-squared)

Question 1

why do we analyse frequencies when using at categorical variables?

Answer 1

• the numerical values you attach to different categories are arbitary
• this means that the mean of a categorical variable is meaningless
• because of this, we analyse frequencies of each category

Question 2

what are the rows and columns of a contingency table?

Answer 2

• the columns are the conditions (i.v)
• the rows are the categories of the measure (d.v)

Question 3

what is the general idea of the chi-squared test

Answer 3

it compares the frequencies you observe in certain categories to the frequencies that you might expect to get in those categories by chance

Question 4

what is the chi-squared equation?

Answer 4

Question 5

what is the equation for expected values, used in the chi squared eqution?

Answer 5

Question 6

what is the degrees of freedom formula for chi squared tests?

Answer 6

(row total-1) *(column total-1)

Question 7

What is the degrees of freedom for a contingency table with two columns?

Answer 7

1

this is because (r-1) * (c-1)

so

(2-1) * (2-1) = 1

Question 8

what theory is the likelyhood ratio statistic based on?

Answer 8

The maximum likelyhood theory

this means that the probability for obtaining the observed set of data is maximised

this model is then compared to the probability of obtaining those data under the null hypothesis

therefore the resulting statistic is comparing the observed frequencies with those predicted by the maximised model

Question 9

when would we use a likelyhood ratio statistic over a chi squared?

Answer 9

When the samples are small

Question 10

what happens to the chi squared distribution as the degrees of freedom increases?

Answer 10

the peak of the curve moves to the right and the distribution spreads out

Question 11

what does greater degrees of freedom mean in terms of how high the chi squared value has to be

Answer 11

the more degrees of freedom the higher the chi squared value has to be to be statistically significant

Question 12

what is a problem with the chi squared test?

Answer 12

• the sampling distribution of the test statistic has an approximate chi squared distribution
• the larger the sample the better the approximation becomes
• however, in small samples the approximation is not good enough making the statistical significance test of the chi squared innacurate

Question 13

what sample size is required for a chi squared?

Answer 13

• the expected frequencies in each cell must be greater than 5 for the chi squared significance test to be accurate

Question 14

1. what is the degrees of freedom of the likelyhood ratio?

Answer 14

the same as chi squared (rows-1)(columns-1)

Question 15

what is a type 1 error and a type 2 error?

Answer 15

TYPE 1 ERROR= rejecting the null hypothesis when its actually true

TYPE 2 ERROR= failing to reject the null hypothesis when its actually false

Question 16

what type of error does 2x2 contingency tables on the chi squared test tend to make?

Answer 16

type 1 error

this is because it tends to produce significance values that are too small

Question 17

what is yates continuity correction?

Answer 17

• a correction to the chi squared formula to correct the fact that 2x2 contingency tables tend to make a type 1 error
• you subtract 0.5 from the numerator in the formula before you square it
• this lowers the value of the chi squared statistic and therefore makes it less significant
• some argues that this overcorrects and produces chi squared values that are too small

Question 18

what are assumptions of the chi squared test?

Answer 18

1. The chi squared test does NOT rely on assumptions that the data is continuous and normally distributed like other tests do
2. data must be independent and contribute to only one cell of the table. this means you cannot use chi squared on repeated measures designs
3. the expected frequencies of each cell should be no less than 5

Question 19

what is a standardized residual?

Answer 19

a residual is the observed value - the predicted value

a standardised residual is a residual divided by its standard deviation

Question 20

what two things can we used to break down the chi squared test statistic?

Answer 20

standardised residuals (z-scores)

or

effect sizes (

Question 21

for larger contingency tables, what assumptions should we make for the chi squared test?

Answer 21

• no cell should have an expected frequency below 1
• up to 20% of expected frequencies can be below 5 but it will result in a loss of statistical power
• if you find yourself in this situation consider using fishers exact test

Question 22

what is an odds ratio?

Answer 22

the ratio of the two categories

Question 23

what is a significant standardized residual?

Answer 23

values outside of +/- 1.96

Question 24

what technique would we use to analyse larger contingency tables with 3 or more variables?

Answer 24

log linear analysis

Question 25

What is parametric statistics?

Answer 25

• Parametric statistics, such as r and t, rest on estimates of population parameters (x for μ and s for σ ) and require assumptions about population distributions (in most cases normality) for their probability calculations to be correct.

Question 26

What are the two main uses of chi squared?

Answer 26

Goodness of fit (involving a single independent variables)

Test for independence (involving multiple independent variables)

Question 27

LINK FOR HELPFUL WORKSHEET TO UNDERSTAND CHI SQUARED

Answer 27

https://www.cedu.niu.edu/~walker/statistics/Chi%20Square%202.pdf

Question 28

What is the difference between residuals, standardised residuals and adjusted standardised residuals?

Answer 28

• The residual is O- E (observed - expected value)
• The standardised residual is O - E / square root of E. The mean of the standardised residual is 0 and the standard deviation is 1. If the standardised residual for a cell is beyond the range of +2 then that cell can be seen as a major contributer of the overall chi-square value
• The adjusted standardised residuals are standardised residuals that are adjusterd for the row and column totals