Binary data

Question 1

Binary data

Answer 1

Categorical usually only two answers ie yes/no, o patients possess attributes or not

NB continuous data can be crudely mapped as binary.

Question 2

Ordinal variable

Answer 2

If large enough with multiple categories can be analysed as continuous variable but require specialist stats. Clear ordering ie tumor stage

Question 3

π

Answer 3

Proportion of population possessing the attribute hence proportion not possessing attribute = 1-π

Question 4

Estimating π

Answer 4

π = r/n Analogous to u

r = possession of attribute
n = population

Question 5

Why new methods for categorical data

Answer 5

Continuous data varies by o around a mean u. Any value of u can vary by a range described by o. In categorical data there is only one parameter.

SE error is used. Once π has been estimated there is no need for further estimate of the spread of data

Question 6

SE continuous variables

Answer 6

SE = σ/√n

Question 7

SE binary variables

Answer 7

SE = √[π(1-π)/n]. Still infers that the larger the sample the smaller the error. This can give CI

Question 8

χ2 test

Answer 8

Binary equivalent of the unpaired t-test ie A=B

Must be performed on independent counts

Question 9

What needs to be calculated in χ2 test

Answer 9

Margins = these are subtotals of the categories. Both sets sum to the total in bottom right corner

Always draw 2x2 table

Expected values = always should add up to the margins despite sometimes not being whole numbers

Question 10

K

Answer 10

Estimate of the proportion similar to both groups

Question 11

χ2 test

Answer 11

Sum of ((O-E)/E)2

Ie difference between observed - expected/ expected squared

Question 12

P value from χ2 test

Answer 12

Asymptomatic approximation

Question 13

When is Fischers exact test used

Answer 13

When expected values <5

NB For larger tables the rule is that if over 20% of the
cells have expected values below 5, or any cells with expected values below 1 then the χ2 method may be unreliable

Question 14

Fischers exact test

Answer 14

Calculates the p-value directly from data all possibilities for analysis are enumerated in tables. Margins ie p values from all possibles should add up to 1

Question 15

Pitfalls for χ2 test

Answer 15

Tables must compare raw counts not proportions/percentages as they don’t give indication of sample size

Independent entities ie school children walking to school. Ensure bottom right number = no independent units

Question 16

P value testing χ2 test

Answer 16

Adding up all probabilities that are less than or equal to the probability of the observed table.

Question 17

π

Answer 17

Proportion of population possessing attribute always inbetween 0 and 1

P = O/ 1+0

Question 18

Odds

Answer 18

Can be above 1.

O = π /(1-π)

Question 19

Absolute difference

Answer 19

πa - πb

Null value = 0

Question 20

Relative risk

Answer 20

πa/πb

Null value = 1

Question 21

Odds ratio

Answer 21

πa/ 1 - πa / πb/ 1 - πb

Null value = 1

Question 22

CI for absolute difference

Answer 22

Using estimate for D the E is calculated using
πa(1-πa)/na + πb(1-πb)b all square rooted

Hence CI = D +/- 2SE

Question 23

CI for OR

Answer 23

1 = Natural log of OR (logOR)
2 SE = root sum of the reciprocal

Hence CI = logOR +/- 2 SE (root sum reciprocals)

Question 24

Flaw of OR

Answer 24

Skewed ie 0-1 represents all values compared to 1-infinite