1. Categorical data analysis

2. Types of variables Numerical Categorical discrete continuous nominal
ordinal

3. Confidence interval two sided confidence interval error
table value – normal distribution
u0,05 = 1,96

4. One – sample test (two sided)
H0: π = π0
test criterion
table value → u0,05 = 1,96

5. Two – sample test (two sided)
H0: π1 = π2
test criterion
table value → u0,05 = 1,96

6. Contingency tables 2 x 2 Var A/Var B B1 B2 Total A1 a b a+b A2 c d c+d
b+d n

7. Contingency tables i x j
Var A/Var B B1 B2 … Bj
Total A1
n11
n12
n1j
n1. A2
n21
n22
n2. Ai
ni1
ni2
nij
ni.
n.1
n.2
n.j n

8. Testing independence in two-way CT
Null hypothesis
Alfa
Test criterion computation
Table value χ2[(m-1).(n-1)]
Conditions for testing
n > 40 → χ2 test
n (20;40>, some expected frequency is < 5 → Fisher test, if all expected freq are > 5 → χ2 test
n <= 20 → Fisher test

9. Theoretical frequencies
Var A/Var B B1 B2 … Bj
Total A1
n11
n12
n1j
n1. A2
n21
n22
n2. Ai
ni1
ni2
nij
ni.
n.1
n.2
n.j n

10. Testing independence in two-way CT
Fisher test
find cell with the lowest value
go down by 1 in the cell (final value is 0), all marginal freq are the same
computation of probability for each created table
∑pi > 0,05 → H0 is valid

11. Testing independence in CT
table value χ2[(m-1).(n-1)]
conditions for testing by χ2 test
max 20 % of expected freq is < 5
no expected freq is less than 1

12. Intensity of dependent
Pearson coefficient
Cramer coefficient V, where h is min (k;m)

13. Two-way tables – dependent observation
Mc Nemar test
2 x 2 table
1 group of units, observation „before – after“
2nd measure (after) + -
1st measure (before) a b c d

14. Two-way tables – dependent observation
McNemar test
test criterion
table value χ2[(m-1).(n-1)]
condition b + c > 8
correction

15. Chances and risks in two-way tables
Threats
Exposition
Var A/Var B B1 B2
Total A1 a b
a+b A2 c d
c+d
a+c
b+d n

16. Chances and risks in two-way tables
Relative risk (part 1)
if the categories of the B variable are independent on categories of the A variable, RR1 = 1
RR > 1 → in the cell „a“ will be occur higher share of the total frequency than in the cell „c“
how many times is higher the probability of threats

17. Chances and risks in two-way tables
Relative risk (part 2)

18. Chances and risks in two-way tables
Odds ratio
ratio of two alternatives of relative risk results (RR1 a RR2)
OR values are between zero and infinity
independent between variables → OR = 1
how many times is higher chance to threats

19. Chances and risks in two-way tables
Attributive risk
difference of probability of incidence B1 for both categories of the first variable – A1 and A2
AR is <-1;1>
indicates changes of threat probability

20. Chances and risks in two-way tables
Relative attributive risk
is based on attributive risk and it is percentage change of probability of incidence B1 for both categories – A1 and A2
basis for computation is share of frequency incidence in the cell „a“ in relation to marginal frequency of category A1 (share a/(a+b))