1-variable Chi square

Question 1

What is a 1-variable Chi-square used for?

Answer 1

To assess whether observed frequencies in categories are different from what might be expected

i.e. Might expect frequencies to be equally distributed or Might expect some pattern in the frequencies

Question 2

A chi square value is always…?

Answer 2

Above 0

Question 3

What is the DoF following a chi-square?

Answer 3

N-1 (N is the number of categories, not sample size)

Question 4

What measures the extent to which observed and expected frequencies differ?

Answer 4

Chi square

Question 5

The DoF od chi-square values are N-1. What is N in this case?

Answer 5

The number of categories, not the sample size

Question 6

We get a chi-squared value of 8.24 from a data following 2 categories. Do we reject or fail to reject H0?

Answer 6

Reject H0

Because on the table, the chi-square of 8.24 is larger than p = 0.05 (7.815) so the probability of our chi-square value being more extreme than 0.05 chi-square is greater

p < 0.05

Question 7

President Zdave from planet Ziltoidia 10 wishes to pick a picture for the new Ziltoidian equivalent of a first class stamp. He has 4 pictures taken and wants to test the hypothesis that some pictures are preferred over others (similar to the situation outlined in the V-lecture). He asks each of 100 Ziltoidians to vote for a preferred picture. The observed (O) frequency data are summarised below:

Pic 1: 23, Pic 2: 35, Pic 3: 24, Pic 4: 18

The null hypothesis suggests that no picture is preferred and so the expected (E) frequencies are equal for each of the 4 pictures in this case.

a) The quantity (E-O)^2/E for Pic 1 is

b) The quantity (E-O)^2/E for Pic 2 is

c) The quantity (E-O)^2/E for Pic 3 is

d) The quantity (E-O)^2/E for Pic 4 is

e) The chi-square statistic is

f) Should President Zdave reject the null hypothesis?
(enter yes or no)

Answer 7

a) 0.16
b) 4.00
c) 0.04
d) 1.96
e) 6.16
f) No

Question 8

What is the formula for 1-variable Chi square?

Answer 8

(E-O)^2/E