lecture 10 - comparing groups (categorical data)

Question 1

how do we know to use the multidimensional Chi-Square (x^2)?

Answer 1

• Three sports groups (Field sports, rowing & netball)
• Three sets of measurements (the weight category of each subject in that sporting group)
• No subjects/participants appears in more than one group
• This research design is independent

Question 2

what is the multidimensional chi-square (x^2)?

Answer 2

• test of association. it is also known as chi-square (x^2) test of independence

Question 3

how is the chi-square carried out?

Answer 3

like other inferential statistics

Question 4

what’s the formula for the Chi-square?

Answer 4

(x^2)= sum of ((O-E)^2/E))

where x^2 is the symbol for chi-square
O is the observed count
E is the expected count

Question 5

what does the chi-square compare?

Answer 5

observed frequencies in our sample with the frequencies we would expect if there was no relationship at all between the two variables in the population that the sample was drawn from.

Question 6

what are the assumptions of the Chi-square?

Answer 6

• measures must be independent
• variables must be categorical
• randomly sampled
• counts, not %
• calculated expected values must not be less than 1
• no more than 20% of expected values should be less than 5
• solution= collect more data, collapse categories, or use an exact test (Fishers exact)

Question 7

what are the null and alternative hypotheses?

Answer 7

null: the variables do not differ
alternative: the variables do differ

Question 8

how do we calculate expected cell count?

Answer 8

expected cell count = (col marginal*row marginal)/grand total

Question 9

what do we do for each cell in the table?

Answer 9

X^2 = sum of (O-E)^2/E

we deduct the expected count from the observed (O-E)
O-E is squared to remove the minus sign
O-E squared is divided by the expected count

all of these values are summed, giving us a chi-square statistic. How different our sample is from what we would expect if H0 is true

Question 10

what are the degrees of freedom?

Answer 10

The more categories there are in the Independent Variable and Dependent Variable, the more chance there is of the analysis being affected by sampling error

Question 11

how to calculate degrees of freedom?

Answer 11

the number of categories in the row variable minus one multiplied by
the number of categories in the column variable minus one
DON’T COUNT THE MARGINAL CELLS

Question 12

what is count equivalent to In SPSS output?

Answer 12

observed counts

Question 13

when do we use Fishers exact test?

Answer 13

More than 20% of cells have an expected count of less than 5

and if the exact sig. (2-tailed) is less than 0.05 we reject the null hypothesis

Question 14

what is the hypothetical paired research design

Answer 14

e.g. an athlete’s weight is measured at beginning and end of season
time is the IV (beginning or end)
each athlete has a measurement in each category of the IV
- this is a paired research design, also called within subjects design or repeated measures design

Question 15

what is the McNemar test for repeated measures?

Answer 15

• if we had a repeated measures design with two dichotomous variables, we would use a McNemar test
• used to test for differences where samples are paired
• dependent and independent variables must be dichotomous (only two categories each)