Lecture 6

Question 1

association = ?

Answer 1

patterned/systematic variation

Question 2

example of an association?

Answer 2

association: gender is linked to patterns of work hours

no association: gender is not linked to patterns of work hours

Question 3

hypothesis = ?

Answer 3

informed speculation to be tested

could be a possible relationship between 2 or more variables

Question 4

what are the two options with regards to systematic variation?

Answer 4

there is systematic variation

there is not systematic variation

Question 5

what are the tools for demonstrating association for discrete variables?

Answer 5

descriptive statistics (contingency tables)

inferential statistics (chi-squared test)

Question 6

alpha = ?

Answer 6

the threshold for statistical significance

Question 7

what are the necessary steps to establishing causality?

Answer 7

1. theoretical rationale linking potential cause and effect
2. demonstrate that the cause happened before the outcome
3. show that there’s an association between the cause and the outcome
4. remove any other factors that could be related to the outcome

Question 8

what type of variables are the cause and the outcomes?

Answer 8

cause = independent variable

effect = dependent variable

Question 9

what is the link between dependent and independent variables?

Answer 9

dependent variables are dependent on the independent variables

dependent variables are the effect and independent variables are the cause

Question 10

what are two types of distributions?

Answer 10

marginal distribution
conditional distribution

Question 11

marginal distribution = ?

Answer 11

focuses on one variable at a time (univariate)

Question 12

conditional distribution = ?

Answer 12

the distribution of one variable given something is true about the other variable

Question 13

how are marginal and conditional distributions represented?

Answer 13

can be represented as counts or percentages

standard practice for conditional distribution is to present it as percentages

Question 14

weird samples = ?

Answer 14

samples are quite different compared to underlying population

samples aren’t representative of the wider population

Question 15

what are the two types of hypotheses?

Answer 15

null hypothesis (H0)

alternative hypothesis (Ha)

Question 16

x squared = ?

Answer 16

chi-squared

Question 17

what is chi-squared all about?

Answer 17

comparing two differences

1. differences we observe in our sample
2. differences we expect if null hypothesis were to be true

Question 18

what is the chi-square test?

Answer 18

a hypothesis test used when you want to determine whether there’s a relationship between two categorical variables

Question 19

categorical variables = ?

Answer 19

nominal or ordinal level data that can be grouped into categories

Question 20

what is the significance level threshold?

Answer 20

5%

for p values smaller than 0.05, the null hypothesis is rejected

if p value is higher than 0.05, the null hypothesis is accepted

Question 21

how do you calculate the chi-square test?

Answer 21

you need the observed frequencies and the expected frequencies

(observed frequency - expected frequency) squared / expected frequency

calculate this for all cells and sum it up to get your chi-square value

Question 22

how do you calculate expected cell count?

Answer 22

(row total * column total) / grand total

Question 23

p-value < 0.001 = ?

Answer 23

there is less than a 0.1% chance of obtaining your value of chi-squared or larger if there’s really no relationship between these variables in the population

Question 24

what does a 5% threshold indicate?

Answer 24

that the null hypothesis is rejected

Question 25

what’s the purpose of p values?

Answer 25

p value helps us weigh the inference value of descriptive evidence

always a number between 0 and 1

tells us how probable the null hypothesis is

a high p value means that the sample data are compatible with true null hypothesis

a low p value means that the sample data aren’t compatible with true null hypothesis

Question 26

how are p values used?

Answer 26

• we get a p value
• we compare the p value to our a (alpha) significance level (e.g., 0.05 / 5%)
• if the p-value < a, then we reject the null hypothesis
• if the p-value > a, then we fail to reject the null hypothesis

Question 27

what are some chi-squared assumptions?

Answer 27

• the chi squared test doesn’t work well with very small samples
• expected cell counts need to be at least 1
• no more than 20% of the expected cell counts should be less than 5