Week 6

Question 1

Probabilities used to reject hypotheses are called

Answer 1

P values

Question 2

A threshold level for the p level, called ___________ needs to be defined prior to the analysis. A usual choice is 0.05

Answer 2

Alpha level

Question 3

-If p-value < 0.05, you ________ your hypothesis

Answer 3

reject

Question 4

-If p-value > 0.05, you reject your hypothesis

Answer 4

accept

Question 5

Null hypothesis

Answer 5

The null hypothesis (Ho) is a hypothesis against the research question, claiming that there is no difference in the result and the only differences observed are just noise/error

Question 6

Research/alternative hypothesis

Answer 6

The research/alternative hypothesis (Ha) is the opposite to the null hypothesis claiming that there is a difference in the result

Question 7

Type 1 error

Answer 7

False-positive
Reject the null hypothesis when it is true
The vaccine is not effective but you conclude it is effective

Question 8

Type 2 error

Answer 8

False-negative
Not to reject the null hypothesis when it is false
The vaccine is effective, but you conclude it is not effective

Question 9

3 types of binomial test

Answer 9

Observed proportion < expected proportion
Cumulative probability from 0 to observed

Observed proportion > expected proportion
1 - cumulative probability from observed to max

Observed proportion /=/ expected proportion
Two tailed cumulative probability same distance from the mean

Question 10

Chi-square goodness of fit test

Answer 10

how the proportions in data fit to fixed (expected) proportions. Can test more than 2 categories

Question 11

What is benfords law

Answer 11

Benford’s law (or first digit law). The frequency of first digits of naturally occuring numerical data (prices, populations) follow a particular proportion.

Question 12

Using benfords law, which digit is the most common?

Answer 12

1 (30.1%), then 2 (17.6%), then 3 (12.5%, then 4, 5, 6….

Question 13

If a set of data does not follow benfords law then…

Answer 13

It is likely that the data set is fabricated

Question 14

How to report a chi goodness of fit test

Answer 14

x^2 (5) = 12.2, p=0.032

x^2 (df) = x^2 value, p = p value

Question 15

Chi square test of association

Answer 15

Checking association between 2 nominal/ordinal variables

E.g. whether the proportion of tories/labours differe depending on the region of the UK. Then seeing whether these variables are associated

Question 16

How to report a chi square test of association

Answer 16

X^2 (2, N = 27) = 1.43, p = 0.490

x^2 (degree of freedom, N = total value) = x^2 value, p = p value

Question 17

Paired samples - McNemars test

Answer 17

Paired samples mean that, data points are paired across two groups

E.g. whether the same subject needs to participate before and after an intervention or whether the 2 sets of data are related

Question 18

t tests

Answer 18

Difference in group of measures (interval or ratio variables)

Measurable variables e.g. what is your 100m PB, what is your vo2 max instead of categorical data like do you prefer red or black cars.

Question 19

3 types of t-test, each corresponds to the test for nominal/ordinal variables that we already learned.

Answer 19

1. One sample t-test – binomial or chi-square goodness of fit (expected measure – testing whether data is different – one group)
2. Indepdent (unpaired) samples t-test – chi square test of association – comapring the mean of 2 sets of data
3. Paired samples t test – Mcnemars test

Question 20

One sample t test

Answer 20

Compares the mean of one sample group against a fixed value

Whether the mean of your data is different from the fixed values’ mean

Question 21

Independent samples t test

Answer 21

Compares the observed difference between the means of two indepdednet samples or categories

Question 22

Which t test is this:
comparing weight before and after covid lockdown

Answer 22

Paired sample t test as same subject, compared before and after

Question 23

Which t test is this:
Compraing body temperatures of vaccine and placebo group one hour after inoculation

Answer 23

Independent samples t test as vaccine and placebo group are different groups of people

Question 24

Which t test is this:
Comparing time spent with children between married couples

Answer 24

Paired sample t test and children and married couples are related

Question 25

Normality

Answer 25

sampling distribution of the mean is normal – if you take groups of n samples from the distribution and calculate the means of each sample group, those means are normally distributed. This holds when the sample size n is large.

Question 25

Test of normality

Answer 25

Test of normality – normality assumption can be checked using another statistical test: violation of the normality indicated by low p value. (I.e. p < 0.05). If P value lower than alpha value (0.05), then normality violated, and you have to do a non-parametric test.

Question 25

Which theory describes normality?

Answer 25

Central limit theorem

Question 26

Parametric tests

Answer 26

Statistical tests based on the normality assumption are called parametric tests

Question 27

Independent samples t test are run when

Answer 27

Independent samples t test are run when equality of variance are equal (variance of two populations are equal). Variance = sd.

Question 28

Which test do we use to test the equality of variance

Answer 28

Levenes test