W5 lectures hypothesis testing + sign test

Question 1

the aim of a hypothesis test

Answer 1

using sample data of a population we determine (through formal concert steps) whether there is enough evidence (from the sample) to support our suspicion or belief about the wider population

Question 2

step 1) of a hypothesis test

Answer 2

Form two opposing hypotheses H𝟎 and H𝟏

Question 3

step 2) of a hypothesis test

Answer 3

Decide on a significance level alpha for the test

Question 4

step 3) of a hypothesis test

Answer 4

Calculate a test statistic x (or later t or z …)

Question 5

step 4) of a hypothesis test

Answer 5

Find the p‐value using the test statistic

Question 6

step 5) of a hypothesis test

Answer 6

Either ‘reject’ or ‘fail to reject’ the null hypothesis

Question 7

step 6) of a hypothesis test

Answer 7

Make a conclusion about the population

Question 8

when should a mean be used
(numerical average)

Answer 8

If the distribution of the data is approximately symmetrical,
the mean is usually considered the more useful average

Question 9

when should a median be used
(the middle number)

Answer 9

if the data includes clear outliers or is skewed,
the median is more useful (it is robust to outliers and skew)

Question 10

Sign Test characteristics

Answer 10

ideal to use when we have a small sample that seems to be skewed.
- it uses the median
- does not need to have an assumed distribution

Question 11

Sign Test Hypotheses

Answer 11

H0: median = 150
H1: median =/ 150 (two-tailed/sided test)
or
H1: median </> 150 (one-tailed/sided test)

Question 12

what are the conditions that need to be met for 𝑋~𝐵𝑖𝑛(n,p) - p-value for a Sign Test

Answer 12

1) Fixed number of trials
2) Fixed probability of ‘success’ (unders or overs)
3) Two possible outcomes
4) Trials are independent

Question 13

when should we double the p-value

Answer 13

in a two-tailed test

Question 14

median > m0

Answer 14

𝑥 = no. of + (overs)

Question 15

median < m0

Answer 15

𝑥 = no. of ‐ (unders)

Question 16

median =/ m0

Answer 16

𝑥 = maximum of (no. of +, no. of ‐)

Question 17

when should we reject H0

Answer 17

if the p-value is less then alpha

Question 18

when should i use a Sign Test for paired differences

Answer 18

when looking at the difference between two scores or the same people are tested twice.

Question 19

Sign Test for paired differences hypotheses

Answer 19

𝐻0 will be that the median of the differences is zero
* 𝐻0 : 𝑚d = 0
* 𝐻1 will be EITHER
- that the median of the differences is not zero (𝐻1 : 𝑚d =/ 0 , two‐tailed test)
OR
- that it is specifically greater than or less than zero (𝐻1 : 𝑚d > 0 or 𝐻1 : 𝑚d < 0, either way a
one‐tailed test)

Question 20

test stat for Sign Test for paired differences

Answer 20

differences are found by subtracting one set of scores from the other
* e.g. 𝑋After - 𝑋Before

Question 21

what is true about standardised score?

Answer 21

If a standardised score is negative, the unstandardised observation is going to be smaller than the population mean.