W5 lectures hypothesis testing + sign test Flashcards
the aim of a hypothesis test
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
step 1) of a hypothesis test
Form two opposing hypotheses H𝟎 and H𝟏
step 2) of a hypothesis test
Decide on a significance level alpha for the test
step 3) of a hypothesis test
Calculate a test statistic x (or later t or z …)
step 4) of a hypothesis test
Find the p‐value using the test statistic
step 5) of a hypothesis test
Either ‘reject’ or ‘fail to reject’ the null hypothesis
step 6) of a hypothesis test
Make a conclusion about the population
when should a mean be used
(numerical average)
If the distribution of the data is approximately symmetrical,
the mean is usually considered the more useful average
when should a median be used
(the middle number)
if the data includes clear outliers or is skewed,
the median is more useful (it is robust to outliers and skew)
Sign Test characteristics
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
Sign Test Hypotheses
H0: median = 150
H1: median =/ 150 (two-tailed/sided test)
or
H1: median </> 150 (one-tailed/sided test)
what are the conditions that need to be met for 𝑋~𝐵𝑖𝑛(n,p) - p-value for a Sign Test
1) Fixed number of trials
2) Fixed probability of ‘success’ (unders or overs)
3) Two possible outcomes
4) Trials are independent
when should we double the p-value
in a two-tailed test
median > m0
𝑥 = no. of + (overs)
median < m0
𝑥 = no. of ‐ (unders)
median =/ m0
𝑥 = maximum of (no. of +, no. of ‐)
when should we reject H0
if the p-value is less then alpha
when should i use a Sign Test for paired differences
when looking at the difference between two scores or the same people are tested twice.
Sign Test for paired differences hypotheses
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)
test stat for Sign Test for paired differences
differences are found by subtracting one set of scores from the other
* e.g. 𝑋After - 𝑋Before
what is true about standardised score?
If a standardised score is negative, the unstandardised observation is going to be smaller than the population mean.
