Explain why it may be appropriate to carry out a hypothesis test based on the PMCC
Because scatter diagram illustrates a rough elliptical shape, so it suggests a bivariate normal distribution.
- also if there’s two big clusters
Spearman’s hypothesis
H0 - there is no association between x and y
H1 - there is association between x and y
Define significance level
The probability of rejecting the null hypothesis when it is in fact true
Discuss briefly what the contingency excel table suggests
- go with each type, e.g:
Type 1 - large contributions to test statistic of __ and __ show that fewer than expected are _ and more than expected are __
Type 2 - for type 2, small contributions of ___, so as expected
Type 3 - ….
Interpolation vs extrapolation
Interpolation good estimate and reliable, extrapolation is probs unreliable
Comment on the fit of the regression line
Because r^2 = ____, fit is bad/moderate/ good
And the points lie fairly far/close from the line of best fit
Lil uniform distribution
Uniform on values {1,2,3….n}
Much larger sample size =
Smaller critical value
Residual =
Real - calculated
Conditions for binomial (4)
- fixed number of observations
- each observation is independent
- each observation is either success or fail
- probability is constant
Conditions to have position distribution
- all events independent of each other
- rate of events through time is constant (mean)
- mean = variance roughly
Explain why for proper inference, PMCC sample should be randomly selected
Because then the probability basis on which the sample has been selected is known
Conditions for geometric distribution
- independent trials
- binary - success or fail
- chance of success is the same each trial
Degrees of freedom tips and tricks
1 - go from final tableau - after possibly merging columns due to small yute
2 - if testing for poisson binomial, you are estimating parameters, so v - 1, then -1 for the merged column
Student concludes no correlation between variables in the summer months, ctm about the students conclusion
- result of hypothesis test always has uncertainty, and then expand related to that question
Give two desirable features that the sample should have
- randomness
- unbiased
- representative of the population
- components selected independently
Explain why random sample was chosen for PMCC
- random sample enables proper inference about population to be undertaken
- unbiased
- for hypothesis test to be valid, necessary to assume sample is random
Explain why binomial and poission can be used
- occurrences are random and independent with constant probability
- number of successes are counted
Therefore binomial appropriate
For poission, sample size is large, and p is small
Sometimes when chatting about rough elliptical
- point out any anomalies too
- also mention POPULATION
Reliability of regression estimate usually related to
EXTRAPOLATION OR INTERPOLATION
- sometimes slide in r value and points closeness to line too
State the distributional assumption which is necessary for this test to be valid
The POPULATION
Must have a bivariate normal distribution
Comment on the outcome of this test with a larger sample but with 0.076 being considered as an effect size
- test shows that there is/ isn’t almost certainly some real correlation in the population
- however this is of little practical consequence since effect size is so small
Would it be appropriate to use regression y on to find a value of x given a venue of y
Not appropriate; the regression line of d on f is needed
Based on weird effect size table + data, two reasons why it would not be appropriate to carry out a hypothesis test based on this data
- sample not random
- distribution of the bivariate population is unknown
