RMB: PARAMETRIC TESTS WEEK 3

Question 1

What are parametric assumptions/tests?

Answer 1

• A parametric assumption assumes things about the data-set
• Assumes data will be normally distributed and that both data sets will have homogeneity of variance
• Usually done on interval or ratio level data > Data measured on a scale, like cm’s measured with a ruler (called ratio-level data), or temperature which has scale but does not have a true 0 (called interval-level data)

Question 2

Parametric vs Non-parametric and why we have them

Answer 2

• Parametric and non-parametric tests are distinct from each other
• Important because based on how the data looks (parametric or non-parametric) depends on what test you can do > if the data doesn’t meet parametric assumptions then a non-parametric test is needed

Question 3

Normal distribution

Answer 3

• Population distribution should be roughly normal (Gaussian distribution)
• We don’t want the results to be significantly different > want them to belong to a normal distribution

Question 4

Homogeneity of variance

Answer 4

• when comparing more than one group, the groups should have equal variance (looks the same/similar) > should not vary too differently from each other
• Homogeneity means same/similar
• We don’t want the results to be significantly different > want them to have similar results

Question 5

Non-parametric tests

Answer 5

• don’t make assumptions about the population distribution (distribution free tests) > these tests are lower in power + less flexible than parametric tests > only used when parametric assumptions are NOT met
• Usually used on ordinal and nominal data (but can be used on interval + ratio)

Question 6

Are parametric tests better than non-parametric tests?

Answer 6

• Prefer using parametric testing because it is more powerful and robust, limitations are well documented
• If the data is not normally distributed or doesn’t have homogeneity of variance we could transform the data using logs to normalise distributions
• Occasionally we can use “equal variances not assumed” if parametric assumptions are not met but we want to use a parametric test (e.g. independent t-test)
• Parametric tests are powerful but can be abused if assumptions aren’t met

Question 7

Kolmogorov-Smirnov test for normality of data

normal distribution test

Answer 7

• Tests to see likelihood of data being distributed normally
• K-S test tests the null hypothesis that the distribution is normal
• if p is less than 0.05 then the data is NOT normally distributed > this is because the p value is significant so the distribution isn’t normal (p has to be non-significant to show a normal distribution)
• if p is over 0.05 then the data is not significant + normally distributed > we want p to be OVER 0.05 (e.g. p = 0.001 is significant so not ND but p = 0.9 is not significant and IS ND)

Question 8

Levene’s test for homogeneity of variance

Answer 8

• determines if the data sets are from the same population > tests null hyp that each sample has a similar variance
• If the samples do have homogeneity of variance, then the test will NOT be significant > p has to be over 0.05 to have similar variance (non-significant) > we want p to be over 0.05 to use parametric testing > if p is under 0.05 then there is NOT homogeneity of variance because the result is significant

Question 9

How do we confirm our assumptions?

Answer 9

• If the data is not significantly different from the normal distribution and (if appropriate, e.g. doing a test of difference) there is no significant difference between the variance of samples (aka there is homogeneity of variance) then we can perform a parametric test
• To perform a parametric test, we need both tests to not be significant > if one out of 2 doesn’t work, a non-parametric test should be used
• If these assumptions are not fulfilled, we have to do the equivalent non-parametric test
  BUT - some parametric tests are very robust + sometimes they will be used even if the tests of parametric assumptions are not fulfilled (standard can vary depending on the test)

Question 10

What is an experiment?

Answer 10

• Manipulation of one or more variables. e.g., coffee intake.
• Determine the effect of this manipulation on another variable. e.g., driving when tired.
• To test of cause-effect relationship between variables.
• Test of causality > e.g., does coffee improve your driving when tired?

Question 11

What is a hypothesis?

Answer 11

• Science is about testing hypotheses.
• Hypotheses are derived from theories (one theory may generate thousands of H’s)
• A hypothesis is a testable prediction.

Question 12

Experimental/alternative hypothesis.

Answer 12

• ‘Learning with background music does lead to lower marks.’

- Treatment leads to an effect.

Question 13

Null hypothesis

Answer 13

• ‘Learning with background music does NOT lead to lower marks.’
• Treatment does not lead to an effect.

Question 14

Independent & Dependent variables

Answer 14

• The independent variable is what you change and the dependent variable is what you measure
• Manipulating the independent variable changes the value of the dependent variable.

Question 15

Nuisance variable

Answer 15

• An additional factor that affects the dependent variable.

- E.g. testing affect of music on marks but nuisance variable could be the environment or time of testing

Question 16

Experimental and control groups

Answer 16

• Experimental group: Group receiving the important level of the independent variable.
• Control group: Group that serves as the untreated comparison group/Group receives comparison level of the independent variable.

Question 17

What are Z-scores?

Answer 17

• Z scores look at distribution of difference between the score we are observing and the mean > takes every value in distribution + look at difference between this value + mean (these values are given in exam)
• Z score = observed X - mean = ? divided by SD

Question 18

Calculating Z-scores

Answer 18

z = (x - mean)/SD

• If asked how probable something is of being in a normal distribution you need the z-score > e.g. Did the brain damage caused a decrease in reading ability for this patient? aka do they fit in a normal distribution
• e.g: (28-50)/10 = -2.2 > the person is at -2.2 of a normal distribution > use a table entry to show how probable it is of this being normal or others getting it > entry shows 0.0139
• Essentially, If you randomly sample one person from the population of healthy people, 1.39% of the time you get a score 28 or lower.
• Threshold for significance is 0.05 and result was 0.01 showing significance so the alternative hyp is accepted