How to Assess Normality

Question 1

What are the examples of methods which perform statistical tests

Answer 1

1. Hypothetical tests
2. Constructing confidence intervals

Question 2

What do non-parametric or distribution free methods not require

Answer 2

An assumption of normality

Question 3

Why are non-parametric or distribution free methods not always needed

Answer 3

1. ASSUMPTIONS OF NORMALITY ARE NOT ALWAYS CRUCIAL
   - unpaired t test can tolerate departures from normality can be tolerated
   - may not be the most important of several assumptions
2. DISTRIBUTION- FREE METHODS ARE NOT ASSUMPTION FREE
   - un paired two sample t test the distribution are assumed to have the same shape and differ only by shift
3. THERE RELIANCE ON THE RANKS OF THE DATA CAN MAKE SOME ASPECTS OF ESTIMATION SEEMS UNNATURAL
4. DISTRIBUTION-FREE METHODS CAN’T COPE WITH DATA DOESN’T HAVE A SIMPLE STRUCTURE
5. TRANSFORMATION CAN BE USEFUL IN CHANGING THE DISTRIBUTION OF DATA TO A MORE MANABLE FORM

Question 4

When are non-parametric or distribution free methods beneficial

Answer 4

When INFERENCES are BASED MORE STRONGLY ON THE ASSUMPTION OF NORMALITY

Question 5

When are INFERENCES BASED MORE STRONGLY ON THE ASSUMPTION OF NORMALITY

Answer 5

When trying to estimate features of the data that DEPENDS ON THE EXTREMES OF THE DISTRIBUTIONS (t-test)

Question 6

What does a normal distribution describe

Answer 6

Data that is distributed over all values (positive andnegative)

Question 7

Is normal distribution appropriate to described a necessarily positive outcome ascribes very little probability (less than 1 to 5%) to negative values

Answer 7

Yes

Question 8

Is normal distribution fitted to a positive variable ascribes substantial probability to negative values appropriate

Answer 8

No

Question 9

If a positive variable that is assumed to be normal has an estimated mean (m) less than the estimated SD (m/s<1) is normal distribution appropriate

Answer 9

No- as the ratio m/s INCREASES TOWARDS 2 the suspicion NORMALITY IS APPROPRIATE WILL DIMINISH

Question 10

What graphical representations can be used to assess normality?

Answer 10

A histogram
- allows for the general shape of the distribution to be estimated
- Too strict an insistance on a suitable ‘bell-shaped appearance can lead to NORMAL DATA being DISMISSED as NON-NORMAL DATA which is the case with small samples

Question 11

Normal Probability plot- basic idea of it being normal

Answer 11

1.As the sample increases, the smallest value is expected to fall further below the mean (u)
2. Middle of the sample being close to the mean
3. Intermediate values will fall in-between, with values clustering more tightly near the mean as their rank increases due to the nature of the bell shape of the normal curve
4. Largest value will be arranged above the mean symmetrically relative to the smallest value

Question 12

What would a normal distribution look like on a normal probability plot

Answer 12

It would look like a straight line

Question 13

Is normal probability plot one of the best methods to assess normality

Answer 13

Yes

Question 14

Can formal hypothesis test assess normality

Answer 14

It can but it lacks power