Inferential Statistics

Learning Objectives:

•Understand the nature of probability• Understand the role of probability in statistical testing• Describe and choose the level of significance• Explain the difference between type 1 + type 2 errors.

Key words you need definitions for:

• Probability• Level of significance• Type 1 error•Type 2 error

Outcomes:ALL – Complete own MEMORABLE notes using mnemonics / mindmaps on each objective.

MOST – Complete activities set

SOME – Complete Tea Test problem by end of the lesson

Inferential Statistics Tests

Make inferences about the populations from which the samples

are drawn

Descriptive Statistics vs. Inferential Statistics

Allows us to draw conclusions

Through use of graphs

Allow us to say whetherdifference is significant

This differenceIs significant

Inferential Stats

Watch the clip – the tea test.

Task:

Why are inferential statistical tests needed?

(Also see Pg 286)

DEFINICIÓN CLASICA DE PROBABILIDADHow likely is it that something will happen?

A number between 0 and 10 = something DEFINITELY will NOT happen1 = something DEFINITELY will happen

PROBABILITY = NUMBER OF PARTICULAR OUTCOMES

NUMBER OF POSSIBLE OUTCOMES

Task:What is the probability of a coin landing heads up?How would you express this as a decimal?

La probabilidad se expresa como “p”

Probability

Inferential tests use probability to ascertain the likelihood that a pattern of results could have arisen by chance.

If the probability of the results occurring by chance is below a certain level we assume these results to be significant

Chance

Real difference

We can state how certain we are the results are not

due to chance

Key questions for Psychologists…

•How far does what we have found in our sample reflect the general population?

•Could differences shown in our test have occurred by chance?

E.g. In a study of 10 yr old boys a positive correlation is found between time spent playing aggressive computer games and observed levels of aggression?

Is this the case for all 10 yr old boys?Inferential tests will tell us how probable it is that the correlation could have occurred by chance.

Watch the clip – P Values

Task:

Also referring to “Chance” pg 286

What does a p value of p ≤ 0.05 mean? Explain this both as a % but also what it tells us about the results of the study / correlation.

P-levels/Significance Levels

CHANCE

P ≤0.10P ≤0.05P ≤0.01P ≤0.001

We can also write these as 10%, 5%, 1%, 0.1%

Significant?

If our test is significant we canReject our null hypothesis and accept our alternative/experimental hypothesis

If our test is not significant we canAccept our null hypothesis and reject our alternative/experimental hyp

“If P is low…null must go.”

Type 1 and Type 2 Errors

Rejecting a null hypothesis when we should notP level too tight

Accepting a null hypothesis when we should notP level too loose

Type 1 error

Type 2 error

Errors

Throwing a coin 10 times there is a 17% probability of getting a head

If we set our p level too low it looks like there is phenomena there is not

Throwing a coin 100 times there is a 0.005% chance of getting a head

If we set it too high we may miss phenomena

Why do we make errors?

Type 1 – if we allow ourselves a p=.05 sig level then we allow yourself a 1 in 20 chance ofmaking an error

Type 2 – too stringent a p level means we may miss something

Watch the Type 1+2 errors video

Task

In your own terms explain the difference between a type 1 and type 2 error

Refer to Pg 287 Type 1+2 errors

Task:Why might researchers choose to use p≤0.01 in preference to p≤0.05?

Finished?•Check in with Mr Beech.

•Re-vsit any clips you are less certain on.

•Re-visit and test yourself on your schizophrenia cue cards.