Inferential Statistics

Objective:An introduction to what you need to

know about statistics

Key Terms

Test statisticCritical valueDegrees of freedomP value/levelSignificanceChanceType 1 errorType 2 errorInterval OrdinalNominal

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

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

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

Levels of measurement

Nominal

Ordinal

Interval

Levels of data: nominal

• Which newspaper paper do you read regularly?

• We can put these into categories.

Levels of Data: ordinal

• What grade did you get for each of your gcse’s?

• These can be put in order… highest to lowest

Levels of data: interval

• How quick is your reaction time?

• We can measure and compare the exact time because the intervals on the ruler are equal.

Inferential Tests

Which test to use depends upon a number offactors:• The type of data• Type of research design (RM vs. IG)• One tailed or two tailed test

Tests to Know

Mann Whitney UChi SquaredWilcoxon T

Spearmans rho

Process

dataComplicated arithmetic

Produce test statistic

Compare testStatistic

with critical valuesfor that test

To determine significance level

critical value: Value that test statistic must reach in order for null hyp to be rejected

Sig levels ½’d for one tailed test

Sig levels ½’d for one tailed test

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