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This document provides an introduction to inferential statistics, including key terms like test statistic, critical value, degrees of freedom, p-value, and significance. It explains that inferential statistics allow inferences to be made about populations based on samples through probability and significance testing. Different levels of measurement are discussed, including nominal, ordinal, and interval data. Common inferential tests like the Mann-Whitney U, Chi-squared, and Wilcoxon T tests are mentioned. The process of conducting inferential tests is outlined, from collecting and analyzing data to comparing test statistics to critical values to determine significance. Type 1 and Type 2 errors in significance testing are also defined.

Inferential Statistics

Objective:
An introduction to what you need to
know about statistics

Key Terms
Test statistic
Critical value
Degrees of freedom
P value/level
Significance
Chance
Type 1 error
Type 2 error
Interval
Ordinal
Nominal

Inferential Statistics Tests

Make inferences about the
populations from which the samples
are drawn

Descriptive Statistics vs. Inferential Statistics

Allows us to draw
Allow us to say whether
conclusions
difference is significant
Through use of graphs

This difference
Is 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

We can state how certain
we are the results are not Real
due to chance difference

P-levels/Significance Levels

P ≤0.10
C
H P ≤0.05
A
N P ≤0.01
C
E P ≤0.001

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

Significant?
If our test is significant we can
Reject our null hypothesis and accept our
alternative/experimental hypothesis

If our test is not significant we can
Accept 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 of
factors:
• The type of data
• Type of research design (RM vs. IG)
• One tailed or two tailed test

Tests to Know
Mann Whitney U
Chi Squared
Wilcoxon T
Spearmans rho

Process

data
Complicated arithmetic

Produce test statistic

Sig levels ½’d for one
tailed test

Compare test
Statistic
with critical values
for that test
To determine significance
level

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

Type 1 and Type 2 Errors
Type 1 error

Rejecting a null hypothesis when we should not
P level too tight

Type 2 error

Accepting a null hypothesis when we should not
P level too loose

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Inferential statistics powerpoint

1. Inferential Statistics Objective: An introduction to what you need to know about statistics

2. Key Terms Test statistic Critical value Degrees of freedom P value/level Significance Chance Type 1 error Type 2 error Interval Ordinal Nominal

3. Inferential Statistics Tests Make inferences about the populations from which the samples are drawn

4. Descriptive Statistics vs. Inferential Statistics Allows us to draw Allow us to say whether conclusions difference is significant Through use of graphs This difference Is significant

5. 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

6. Chance We can state how certain we are the results are not Real due to chance difference

7. P-levels/Significance Levels P ≤0.10 C H P ≤0.05 A N P ≤0.01 C E P ≤0.001 We can also write these as 10%, 5%, 1%, 0.1%

8. Significant? If our test is significant we can Reject our null hypothesis and accept our alternative/experimental hypothesis If our test is not significant we can Accept our null hypothesis and reject our alternative/experimental hyp

9. Levels of measurement Nominal Ordinal Interval

10. Levels of data: nominal • Which newspaper paper do you read regularly? • We can put these into categories.

11. Levels of Data: ordinal • What grade did you get for each of your gcse’s? • These can be put in order… highest to lowest

12. 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.

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

14. Tests to Know Mann Whitney U Chi Squared Wilcoxon T Spearmans rho

15. Process data Complicated arithmetic Produce test statistic

16. Sig levels ½’d for one tailed test Compare test Statistic with critical values for that test To determine significance level critical value: Value that test statistic must reach in order for null hyp to be rejected

17. Sig levels ½’d for one tailed test

18. Type 1 and Type 2 Errors Type 1 error Rejecting a null hypothesis when we should not P level too tight Type 2 error Accepting a null hypothesis when we should not P level too loose

Inferential statistics powerpoint

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