Inferential tests

for

Dummies

If your experiment needs statistics, you ought to have done a better experiment. (Rutherford)

Do not put your faith in what statistics say until you have carefully considered what they do not say.  (William W. Watt) For example… The average human has one breast and one testicle.  (Des McHale)

The manipulation of statistical formulas is no substitute for knowing what one is doing. (Blalock Jr)

He uses statistics as a drunken man uses lampposts - for support rather than for illumination.  (Lang)

words of wisdom

Aim

Understanding…. Which inferential test to use and why Levels of significance Degrees of freedom Critical and observed value What ‘it is significant’ means

aim

“A statistical procedure that uses data from a sample to test an hypothesis about a population”

In simple terms: If an interesting difference between treatment groups is seen in an experiment will this difference be reflected in the population generally?

hypotheses testing

We use results of statistical tests to chose between the following:

null hypothesis H0 (loud noise has no effect on learning) and alterative/experimental hypothesis H1 (loud noise disrupts learning)

hypotheses testing

Non-parametric When we have nominal or ordinal data

we use non-parametric tests: Chi-squared, Sign test, Wilcoxon sign

test, Spearman rank and Mann-whitney U test. They are not precise.

Types of inferential tests

Parametric Independent t test, related t test, Pearsons

product momentTo use a parametric test you need to: have scores measured on an interval scale scores must be normally distributed variability of scores for each condition

should be the same (homogeneity of variance).

Types of inferential tests

Tests of difference

Participant design

Level of measurement

Nominal data Ordinal data Interval/ratio data

Repeated measures or matched pairs

Sign test Wilcoxon Matched Related t test*

Independent groups chi-squared test Mann-Whitney Unrelated t test*

Tests for relationship (correlations)

Ordinal data Interval/ratio data

Spearman’s Rank Correlation Co-efficient Pearson’s Product Moment Correlation Co-efficient*

1. State the Hypothesis2. Set the significance level and the

appropriate statistical tests to use3. Collect data through experimentation and

Compute Sample Statistics4. Compare observed value and critical value

in the statistical table 5. Make a Decision as to whether you accept

your null or experimental hypothesis

Steps in hypotheses testing

State two hypotheses about the unknown population NULL HYPOTHESIS:

states that there is no effect, no difference, or no relationship or specific effect, difference or relationship

H0: loud noise has no effect on learning

ALTERNATIVE HYPOTHESIS: states that there is an effect, there is a difference,

or there is a relationship H1 : loud noise disrupts learning

State the hypotheses

The significance level is the percentage of results that you would accept as being due to chance and still accept that your study worked.

If you are willing to accept that 5% (or lower) of your results are due to chance and 95% (or more) are due to your IV then your level of significance is 5%. This is what psychologists usually use.

α = .05 If you are willing to accept only 1% due to chance

then 1% is your level of significance. α = .01

Set the significance level (α level)

In other words, the probability (p) of your results being due to chance is:

p ≤ 0.05

Set the significance level (α level)

Collect data through experimentation, calculate sample statistic and compare it to the critical value.

Set the significance level (α level)

E.g. A teacher records whether her 8 Year 13 students improved or got worse after she implemented a revision programme.

The probability of improvement is p and getting worse is q.

H0: p = .5 H1: p ≠ .5 p + q = 1level of significance is α = .05

An example of a statistical test: Sign

Test

Lets pretend that 3 out of the 8 students got worse and 5 out of the 8 improved.

X = no. of positive changesn = no. of participants

Z = X – pn = √ npq

An example of a statistical test: Sign

Test

0.71 observed value

Now compare your observed value of z = 0.71 to the critical value in the statistical table

N = 82 tailed, level of significance 0.05Critical value is 0Your observed value must be equal or less

than the critical value to be significant.

An example of a statistical test: Sign

Test

So your observed value is not significant so you accept your null hypothesis that the revision programme had no effect.

An example of a statistical test: Sign

Test

Some statistical tables require you to work out the degrees of freedom, df. In the exam you will be told how to work this out. Sometimes it is simply n – 1For some tests the observed value has to be greater than critical value in table and for some equal to or less.

Other tests

If your results were significant it means your experiment worked

and you did find a difference. You reject your null hypothesis and

accept your experimental/alternative

hypothesis.

What significance means

Now do exercise 16

Any questions?