Scientific Method

Probability and Significance

Probability

Q: What does ‘probability’ mean?A: The likelihood that something will happen

Probability = number of particular outcomes number of probable outcomes

Calculating probabilityImagine that you monitor the weather for a period of 10 days.

The forecast is correct on 4 days and incorrect on 6.

The probability of correct weather forecasts is:

Correct weather forecasts = 4 = 0.4 10

The closer your answer is to 1, the better the prediction.

Calculating probability

Express the following probabilities:

• The likelihood of tossing a coin and it landing on ‘tails’

• The likelihood of rolling a 6 on a dice• The likelihood of rolling two 6s on two die

Calculating probability

Express the following probabilities:

• The likelihood of tossing a coin and it landing on ‘tails’ ½ or 50% or 0.5

• The likelihood of rolling a 6 on a dice1/6 or 16.7% or 0.167

• The likelihood of rolling two 6s on two die1/6 x 1/6 = 1/36or 2.7% or 0.027

Why bother?

Psychologists are interested to see from their data analysis how likely it was that their results were due to chance. Note: usually we predict the likelihood of an outcome but in psychology we work out how likely it is that chance has affected our results.

Probability, or p in science, is expressed as a value between 0 and 1.

Rank the following probabilities in terms of how likely they are that results were due to chance:

p = 0.05p = 0.45p = 0.95p = 0.78

Rank the following probabilities in terms of how likely they are that results were due to chance:

p = 0.95p = 0.78p = 0.45p = 0.05

This is the least significant probability rating because it is the closest to ‘1’ (in other words, there is a higher likelihood that results were due to chance).

Significance

Q: What does ‘significance’ mean?

A: The level at which the null hypothesis is accepted or rejected

Significance

Scientists try to generalise from their sample to the target population. The role of statistical tests is to identify how likely it is that the results from our sample accurately reflects what would happen in the population. Statistical tests tell us how probable something is.

Hypotheses

Define the experimental hypothesis and the null hypothesis in your own words.

Hypotheses and statistical tests

Statistical tests give an idea of whether the results are probable or likely in the wider population. If the probability is small enough it suggest that the results in our sample are unlikely to be due to chance. We can infer that the results reflect the population and we can reject the null hypothesis.

Level of significance

The level of significance in psychology is 0.05 or 5%.

So, p = 0.05

This is the likelihood of getting the findings if the null hypothesis is true.

Significance

Are these results significant?

p = 0.75p = 0.03p = 0.50p = 0.125

Test your understanding

What does p = 0.05 mean? Explain why the 0.05 level of significance is normally used in psychology.

Key points

• Probability is a measure of how likely it is that something will happen

• Statistics are used to test the probability that the null hypothesis is true

• The null hypothesis is that there is no relationship or difference between variables in the population

• If the probability of the null hypothesis being correct is lower than the level of significance then it can be rejected