Psychology: Research methods 20 (Inferential statistics)

What is inferential statistics

Inferential statistics allows us to infer from the data collected from the sample what is happening in the whole population. Therefore, we can accept or reject a hypothesis. Inferential statistics are based on the concept of the probability that the results are true.

Descriptive statistics (mean, mode, medium, standard deviation etc) only describe and summarise the data.

What does an alternative hypothesis do

An alternative hypothesis (directional or non-directional) predicts a significant difference or relationship.

What does significant mean

unlikely to have occurred by chance

What do statistical tests do

Statistical tests work on the concept of probability - the likelihood of something being true. Probability is written as a number between 0-1 or as a percentage

In psychology, when is data significant

In Psychology, data is significant (unlikely to have occurred by chance) if the probability of it occurring by chance is less than or equal to 5%.

When do we accept or reject the alternative hypothesis

p < 0.05: The probability that a (difference/correlation) occurred by chance is less than 5% (95% probability that the results did not occur by chance).  

If p < 0.05   accept the alternative hypothesis, reject the null hypothesis 

If p > 0.05   reject the alternative hypothesis, accept the null hypothesis 

If p < 0.05 we accept our alternative hypothesis, as the results are unlikely to have occurred by chance. To find out if p < 0.05, we need to do a statistical test. 

What significance level is appropriate

0.05 is the minimum acceptable level, and represents a balance between making a type 1 and a type 2 error.  

How do we choose a statistical test

Statistical tests are used to test whether a difference/correlation is significant (unlikely to have occurred by chance). To decide which statistical test to use 3 factors need to be considered: 

• Difference or correlation – is the research looking for a difference or a correlation. This should be obvious from the hypothesis. 

 

• Design – is the design of the research related (repeated measures or matched pairs) or unrelated (independent groups). 

 

• Level of measurement – is the data nominal, ordinal or interval. 

 

Are levels of measurement quantitative or qual

quantitative

What is nominal data

• Nominal (data in form of categories) 

 

Participants do not get a score, but are put into a category e.g. the number of ppts in each category. The most appropriate measure of central tendency is the mode. 

What is ordinal data

• Ordinal (data that can be put in rank order) 

  

Each participant gets a score. The data is not from a safe scale (does not have units of equal size) e.g., score on a questionnaire which is subjective. The data can be ranked in order. The most appropriate measure of central tendency is the median and dispersion is the range

What is interval data

• Interval (data on numerical scale with equal intervals between the units) 

 

Each participant gets a score. The data is from a safe scale (a standardised scale with units of equal size) e.g., a measuring instrument (e.g., timer) or standardised test (e.g., IQ test, maths test).  The most appropriate measure of central tendency is the mean and dispersion is the standard deviation. 

Tests that use interval data and are robust (they use actual scores, so are more sensitive to changes in the data) than other statistical tests.  

Interval data can be converted into ordinal data by ranking it. 

What are the different statistical tests

To select the statistical test:  

 

Type of data	Difference		Relationship (association or correlation)
	Unrelated design	Related design
Nominal	Chi-squared test	Sign test	Chi-squared test (a)
Ordinal	Mann-Whitney U test	Wilcoxon test	Spearman’s rho (c)
Interval	Unrelated t-test	Related t-test	Pearson’s r (c)

 

Carrots Should Come 

Mashed With Swede 

Under Roast Potatoes