Inferential statistics notes

Descriptive statistics- measures of central tendency and measures of dispersion- summarise and describe the raw data researchers have collected from their sample

Inferential statistics- use the data collected from the sample to make inferences (assumptions) about the behaviour of the entire target population

Probability- researchers test the data they collect from the sample to assess the probability these results are due to chance variation. If the likelihood of the result occurring due to chance is less than 1 in 20 (0.05) then the results are judged to be significant, the alternate hypothesis is accepted, and the null hypothesis is rejected. If the results do not pass this test of significance, the null is accepted, and the alternate hypothesis is rejected

Statistical tests- the tools that researchers use to determine if the results are significant, there are a range of statistical tests, and different tests are appropriate depending on the research design and the level of data collected

To decide which statistical tests is needed, use the following table:

Related data- repeated measures and matched pairs

Unrelated data- independent groups design

How to use a table of critical values:

• Find the calculated value in the stem

• Identify the number of participants/degrees of freedom in the study

• Identify the level of significance used, usually 0.05, but it can be other values

• Identify if the study is one-tailed/directional, previous research suggests direction or two-tailed/non-directional, there is no/incosistent previous research

• Find out if the critical value is greater than or less than the calculated value

Working out degrees of freedom- for some of the statistical tests, degrees of freedom are used instead of number of participants. Its likely that the degrees of freedom will be in the stem, however you can be asked to calculate degrees of freedom using a formula

• Degrees of freedom (df)=(r-1)x(c-1)

  • R= number of rows

  • C=number of columns

Calculating the sign test:

• Subtract each participants score in condition B from A. Clearly note the sign of each result (+ or -)

• Work out the number of participants, excluding any participants with the same score in both conditions

• Work out (s), which is the least frequent sign

• Use the critical value table to find the critical value, read across from n calculated in step 3 and down from the level of significance required

• Compare the critical value to S. if it is equal to or less than the critical value the results are significant

Levels of data:

• Nominal- the data can only be categorised

  • Eg city of birth, marital status

• Ordinal- the data can be categorised and ranked

  • Eg top 5 Olympic medalists, likert scales

• Interval- the data can be categorised, ranked and evenly spaced

  • Test scores, temperature