Inferential statistics

• Why do we use statistical testing?

  Shows us how likely it is that the patterns found in descriptive statistics are down to chance

  • Therefore it tells us the probability of the difference/relationship found happening by chance alone
• What is the level of significance?

  The probability of the results being down to chance that researchers are willing to accept when deciding if they can accept their hypothesis

  • Usually 0.05 (5%) in psychology
  • = probability of making an error when deciding to accept hypothesis is a 1 in 20 chance
  • Balances likelihood of Type 1 and Type 2 errors -> minimises possibility of both
• What is a Type 1 error?

  False positive

  • Accepting the alternative hypothesis when the null hypothesis is true -> apparent difference/relationship is just down to chance
• What is a Type 2 error?

  False negative

  • Accepting the null hypothesis when the alternative hypothesis is true -> results were just down to chance
• What is the level of significance used when trying to limit the chance of a Type 1 error?

  0.01 (1%)

  • Used when dealing with small samples + controversial/socially sensitive areas of research
  • However also increases chance of making a Type 2 error
• What are levels of data measurement?

  The way of describing/classifying the nature of values being used to record variables

  • Describes the operationalisation used on variables
  • Some ways of counting/recording variables = more precise than others = they can have more meaningful info about the difference/relationship being investigated
• What are the 3 levels of data measurement?

  ION

  • Interval
  • Ordinal
  • Nominal

  (In order from most to least sensitive)
• What is nominal data?

  Categorical data

  • No quantitative value of its own
  • Counts number of items in groups separated by name/category
• What is ordinal level data?

  Data on a scale where the values exist in a relative order

  • Can be ranked scales/score on a subjectively created scale
  • Relative order of values in scale matter but not the difference between them -> not a set interval = cannot be meaningfully compared
• What is interval level data?

  An objective scale which has values at fixed points of equal distance from each other

  • Allows for meaningful comparisons to be made between points on the scale
• Nominal data -> pros and cons

  Pros:

  • Useful when data needs to be counted/cannot be scored
  • Increases reliability
  • Large amounts of questions can be collected quickly

  
  

  Cons:

  • Least sensitive level of data measurement = harder to manipulate + reveals less info regarding patterns in data
  • Can only use the mode as a measure of central tendency
• Ordinal data -> pros and cons

  Pros:

  • Useful when data is on a continuous scale/being subjectively ranked or created

  Cons:

  • Not as sensitive as interval data = reveals less info regarding patterns in data
  • Gaps between values aren't equal = mean cannot be used to assess central tendency
• Interval data -> pros and cons

  Pros:

  • Useful -> most sensitive level of data measurement because equal, fixed intervals on a scale make data easier to manipulate to find meaningful patterns
  • Scientific measures used to record distance between values
  • Highly reliable

  Cons:

  • Not suitable for nominal or ordinal data
• What are the 3 questions we need to ask to choose the right stats test?

  1. Am I looking for a relationship or a difference?
  2. What is the level of data measurement?
  3. Is the data related or unrelated? (does it use the same ppts or diff. ones?)
• What are the 2 stats tests for nominal data expressing a relationship of difference?

  Related: Binomial Sign test

  Unrelated: Chi-Squared X²
• What are the 2 stats tests for ordinal data expressing a relationship of difference?

  Related: Wilcoxons T test

  Unrelated: Mann-Whitney U
• What are the 2 stats tests for interval data expressing a relationship of difference?

  Related: r test

  Unrelated: t test
• What is the stats test for nominal data expressing a correlation?

  Chi-Square X²
• What is the stats test for ordinal data expressing a correlation?

  Spearman's p (or Spearman's rho)
• What is the stats test for interval data expressing a correlation?


  Pearson's r
• What is the mnemonic to remember the order of the stats test?

  Carrots Should Come

  Mashed With Swede

  Under Roast Potatoes
• How does a stats test show that results are significant?

  • Putting raw results into stats test = calculated value
  • Must compare calculated value with critical value
• How do we find the critical value from a table in an exam question about a stats test?

  1. Is the hypothesis one-tailed or two-tailed?
  2. What level of significance is being used?
  3. What is 'N'? (how many items in the data set)