Types of Tests

Types of Tests

1. INFERENTIAL stats: Inferential statistics: allow you to make inferences about a population, based on your sample data.

   • NULL (H0) vs ALTERNATIVE Hypoth
     • Take our data, and compare it against known distribution
       • E.g. Take a chance distribution, take your data and compare the two.
         • If it is unlikely to be preoduced by chance it is 'statistically significan't' (Probablility <0.05)
           • Also 5% or 1/20
   • POWER = Power is the likelihood you’ll correctly reject the null hypothesis
     • More power, less chance type II error
   • They produce a value (e.g. like a z-score, a t value, an F value etc.) and this has an associated probability. From this, we can test whether the data is likely to occur by chance, if not, we say it is significant.
   • Risky business
     • TYPE 1 Error: Type I Error – tests say it is significant and actually it isn’t
     • TYPE 2 Error: Tests say it is not significant and actually it is

2. ASSOCIATION: A relationship between two variables

   • CHI SQUARE
     • Each data point can only belong to one category
   • CORRELATION
     • Scale or ordinal data
       • Perfect positive correlation = 1.00
     • Parametric correlation (Pearson’s) = r
     • Non-parametric correlation (Spearman’s) = ‘rho’ (p / rs)
     • One-tailed – the correlation will be in a specific direction +/-
       • Two-tailed – there will be a correlation: One changes and other one changes (positive or negative)
         • Two-tailed test for correlation does not ask about the direction, it just asks ‘is there a relationship’?
     • We know the distributions of these test statistics, so we know when a correlation is significant
       • The closer the value is to 1, the stronger the correlation.
         • Correlations only look for linear relationship (in stright line), but your data might be curved or have a floor effect - LOOK AT THE DATA FIRST.
   • REGRESSION: More advanced version of correlation.
     • Allows you to see how much variance in your DV is accounted for by an IV.
     • BETA VALUES ß are like correlation coefficient - the bigger the beta, th emore important that regression is.
       • The Beta value also has a significance value (a p value) attached to it,
     • The overall regression equation will get an r squared value,
       • Like the correlation analysis, it ranges from 0 to 1. Values closer to 1 mean that a greater proportion of change in the DV is accounted for by the equation
     • you can have more than one independent variable.
     • The test statistic for the whole equation/model is R2

3. Correlation is not causation: an association may indicate a causal / predictive relationship, which can then be tested by experiment. Only controlled studies allow causation to be inferred.

4. The DEGREES OF FREEDOM = the number of independent bits of data in the sample that are free to vary.

   • Like a restriction we have to put in place
   • Always related to the sample size

5. N.B. The p value tells you how likely it is that you would get your data, if the null hypothesis were true.

   • If a result is significant, you reject the null. You DO NOT prove the alternative.

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