Descriptive and Inferential Statistics

Descriptive and Inferential Statistics

1. Descriptive Statistics

   • Measures of Central Tendency
     • A single score that represents the data
     • For example
       • Mean
       • Median
       • Mode
   • Measures of Dispersion
     • A measure of variability within the data
     • For example
       • Standard Deviation
   • Using means and SDs we can...
     • Z-scores
       • Compare a range of measurements
       • Express how many SD units a point in the normal curve is from the mean
       • A z-score is the number of SD units a score is from the mean
     • Summarise data visually
   • Populations
     • Every single possible observation
     • We know how these tend to be distributed
   • Samples
     • Make inference about the population from the sample
     • Summarise from sample data what population mean is
     • Central Limit Theorem
       • Representative samples
         • sampling distribution approaches normal distribution
         • Mean of all sample means equals population mean
         • Sample size increases, SD of sampling distribution decreases
     • Sample size increase = more certainty of population mean
     • Standard Error
       • Confidence that sample mean represents population mean

2. Inferential Statistics

   • Allow us to make inference or generalisation
     • Is this group different from the population?
     • Are these two groups different from each other?
     • Does an experimental manipulation have an effect?
   • Basic Principles
     • Test statistic
       • How different your sample is from another mean
     • Critical value
     • Alpha level
       • p<0.05
     • Test statistic < critical value at alpha level = significant results
   • Errors
     • Type I
       • Too loose alpha level
     • Type II
       • Too strict alpha level
   • Student's t-distribution
     • Gossett
       • Worked for Guinness in Dublin
         • Assessed grain quality
         • Used small samples to make assumptions about general population
         • Published under a pseudonym
       • Realised that...
         • As sample n gets larger, sampling distribution looks more normal
         • Small samples, pointier around mean and fatter at edges
         • Shape differs at all degrees of freedom in a sample
   • t-tests
     • Uses
       • Single sample is drawn from a population where mean is known
         • Between samples t-test
         • One Sample Wilcoxon Signed Ranks T-test
       • Two sets of measurements are drawn from same population
         • In different groups
           • Independent samples t-test
           • Mann-Whitney U
         • Before and after intervention
           • Paired samples t-test
           • Wilcoxon Signed Rank T-test
       • Quantifying the differences in the data relative to the variation that exists in the data