Statistics

Statistics

1. Descriptive Statistics

   • Measures of Central Tendency
     • Three Kinds
       • Mean
       • Median
       • Mode
   • Measures of Dispersion
     • A measure of variability within the data
       • Standard Deviation
       • Variance
   • From means and SD
     • 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 (n=30 min.) = more certainty of population mean
     • Standard Error
       • Confidence that sample mean represents population mean

2. Inferential Statistics

   • 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
         • Less harmful for Data Analysis
     • Type II
       • Too strict alpha level
         • Very harmful for Data Analysis
   • t-tests
     • Uses
       • Single sample is drawn from a population where mean is known
         • Between samples t-test
       • Two sets of measurements are drawn from same population
         • In different groups
           • Independent samples t-test
         • Before and after intervention
           • Paired samples t-test
       • Quantifying the differences between actual and expected data