PS2518 (1)

PS2518 (1)

1. T-tests

   • Estimated population standard deviation
     • Use Sample Standard Deviation to estimate Population S.D
   • One Sample
     • Comparing a single sample from a reference mean
   • Within Subjects
     • 2 samples of observations from the same source
       • Tests if a population is equal to a pre-specified value
   • Independent Samples
     • Two samples of observations from different sources
       • Mean= difference between two parent distribution means
   • T-distribution
     • Probability distribution used to estimate population parameters when sample size is small or variance is unknown
   • Used when IV is nominal/ordinal and DV is Interval/Ratio

2. Z-Scores

   • Position of a score in relation to the mean of the distribution, using the S.D as a unit of measurement
   • Allow normal distribution => Standard Normal
   • Mean= 0 and S.D=1
   • Known S.D.
   • Normal distribution converted to a standard normal by changing to Z.
   • Specific probabilities associated with each Z-Score
     • Observation to Probability
       • Observation=>Convert to Z-score=>Probability
     • Probability to Observation
       • Probability=>Z-score to original=>Observation

3. Inferential Statistics

   • Measurement Scales
     • Nominal: Divided into categories
     • Ordinal: Ordered along a continuum
     • Interval: Ordered along a continuum in intervals of equal size
     • Ratio: Interval scale with meaningful 0
   • Mean Absolute Deviation
     • Average distance between each data value and the mean
   • Degrees of Freedom
     • No. observations that are free to vary
   • Standard Deviation
     • Measure of central tendency of the deviation of scores
     • Returns scores to original units of measurement from variance
   • Variance
     • Mean of the squares of the deviation scores

4. Distributions

   • Known patterns of variation in population chacteristics
   • Probability on Y, Observations on X
   • Normal Distribution
     • Distribution most assumed by inferential statistics
     • Standard Normal
       • Mean= 0, S.D =1.
       • Convert to Standard Normal using Z scores
   • Central Limit Theorem
     • Take many samples from sample population, sample means of distribution are normal and mean of sample means= population mean
     • The approximation to the normal distribution increases as sample sizes increases
   • Maps probability information as area under curve

5. Hypothesis Testing

   • Null Hypothesis
     • Default statement that there is no relationship between the two measured phenomena
       • Level of significance
         • Criterion required to decide to reject or retain Ho
         • Usually 0.05
   • Errors
     • Type I
       • Rejecting Ho when it's true
         • Probability denoted as Alpha
     • Type II
       • Retaining Ho when it's false.
         • Probability denoted as Beta.

6. Correlation

   • Linear direction and magnitude of a relationship
   • Pearson's Coefficient
     • Denoted at 'r'
     • Can take values between -1 and +1
   • Standardised form of Covariance
     • Covariance
       • The relationship of two variables as they move in tandem
       • Deviations from 0 mean more covariance
   • How one variable affects another
   • Regression used as predictor