Descriptive Statistics

• Measures of central tendency


  Mean

  Median

  Mode

  Are averages
• Measures of dispersion 


  Range

  Variance

  Standard deviation

  How spread a data set is
• When to / not use mean

  To = is the most sensitive value

  Not = extreme values or outliers as can be skewed
• When to / not use median

  To = when there are extreme values the median is less affected

  Not = less sensitive to variations so may not give a true picture
• When to / not use mode

  To = there is frequency/categorical data

  Not = there will be not modal value or several
• Variance

  How much a set of score is spread out

  Zero - values are identical

  Small - values are close to mean

  Large - data is very spread out around the mean
• Standard deviation

  The average amount a number differs from the mean

  Is the square root of variance

  Is plotted on a normal distribution graph
• When to use range

  When you have extreme high or low scores within a set of data
• When to use Variance

  When you want to know how scores are spread across a data set
• When to use Standard deviation

  When you want to look at the value of every score in comparison to the mean
• Strengths / weaknesses of range

  +easy to calculate

  -affected by extreme values

  -fails to take account of the distribution of numbers
• Strengths / weaknesses of variance

  +precise measure as all data is taken into account

  -may hide some characteristics of the data
• Strengths / weaknesses of standard deviation

  Same as variance

  + same value as the mean
• Normal distribution

  Proportion of scored falling either side of the mean are the same

  Mode, median and mean fall in the same place

  Known as a bell-shaped curve
• Skewed distributions

  The mean is different from the mode and median

  Negative skew = mean is less than mode so more people have higher scores and tail is to the left

  Positive skew = mean is greater than the mode so more people have lower scores and the tail is to the right

  In skewed distribution the standard deviation cannot be used
• 2 types of statistical tests

  Parametric

  Non-parametric
• Parametric tests

  Populations are normally distributed

  Variances of data and population should be approximately equal

  Should have at least interval or ratio data

  No extreme scores
• Non-Parametric tests

  Mann-Whitney U

  Wilcoxon Signed Ranks

  Chi-Square

  Binomial Sign

  Spearman's Rho