4. Data Analysis - Descriptive Statistics

• 1. Data Analysis - Descriptive Statistics

  Descriptive Statistics:

  • Ways of describing quantitative data + identifying patterns/trends using graphs, tables + summary statistics.
• 2. Data Analysis - Descriptive Statistics

  Method - Measures of Central Tendency:

  • any measure of average value in set of data.
  • calculated differently for each situation.
  • Mean, Median, Mode.
• 2a. Data Analysis - Descriptive Statistics

  Measures of Central Tendency - Mean:

  • add all data items; divide by number of items.

  Strength - most sensitive measure of central tendency (takes account of exact distance between all values of all data).

  Limitation - sensitivity = distorted by extreme values = unrepresentative.
• 2b. Data Analysis - Descriptive Statistics

  Measures of Central Tendency - Median:

  • items in order; tick off each side until left w/ middle number.
  • 2 middle numbers = find average (add , ÷ 2).

  Strength - not affected by extreme scores, easier calculate than mean; used for ordinal data.

  Limitation - not sensitive, exact values not reflected.
• 2c. Data Analysis - Descriptive Statistics

  Measures of Central Tendency - Mode:

  • work out most common data item.

  Strength - unaffected by extreme values; nominal data.

  Limitation - not useful explaining data when more than one mode.
• 3. Data Analysis - Descriptive Statistics

  Method - Measures of Dispersion:

  • based on spread scores - how dispersed (spread out) data items are.
• 3a. Data Analysis - Descriptive Statistics

  Measures of Dispersion - Range:

  • find lowest value and highest value.
  • lowest - highest then +1.

  Strength - easy calculate; provide margin of error (+1).

  Limitation - affected by extreme values (outliers).
• 3c. Data Analysis - Descriptive Statistics

  Measures of Dispersion - Standard Deviation:

  • measure of average distance between each data item above and below mean.
  • greater the standard deviation, greater the dispersion (spread) of data.
  • large standard deviation = not all participants affected by IV in same way; some anomalies.
  • small standard deviation = data is clustered around the mean; participants affected by IV in similar way.

  Strength - sophisticated measure of dispersion bc considers exact values in data set.

  Limitation - distorted by extreme values.
• 4. Data Analysis - Descriptive Statistics

  Data Distributions:

  • When data displayed on graph, see bell curve.
  • Way the bell curve looks = find out how data distributed.
  • Use average then standard deviation to work out how data distributed.
• 4a. Data Analysis - Descriptive Statistics

  Normal Distribution:

  • Classic bell-shaped curve + shows data equally distributed.
  • Mean, median, mode in exact midpoint.
  • Distribution is symmetrical around middle point.
  • Dispersion of scores either side of midpoint consistent and can be expressed w/ standard deviation.
• 4b. Data Analysis - Descriptive Statistics

  Skewed Distributions:

  • In some population scores aren’t distributed equally around the mean = skewed distribution (positively/negatively skewed).
• 4c. Data Analysis - Descriptive Statistics

  Skewed Distribution - Negatively Skewed:

  • right skewed - bulk of scores concentrated on right = anomalous results on left.
  • mean pulled to left (bc lower scorers minority).
  • mode, highest peak.
  • median middle.
• 4d. Data Analysis - Descriptive Statistics

  Skewed Distributions - Positively Skewed:

  • left skewed; long tail on right.
  • mode, highest peak; median comes next, followed by mean (bc outliers pulling mean to right as it includes all scores).
• 4e. Data Analysis - Descriptive Statistics

  What do Skewed Distributions Show?

  • mean not representative score - most scores either above (i.e. bigger than) or below (smaller than) the mean.
  • the mean shouldn’t be used as sole measure of tendency when distributions skewed.