(11) Measure of Averages in Psychology

• psychologists can carry out correlation studies
• correlation is a method of analysis rather than a research method
• a correlation is a mathematical technique which a researcher investigates an association between two variables
• the two variables investigated in a correlation study are known as co variables (not the IV or the DV)
• co variables = the variables investigated within a correlation
• a correlation investigates the association between variables rather than trying to show a cause and effect relationship, so co-variables are not the IV or DV
• correlations are plotted on a scattergram
• correlation illustrates the strength and direction of an association between two or more co-variables
• Types of Correlation :

  • positive correlation - as one variable increases, the other also increases
  • negative correlation - as one variable increases the other decreases
  • zero/ no correlation - there is no relationship between variables
• • in an experiment the researcher controls or manipulates the IV in order to measure the effect on the DV
  • deliberate change in one variable - possible to infer that the IV caused any observed changes in the DV
• Correlation :

  • no manipulation of one variable and so it is not possible to establish cause and effect between one co variable and another
  • even if theres a strong positive correlation, we can not assume that one co-variable causes another
  • intervening variables - other variables which could have led to the relationship that established
  • influence of intervening variables cannot be disregarded
• EVALUATION of Correlation Studies

  Strength :

  • provide a precise and quantifiable measure of how two variables are related
  • suggests ideas for possible future research if variables are strongly related or demonstrate an interesting pattern
  • often used as a starting point to assess possible patterns between variables before researchers commit to an experimental study
  • quick and economical to carry out
  • no need for controlled environment & manipulation of variables
  • secondary data can be used - less time consuming than experiments
• EVALUATION of Correlation Study

  Limitations :

  • lack of manipulation and control - tell us how variables are related but not why
  • correlations cannot demonstrate cause and effect between variables - do not know which co-variable is causing the other to change
  • establishing direction of the effect is an issue
  • third variable problem - can cause the relationship between the two co-variables
  • correlation can occasionally be misused or misinterpreted - especially in the media
  • media:relationship between variables are sometimes presented as causal 'facts' - may not be true
• Measures of Central Tendency :

  • use descriptive statistics when analysing numerical data
  • includes measure of central tendency, dispersion and displaying data on graphs
  • 'averages' - the most typical values in a data set
  • are the mean median and modes
• Descriptive Statistics :

  • use of graphs, tables and summary statistics to identify trends and analyse sets of data
• Measure of Central Tendency :

  • the term for any measure of the average value in a set of data
• Mean :

  • arithmetic average
  • calculated by adding up all the values in a set of data and dividing by the number of values there are
• Median :

  • the central value in a set of data when values are arranged from lowest to highest
• Mode :

  • the most frequently occurring value in a set of data
• EVALUATION of the Mean

  Strength :

  • most sensitive of the measures of tendency as it includes all the scores/ values in the data set within the calculation
  • more representative of the data as a whole
• EVALUATION of the Mean

  Limitations :

  • is easily distorted by extreme values
  • by including outliers, it can make the mean less representative of the data overall
• EVALUATION of the Median

  Strength :

  • extreme scores do not affect it
  • even if there are extreme values the median does not change/ remains the same
  • easy to calculate after the numbers are arranged in order
• EVALUATION of the Median

  Limitations :

  • less sensitive than the mean
  • not all scores are included in the final calculation
• EVALUATION of the Mode

  Strength :

  • very easy to calculate
  • but if data is in categories, the mode is the only method that can be used to identify the most 'typical'/ average value of the data would be to select the modal group
• EVALUATION of the Mode

  Limitations :

  • a very crude measure
  • not very representative of the data as a whole
  • can be quite different from the mean
• Measure of Dispersion :

  • based on the spread of scores - how far scores vary and differ from one another
  • involves the range and standard deviation
• Measures of Dispersion :

  • term for any measure of the spread or variation in a set of scores
• Range :

  • a simple calculation of the dispersion in a set of scores
  • worked out by subtracting the lowest scores from the highest scores
  • (and adding 1 as a mathematical correction)
• Stabdard Deviation :

  • a sophisticated measure of dispersion in a set of scores
  • tells us how much scores deviate from the mean by calculating the difference between the mean and each score
  • all the differences are added up and divided by the number of scores - gives the variance
  • standard deviation is the square root of the variance
• EVALYATION of the Range

  Strength :

  • easy to calculate
• EVALUATION of the Range

  Limitation :

  • only takes into account the two most extreme values
  • not a fair representation of the general spread of scores
• EVALUATIONA of the Standard Deviation

  Strength :

  • more precise measure of dispersion than the range as it includes all values within the final calculation
• EVALUATION of the Standard Deviation

  Limitations :

  • like the mean it can be distorted by a single extreme value
• Standard Deviation :

  • sophisticated measure of dispersion
  • is a single value that tells us how far scores deviate (move away from) the mean
  • the larger the SD the greater the dispersion or spread within a data
  • 5.3 - high so more variance from the mean - participants performed differently from one another
  • a low SD value reflects that the data are tightly clustered around the mean
  • 0.1 - low SD so participants are highly clustered around the mean
• in psychology, results are usually presented as :

  • graphs
  • tables
  • scattergrams
  • bar charts
• Summarising Data in a Table :

  • are not merely raw scores - have been converted to descriptive statistics
  • a summary graph is usally used to explain the table of results
• Bar Charts :

  • is used so differences in mean values can easily be seen
  • used when data is divided into categories - discrete data
  • categories / IV - on the x axis
  • frequency/ amount/ DV - on the y axis
  • bars are separated on a bar chart to denote we are dealing with separate conditions
• Scattergram :

  • used to show an association between two variables
  • used to display data from correlations
  • one co variable on the x axis and the other on the y axis
  • can show psotive/negative/no correlation
• Histograms :

  • vars touch each other
  • shows data is continuous rather than discrete
  • x axis is made up of equal sized intervals of a single category
  • y axis represents the frequency within each interval
  • if there is a zero frequency for one of the intervals, the interval. remains but without a bar
• Line Graphs :

  • represent continuous data
  • use points connected by lines to show how something changes in value
  • IV plotted on x axis
  • DV plotted on the y axis