Correlations + Measures of central tendency and dispersion

• Correlations

  • Correlations illustrate the strength and direction of an association between two or more co-variables
  • Correlations are plotted on a scatter graph
  • One co-variable is represented on the x-axis and the other on the y-axis. Each point or dot on the graph is the x and y position of each co-variable.
• Positive correlations

  As one co-variable increases so does the other.

  Example: 

  • Frequent use of  caffeine is correlated with high anxiety. 
  • We might get people to work out how many caffeine drinks they consume over a weekly period and then have them self-report their level of anxiety at the end of the week.
  • Positive correlation means 
  • Higher caffeine = higher anxiety
• Negative correlations

  As one co-variable increases the other decreases.

  Example: 

  • We have the same caffeine drinkers to record the number of hours of sleep they have.
  • Caffeine consumption is often associated with less sleep
  • Negative correlation means
  • Higher caffeine = less sleep
• Zero correlations

  When there is no relationship between the co-variables.

  Example: 

  • The association between the people in at a shopping centre in manchester and the total daily rainfall in Peru is likely to be zero.
• Experiments

  The  researcher manipulates the IV in order to measure the effect on the DV. 

  We can assume that any changes observed in the DV have been therefore caused by the IV.

  Correlations

  No manipulation of variables and therefore, not possible to determine a cause and effect relationship.

  Even if we find a strong correlation we cannot assume that that one variable is the cause of another.
• AO3 - Strengths

  • Useful preliminary tool for research.
  • This can suggest ideas about possible research in future.
  • Quick and economic
  • No need for controlled environment and no manipulation of variables.
  • Data collected be others (secondary data) can be used.
• AO3 - Limitations

  • Cannot tell us why variables are related
  • Potential that an untested variable is the cause for the relationship
  • Eg. Perhaps people who drink a lot of caffeine do so because they work a job that requires long hours and high concentration therefore, there is a third variable - job type
  • Potential to be misused or misinterpreted
  • Eg. correlations between criminal activity and ‘broken homes’. Assumption that it is due to a ‘broken home’ people commit crime and doesn’t consider other factors.
• Mean - The average

  • Adding all the scores together and dividing by the total number of scores

  Example:

  5, 7, 7, 9, 10, 11, 12, 14, 15, 17
• Mean - the average

  Includes all the scores in the data set within the calculation This means it is more representative of the data as a whole.

  However, the mean is easily distorted by extreme values.
• Median

  • The middle value in a set of data set when the scores are arranged from lowest to highest. 
  • In an even number of scores the median is halfway between the two middle scores.

  Example:

  5, 7, 7, 9, 10, 11, 12, 14, 15, 17
• Median

  Extreme scores do not affect in the same way that it way it does with the mean.

  However, it is less sensitive than the mean as the actual value of lower and higher numbers are ignored and extreme values may be important 
• Mode

  • The most frequently occurring value
  • There can sometimes be more than one mode or no mode if all scores are different

  Example:

  5, 7, 7, 9, 10, 11, 12, 14, 15, 17
• Mode

  For data in categories it can be the only measurement you can use.

  The mode can be a wildly different score from our mean and median

  If there are several modes then thats not useful information.
• Range

  • (Highest score - Lowest score) + 1 = range

  Example:

  5, 7, 7, 9, 10, 11, 12, 14, 15, 17
• Range

  Easy to calculate.

  Only takes into account the two most extreme values, this might not be representative of the data set as a whole.

  Influenced by outliers.
• Standard Deviation

  • A single value that tells us how far scores deviate (move away) from the mean.
  • Larger the deviation the greater the spread within the data set. Smaller the deviation the smaller the spread within the data set.

  Example:

  5, 7, 7, 9, 10, 11, 12, 14, 15, 17
• Standard Deviation

  More precise measure of dispersion as it includes all values within the final calculation.

  However, this means that it can be distorted by one extreme value.