graphs

• Summarising Data in a Table

  There are various ways of

  representing data; one of these is

  in the form of a summary table. It

  is important to note that when

  tables appear in the results

  section of a report they are not

  merely raw scores but have been

  converted to descriptive statistics.
• Summarising Data in a Table

  It is standard practice

  to include a summary

  paragraph beneath

  the table explaining

  the results:
• Summarising Data in a Table

  We can see from the mean values

  that there were more words

  spoken, on average, in the five

  minutes following the

  consumption of the energy drink

  (119 mean words) than the water

  drink (96 mean words). This suggests that drinking an energy drink

  makes people more talkative than drinking water.
• Summarising Data in a Table

  The standard deviation is higher in

  the RedBull condition (53.8)

  suggesting that there was a larger

  spread of scores than in the water

  group condition (35.8). This

  suggests that not all participants

  were equally affected by the energy drink. In the water group

  scores were clustered around the mean to a greater degree.
• Bar Charts

  Data can be represented

  visually using a suitable

  graphical display so the

  difference in mean

  values can easily be seen.

  The most suitable graph

  in this case is a bar chart.
• Bar Charts

  Bar charts are used when data

  is divided into categories,

  otherwise known as discrete

  data. In the example before,

  the categories are our two

  conditions (the RedBull

  condition and the water

  condition) and these occupy the horizontal x-axis.
• Bar Charts

  The frequency or amount

  of each category is plotted

  on the vertical y-axis

  (effectively the height of

  the bar). Bars are

  separated on a bar chart to

  denote that we are dealing

  with separate conditions.
• Scattergrams

  We came across scattergrams in a

  previous lesson, during our

  discussion of correlations. Unlike

  the other forms of graph,

  scattergrams do not depict

  differences but associations

  between co-variables.
• Scattergrams

  Either of the co-variables

  occupies the x-axis and the

  other the y-axis (it does not

  matter which) and each

  point on the graph

  corresponds to the x and y

  position of the co-variables.
• Histograms

  In a histogram the bars touch

  each other, which shows that

  data is continuous rather than

  discrete (as in a bar chart). The

  x-axis is made up of equal-sized

  intervals of a single category, for

  instance, percentage scores in a maths test broken down

  into intervals such as 0–9, 10–19, 20–29, etc.
• Histograms

  The y-axis represents the

  frequency (number of people

  who scored a certain mark)

  within each interval. If there

  was a zero frequency for one

  of the intervals, the interval

  remains but without a bar.
• Line Graphs

  Line graphs also

  represent continuous

  data and use points

  connected by lines to

  show how something

  changes in value, for

  instance, over time.
• Line Graphs

  Typically, the IV is plotted

  on the x-axis and the DV

  on the y-axis. For instance,

  in an investigation of how

  the passage of time affects

  our ability to remember

  information, the decline in

  recall would be shown as a continuous line.
• Distributions

  Normal distribution

  If you measure certain

  variables, such as the height of

  all the people in your

  school/college, the frequency

  of these measurements should

  form a bellshaped. This is called

  a normal distribution which is symmetrical.
• Distributions

  Normal distribution

  Within a normal distribution, most

  people are located in the middle

  area of the curve with very few

  people at the extreme ends. The

  mean, median and mode all occupy

  the same mid-point of the curve. The ‘tails’ of the curve, which extend

  outwards, never touch the horizontal x-axis (and therefore never

  reach zero) as more extreme scores are always theoretically possible.
• Distributions

  Skewed distributions

  Not all distributions form such

  a balanced symmetrical

  pattern. Some data sets derived

  from psychological scales or

  measurements may produce

  skewed distributions, that is,

  distributions that appear to lean to one side or the other.
• Distributions

  Skewed distributions

  A positive skew is where most of

  the distribution is concentrated

  towards the left of the graph,

  resulting in a long tail on the right.

  Imagine a very difficult test

  in which most people got low marks with only a handful of

  students at the higher end. This would produce a positive skew.
• Distributions

  Skewed distributions

  It is interesting to note how the various measures

  of central tendency are affected by this situation.

  The mode (as we would expect) remains at the

  highest point of the peak, the median comes

  next, but the mean has been dragged across to

  the right. Remember how extreme scores affect

  the mean. Here, the very high-scoring candidates

  in the test have had the effect of pulling the mean

  to the right, whereas the median and mode – neither of which include all the

  scores when they are calculated – remain less affected by this.
• Distributions

  Skewed distributions

  The opposite occurs in a negative skew.

  A very easy test would produce a

  distribution where the bulk of the scores

  are concentrated on the right, resulting

  in the long tail of anomalous scores on

  the left. The mean is pulled to the left this time (due to the lower

  scorers who are in the minority), with the mode dissecting the

  highest peak and the median in the middle.