Presentation of quantitative data

Summarising data in a table

- When tables appear in the results section of a report they are not merely raw scores but have been converted to descriptive statistics

- (Table in book page 196) Table showing the mean number of words spoken in 5 minutes and standard deviations for the energy drink condition and the water condition

Summarising data in a table: Explaining the mean

- 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: Explaining the standard deviation

- The standard deviation is higher in the energy drink condition (53.8) suggesting that there was a larger spread of scores than in the water condition (35.8)

- This suggests that not all participants were equally affected by the energy drink. In the water condition, scores were clustered around the mean to a greater degree

Bar charts

- Used when data is divided into categories (discrete data). The categories (conditions) occupy the horizontal x-axis. The frequency or amount of each category is plotted on the vertical y-axis (height of the bar)

- Separated to denote that we are dealing with separate conditions

Histograms

- Bars touch each other, which shows that x-axis data is continuous rather than discrete. X-axis is made up of equal-sized intervals of a single category. The y-axis represents the frequency within each interval. If there was a zero frequency for one of the intervals, the interval remains but without a bar

Scattergrams

- Do not depict differences but instead associations between co-variables. 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

Presenting a table/graph

- Must always have a title and clearly label columns and axes

Distributions: Normal distribution

- If you measure certain variables, the frequency of these measurements should form a bell-shaped curve. Most people (or items) 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 midpoint of the curve

Distributions: Normal distribution (tails)

- The 'tails' of the curve, which extend outwards, never touch the horizontal x-axis as more extreme scores are always possible

Distributions: Skewed distributions

- Not all distributions form a balanced symmetrical pattern. Some data sets derived from psychological scales or measurements may produce this type of distribution, that is, distributions that appear to lean to one side or the other

Distributions: Skewed distributions (positive skew)

- Where most of the distribution is concentrated towards the left of the graph, resulting in a long tail on the right. In this, the mode remains at the highest point of the peak, the median comes next, but the mean is dragged across towards the 'tail'

- Very high scoring candidates in a test pull the mean to the right, whereas the median and mode- neither of which include all the scores when calculated- are less affected by this

Distributions: Skewed distributions (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 (due to the lower scores who are in the minority), with the mode dissecting the highest peak and the median in the middle