Interpreting Data: Graphs & Charts (1) Numeracy & Quantitative Methods: Numeracy for Professional Purposes Interpreting Data: Graphs & Charts (1) Laura Lake

Recap Types of data Descriptive statistics Interpreting data Presenting data to different audiences. So far, we have looked as types of data and basic descriptive statistics including measures of distribution, central tendency and dispersion. Now moving on to look at useful mechanisms for interpreting statistical data.

Graphs Choice of graph dependent on data type. Nominal and ordinal data based on the selection of categories (yes or no, strongly agree to strongly disagree) - therefore graphs need to have categories (bars or pie slices) Scale data numeric therefore line graphs or histograms. Nominal Pie chart or bar chart Ordinal Scale (interval or ratio) Line graph, histogram As with the choice of measure of central tendency, the choice of graph is also dependent on the type of variable that is being interpreted – i.e. Whether it is nominal, ordinal or scale data.

Pie charts Pie charts use a slice or segment for each category. Each slice is shown in relation to the whole pie. It is often used for nominal data. It can be sometime hard to judge relative size of each slice if there is no real difference in size between them. It is not particularly useful when there are a large number of categories – leads to too many slices of the pie and can look confusing. Useful to include value labels stating % for each category. If there are a large number of categories then the only way to avoid presenting pie charts with too much detail is to aggregate categories into broad groups and/or combine all rare values into an “other” category.

Pie charts Chart 1: Hours worked per week

Bar charts Bar charts use a bar to represent each category. Size of each bar is clear. Easy to judge relative size of bars. Better for ordinal data: shows order of categories. Useful for comparing categories with clustered bar charts. A bar charts uses a bar to represent each category. The size of each bar is visually clear to see and this makes it easy to judge relative size of bars. Bar charts work well for ordinal data as it shows order of categories. As with pie charts, there is a limit to how many categories that can reasonably be represented on a bar chart. Too many bars and the visual display of the data becomes lost. Therefore, it may be useful to aggregate or combine some categories if there are too many to present. Bar charts are also useful for presenting categories that you want to compare.

Bar charts (single) Chart 2: Age of respondents in years Bar charts can also be represented in horizontal bars.

Bar charts (clustered) Chart 3: Age of respondents in years by gender Bar charts can also be represented in horizontal bars.

Histograms Bar charts for categorical data. With scale data (interval or ratio) use histograms. Difference between bar charts and histograms – bars touch to represent continuous data. A histogram is constructed from a frequency table. Intervals from the frequency table are placed on the horizontal axis (x-axis) Values needed for the frequencies are represented on the horizontal axis (y-axis). The frequencies are depicted by the height of a bar corresponding to each interval.

Histograms EXAMPLE: Consider the following interval data set: 4, 9, 10, 17, 20, 21, 23, 24, 29, 32, 35, 38, 39, 46, 47. A graph which shows how many of each value occurred (e.g. number of 1s, 2s, 3s, 4s and so on) which is meaningless. Put the data into ranges (called bins). Instead we bin the data into convenient ranges. This data set uses a bin width of 10. Data range Frequency 1 to 10 2 10 to 20 20 to 30 5 30 to 40 4 40 to 50 Changing the size of the bin changes the appearance of the graph and the conclusions you may draw from it.

Histograms Chart 4: Age of respondents in years Mean = 26.3 Median = 23.5 Standard deviation = 13.3

Line graphs Scale data (interval or ratio) can use line graphs. Shows a simple representation of the data. Is particularly useful for showing a change in scale data over time. Chart 5: Temperature (°C) over one week

Line graphs If showing a distribution of values in one variable sometimes if can be easier to display this in a histogram. Chart 6: Test scores for students, 2011 When looking at the distribution of values in one variable we are really looking at the frequency which is better suited to a histogram. In the example above. a line graph can not really clearly show the distribution of students and gives the impression that there is some relationship between the test score of one student to the next – they are of course discrete values that are simply a test score for each student. Line graphs typically show trends rather than all the values of a variable.

References Bryman, A. (2008) Social Research Methods. 3rd Ed. Oxford: Oxford University Press. David, M. and Sutton, C. (2011) Social Research : An Introduction. 2nd ed. London: Sage. Click to add notes

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