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Analysing quantitative data

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Quantitative data analysis

Key points

Data must be analysed to produce information

Computer software analysis is normally used for this process (Microsoft Excel, SPSS etc.)

Present, explore, describe & examine relationships

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Examples of basic chartPie chart

Saunders et al. (2009)

Figure 12.8 Pie chart

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More advanced work requires Statistical analysis

Establishing the statistical relationship between two variables (e.g. If I am in this group I am have a % probability of doing X).

If you need to do this then see:

http://www.statsoff.com/textbookhttp://oli.web.cmu.edu/openlearning/

forstudents/freecourses/statistics

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Quantitative data analysis: Main Concerns Preparing, inputting and checking data

Choosing the most appropriate statistics to describe the data

Choosing the most appropriate statistics to examine data relationships and trends

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Type of Data: category data Example: Number of cars hatchback / saloon / estate

Can’t measure it, just simply count occurrences Focus on one discrete variable (i.e. Hatchback)

Dichotomous data (e.g. either Male or Female) Ranked data (how strongly you agree with statement

X)

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Type of Data: numerical data Example: temperature in Celsius

Quantifiable data that can be measured

Interval data e.g. Degrees Celsius [zero degrees is not actually ZERO]

Ratio (calculate the difference) data e.g. Profits up 34% for a year

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Type of Data: continuous data Example: height of students

Can be any value [within a range]

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Level of Precision

LESS MORE

Precise data can be grouped to make it less precise (e.g. Mark of 85% grouped into a ‘Very Good’ category but

Not the other way round)

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Exploring Data: Tukey’s (1977) exploratory data analysis approach focus on tables & diagrams

Great Tables & Diagrams Need:

Clear & Distinctive TitleClearly stated units of measurementClearly stated source of dataAbbreviations explained in notesSize of the sample is stated “n = 43”Column / Row / Axis LabelsDense shading for smaller areasLogical Sequence of columns & rows

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Exploratory Analysis: Individual unit of data

Highest and lowest values

Trends over time

Proportions (relative size)

Distributions (number in a group)Sparrow (1989)

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What Do You Want To Show?Highest / Lowest: Bar Chart / Histogram for Categories

You can reordered it for Non-continuous data

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What Do You Want To Show?Frequency: Again a Histogram / Bar Chart (reorder it

to make it clearer)

Perhaps a pictogram

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What Do You Want To Show?Trend: Line Chart or histogram

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What Do You Want To Show?Proportion: Pie chart or bar chart

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Distribution of values

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Normal DistributionSample of 100+ people should produce a normal curve.

Standard deviation shows how widethe spread of results are.

Low standard deviation shows a narrow range of values

High standard deviation shows a wide range of values

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How to calculate it:Consider a population consisting of the following eight values:

2, 4, 4, 4, 5, 5, 7, 9Calculate the Mean (2, 4, 4, 4, 5, 5, 7, 9) / 8 = 5Calculate the difference between each individual data point and

the mean. Then square each one

Calculate the average of these values (i.e. 32 / 8 = 4)Find the sqaure root of this number (square root of 4 is 2)

http://www.statsoff.com/textbookhttp://oli.web.cmu.edu/openlearning/forstudents/freecourses/statistics

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Negative skew / Positive skew

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What to do with your distribution?Try to understand what is the story behind the data:

Is the data ‘unrepresentative’?

Are the categories the wrong width?

Is there something going on we did not know about at the start?

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Comparing variables to show

Totals

Proportions and totals

Distribution of values

Relationship between cases for variables

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Multiple bar chart: Totals & Highest / Lowest

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Comparing proportions

Would you buy this product again? – products 1 to 6

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Compare Trends

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A final word of caution

GI-GO

Garbage In – Garbage Out