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Quantitative data analysis In plain English Need to know • Information collected in study called “data” • Numerical data are called “quantitative” • Levels of data – Nominal – Ordinal – Interval – Ratio Mnemonic technique (acronym) to remember these: NOIR Levels of data: Nominal • Data goes into categories. • Can only be used as frequencies. • Example: Which newspaper paper do you read regularly? Levels of Data: Ordinal • Data can be put in order… highest to lowest Finish line Example: What grade did you get for each of your gcse’s? Example: Races Levels of data: Interval • Data are measured using units of equal measure Example: How anxious are you? 1 2 3 4 5 6 7 8 9 10 Levels of data: Ratio •Must have all properties of interval data •There is also a true zero point Reaction times: We can measure and compare the exact time because there is an absolute zero point (0 seconds). Example: How quick is your reaction time? Measures of central tendency Tell us about a ‘typical’ response for a data set o Mean – average (add up all the values and divide by the total number of values) o Median – middle value o Mode – value that is most common Mean Median Mode -Cannot be used with nominal data sets - Not good if too many extreme values -Uses all the values -Not as affected by extreme scores -Not as ‘sensitive’ as the mean -Useful with nominal data -Not useful if there are several modes Measures of dispersion Describes how spread out the data is o Range – lowest to highest 3, 5, 8, 8, 9, 10, 12, 12, 13, 15 1, 5, 8, 8, 9, 10, 12, 12, 13, 17 Range = 12 (3-15) Mean = 9.5 Range = 16 (1-17) Mean = 9.5 Measures of dispersion o Standard deviation – shows amount of deviation in a set; describes data around the mean. Visual Displays: Tables • Numbers you collect, untreated “raw data” • Can be summarized using mean, median, mode 3, 5, 8, 8, 9, 10, 12, 12, 13, 15 1, 5, 8, 8, 9, 10, 12, 12, 13, 17 Visual Displays: Bar Chart • Shows frequency • Can be used with nominal data (categories) or numbers Visual Displays: Line Graph • Y-axis shows frequency • X-axis Cannot use with nominal data (categories) Visual Displays: Scattergram • Graph used with correlational analysis (we’ll look at this later!!) Practice! Fakedata and Fraud (2004) carried out an investigation to decide what colour to paint the walls of their Psychology department. They assigned each possible colour to a number (white=1, green=2, brown=3, red=4 etc.) and then carried out a survey to see which colour the staff and students would prefer. Once they had asked everyone their preference, they decided on the final colour by calculating the mean of all the colour values to find an average colour that everyone would like. The mean came out at 3.1, so the researchers painted the department brown. Everyone hated it. 1. Explain where Fakedata and Fraud went wrong, referring to their choice of measure of central tendency in your answer. More practice Take a look at each of the following data sets. For each one, state which measure of central tendency you would choose to summarise it, and explain why your choice is appropriate. (a) 1, 3, 4, 4, 7, 9, 10, 10, 12 (b) yes, yes, no, yes, no, no, yes, no, yes, yes, yes, no, no, no, no (c) 13, 17, 19, 20, 24, 25, 26, 31, 36, 37, 56 (d) 0, 0, 0, 0, 0, 0, 0, 12, 14, 17, 20 (e) 3, 21, 25, 26, 30, 32, 32, 35, 36, 45, 47, 50 Into groups Group A: Question 2: Why is it better to know about the mean and range of a data set rather than just the mean? Also Data Set 1 (Question 1) Group B: Question 3: Explain why it might be better to know the standard deviation of a data set rather than the range. Group C: Question 4: Look at the following data sets. Which one do you think would have the smaller standard deviation? 2 2 3 4 5 9 11 14 18 20 21 22 25 2 5 8 9 9 10 11 12 14 15 16 20 25 Group D: There are three graphs on page 81. a. What can you conclude from graph C? b. Write a title that would be suitable for all three graphs. c. Describe the y axis of all three graphs. Also Data Set 4 (Question 1) Also Data Set 3 (Question 1) Also Data Set 2 (Question 1)