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### Quants

1. 1. What is a Variable?<br />any entity that can take on different values<br />not always 'quantitative' or numerical, but we can assign numerical values<br />attribute = a specific value of a variable<br />Examples: <br />gender: 1=female; 2=male<br />attitudes: 1 = strongly disagree; 2 = disagree; 3 = neutral; 4 = agree; 5 = strongly agree<br />
2. 2. Coding in a data matrix<br />
3. 3. Coding in a data matrix<br />Gender: Male = 1; Female=2<br />Political Orientation: Traditionalist=1; Moderate=2; Progressive=3<br />Social Class: Working=1; Upper working=2; Lower middle=3; Middle=4; Upper middle=5<br />
4. 4. Levels of Measurement<br />different kinds of variables<br />(1) Nominal<br />(2) Ordinal<br />(3) Interval and Ratio<br />
5. 5. Nominal Variable<br />used to classify things<br />represents equivalence (=)<br />adding, subtracting, multiplying or dividing nominal numbers is meaningless <br />tells you how many categories there are in the scheme<br />
6. 6. Ordinal Variable<br />ordering or ranking of the variable<br />the relationship between numbered items<br />‘higher’, ‘lower’, ‘easier’, ‘faster’, ‘more often’<br /> equivalence (=) and relative size (greater than) and < (less than)<br />
7. 7. Interval (and Ratio) Variable<br />All arithmetical operations are allowed<br />intervals between each step are of equal size<br />Examples:<br /><ul><li>length, weight, elapsed time, speed, temperature</li></li></ul><li>
8. 8. Levels of measurement<br /> <br />
9. 9. Frequency distributions<br />count number of occurrences that fall into each category of each variable<br />allow you to compare information between groups of individuals<br />also allow you to see what are the highest and lowest values and the value at which most scores cluster<br />variables of any level of measurement can be displayed in a frequency table<br />
10. 10. Frequency table<br />
11. 11. Percentages<br />number of cases belonging to particular category divided by the total number of cases and multiplied by 100.<br />the total of percentages in any particular group equals 100 per cent.<br />
12. 12. Graphical presentation<br />Pie charts<br />Barcharts<br />Line graphs<br />Histograms<br />
13. 13. Pie chart<br />illustrates the frequency (or percentage) of each individual category of a variable relative to the total. <br />Pie charts are not appropriate for displaying quantitative data.<br />
14. 14. 15<br />Barcharts<br />the height of the bar is proportional to the category of the variable - easy to compare <br />used for Nominal or Ordinal level variables (or discrete interval/ratio level variables with relatively few categories)<br />
15. 15. Multiple barchart<br />
16. 16. Compound or Component barchart<br />
17. 17. Line graphs<br />interval/ratio level variables that are discrete<br />need to arrange the values in order<br />
18. 18. Histograms<br />represents continuous quantitative data<br />The height of the bars corresponds to the frequency or percentage of cases in the class.<br />The width of the bars represents the size of the intervals of the variable<br />The horizontal axis is marked out using the mid points of class intervals<br />
19. 19. Example: Histogram<br />
20. 20. Graphs have the capacity to distort<br />
21. 21. Measures of Central Tendency<br />describe sets of numbers briefly, yet accurately <br />describe groups of numbers by means of other, but fewer numbers<br />Three main measures:<br />mean<br />median<br />mode<br />
22. 22. The Mean<br /><ul><li> most common type of average that is computed.</li></li></ul><li>When to use the Mean<br />When values in a particular group cluster closely around a central value, the mean is a good way of indicating the ‘typical’ score, i.e. it is truly representative of the numbers.<br />If the values are very widely spread, are very unevenly distributed, or clustered around extreme values, than the mean can be misleading, and other measures of central tendency should be used instead.<br />
23. 23. The Median<br />Also an average, but of different kind.<br />It is defined as the midpoint in a set of scores. It is the point at which one-half, or 50% of the scores fall above and one-half, or 50%, fell below. <br />Computing the Median:<br />(1) List the scores in order, either from highest to lowest or lowest to highest.<br />(2) Find the middle score. That’s the median.<br />
24. 24. The Median: Pros and Cons<br />time-consuming<br />if one of the numbers near the middle of the distribution moves even slightly, than the median would alter, unlike the mean, which is relatively unaffected by a change in one of the central numbers<br />if one of the extreme values changes, than the median remains unaltered.<br /><ul><li>2, 80, 100, 120, 130, 140, 160, 200, 3150</li></ul>single scores which are quite clearly ‘deviant’ when compared with others, are known as outliers – 2 and 3150<br />
25. 25. The Mode<br />the value in any set of scores that occurs most often<br />example 1:<br />5, 6, 7, 8, 8, 8, 9, 10, 10, 12 – the mode = 8<br />example 2:<br />5, 6, 7, 8, 8, 8, 9, 10, 10, 10, 12 –two modes: 8 and 10 – bimodal<br />very unstable figure<br />1,1,6,7,8,10 – mode = 1<br />1,6,7,8,10,10 – mode = 10<br />
26. 26. When to Use What?<br />depends on the type of data that you are describing<br />for nominal data - only the mode<br />for ordinal data - mode and median<br />for interval data - all of them<br />but, for extreme scores - use the median<br />
27. 27. Measure of dispersion (spread) <br />better impression of a distribution’s shape<br />measures indicate how widely scattered the numbers are<br />how different scores are from one particular score – the mean<br />variability - a measure of how much each score in a group of scores differs from the mean<br />
28. 28. The range <br />tells us over how many numbers altogether a distribution is spread<br /><ul><li>where
29. 29. r is the range
30. 30. h is the highest score in the data set
31. 31. l is the lowest score in the data set.</li></li></ul><li>r = biggest value - smallest value = 55-10 = 45<br />
32. 32. The mean deviation<br />number which indicates how much, on average, the scores in a distribution differ from a central point, the mean.<br />Mean deviation =<br />
33. 33. 210<br />368<br />364<br />319<br />-210<br />-368<br />-319<br />-364<br />Mean=370<br />X - mean= (-210)+210+(-368)+368+(-364)+364+(-319)+319 = 0<br />X - mean= 210+210+368+368+364+364+319+319 = 2522<br />mean deviation = 2522/8 = 315.25<br />
34. 34. The standard deviation (SD)<br />represents the average amount of variability<br />It is the average distance from the mean<br /><ul><li> sthe standard deviation
35. 35. find the sum of what follows
36. 36. Xeach individual score
37. 37. the mean of all the scores
38. 38. Nthe sample size</li></li></ul><li>Standard deviations<br />
39. 39. Shape of Normal Distribution<br />Symmetrical<br />Asymptotic tail<br />Mean <br />Median<br />Mode<br />
40. 40. The area under the curve<br />A normal distribution always has the same relative proportions of scores falling between particular values of the numbers involved.<br />Areas under the curve = proportion of scores lying in the various parts of the complete distribution<br />
41. 41. SS2008N - Surveys<br />Median<br />50%<br />50%<br />Median<br />
42. 42. SS2008N - Surveys<br />Quartiles<br />25%<br />25%<br />25%<br />25%<br />Median<br />Quartile 1<br />Quartile 3<br />
43. 43. Standard Deviation<br />