1. What is a Variable? any entity that can take on different values not always 'quantitative' or numerical, but we can assign numerical values attribute = a specific value of a variable Examples: gender: 1=female; 2=male attitudes: 1 = strongly disagree; 2 = disagree; 3 = neutral; 4 = agree; 5 = strongly agree

2. Coding in a data matrix

3. Coding in a data matrix Gender: Male = 1; Female=2 Political Orientation: Traditionalist=1; Moderate=2; Progressive=3 Social Class: Working=1; Upper working=2; Lower middle=3; Middle=4; Upper middle=5

4. Levels of Measurement different kinds of variables (1) Nominal (2) Ordinal (3) Interval and Ratio

5. Nominal Variable used to classify things represents equivalence (=) adding, subtracting, multiplying or dividing nominal numbers is meaningless tells you how many categories there are in the scheme

6. Ordinal Variable ordering or ranking of the variable the relationship between numbered items ‘higher’, ‘lower’, ‘easier’, ‘faster’, ‘more often’ equivalence (=) and relative size (greater than) and < (less than)

8. Levels of measurement

9. Frequency distributions count number of occurrences that fall into each category of each variable allow you to compare information between groups of individuals also allow you to see what are the highest and lowest values and the value at which most scores cluster variables of any level of measurement can be displayed in a frequency table

10. Frequency table

11. Percentages number of cases belonging to particular category divided by the total number of cases and multiplied by 100. the total of percentages in any particular group equals 100 per cent.

12. Graphical presentation Pie charts Barcharts Line graphs Histograms

13. Pie chart illustrates the frequency (or percentage) of each individual category of a variable relative to the total. Pie charts are not appropriate for displaying quantitative data.

14. 15 Barcharts the height of the bar is proportional to the category of the variable - easy to compare used for Nominal or Ordinal level variables (or discrete interval/ratio level variables with relatively few categories)

15. Multiple barchart

16. Compound or Component barchart

17. Line graphs interval/ratio level variables that are discrete need to arrange the values in order

18. Histograms represents continuous quantitative data The height of the bars corresponds to the frequency or percentage of cases in the class. The width of the bars represents the size of the intervals of the variable The horizontal axis is marked out using the mid points of class intervals

19. Example: Histogram

20. Graphs have the capacity to distort

21. Measures of Central Tendency describe sets of numbers briefly, yet accurately describe groups of numbers by means of other, but fewer numbers Three main measures: mean median mode

23. The Median Also an average, but of different kind. 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. Computing the Median: (1) List the scores in order, either from highest to lowest or lowest to highest. (2) Find the middle score. That’s the median.

25. The Mode the value in any set of scores that occurs most often example 1: 5, 6, 7, 8, 8, 8, 9, 10, 10, 12 – the mode = 8 example 2: 5, 6, 7, 8, 8, 8, 9, 10, 10, 10, 12 –two modes: 8 and 10 – bimodal very unstable figure 1,1,6,7,8,10 – mode = 1 1,6,7,8,10,10 – mode = 10

26. When to Use What? depends on the type of data that you are describing for nominal data - only the mode for ordinal data - mode and median for interval data - all of them but, for extreme scores - use the median

27. Measure of dispersion (spread) better impression of a distribution’s shape measures indicate how widely scattered the numbers are how different scores are from one particular score – the mean variability - a measure of how much each score in a group of scores differs from the mean

29. r is the range

30. h is the highest score in the data set

32. The mean deviation number which indicates how much, on average, the scores in a distribution differ from a central point, the mean. Mean deviation =

33. 210 368 364 319 -210 -368 -319 -364 Mean=370 X - mean= (-210)+210+(-368)+368+(-364)+364+(-319)+319 = 0 X - mean= 210+210+368+368+364+364+319+319 = 2522 mean deviation = 2522/8 = 315.25

35. find the sum of what follows

36. Xeach individual score

37. the mean of all the scores

39. Shape of Normal Distribution Symmetrical Asymptotic tail Mean Median Mode

40. The area under the curve A normal distribution always has the same relative proportions of scores falling between particular values of the numbers involved. Areas under the curve = proportion of scores lying in the various parts of the complete distribution

41. SS2008N - Surveys Median 50% 50% Median

42. SS2008N - Surveys Quartiles 25% 25% 25% 25% Median Quartile 1 Quartile 3

43. Standard Deviation