DESCRIPTIVE STATISTICS

1. Summarizing, organizing, simplifying and communicating the nature of a data set in numerical terms. These numerical accounts are intended to describe the data set without inferring causal factors ( what caused the data). DESCRIPTIVE STATISTICS ….To describe the data set

2. 3 primary concerns • CENTRALITY • VARIABILITY • RELATEDNESS

3. CONSIDERATION: • SCALES OF DATA

4. NOMINAL Scales of data

8. Continuous data scalesInterval and ratio

12. MEASURES OF CENTRALITY MEAN MEDIAN MODE

13. MEAN (which scales of data can be represented in this way?)

14. (which scales of data can be represented in this way?) • Median-most central value • Mode most frequently occurring data point

15. Centrality • Can you find the mean hair color in the class? • MEDIAN? • MODE?

16. Centrality-for ordinal data makes little sense • Can you find the mean? • Median? • Mode? • TRANSFORM YOUR DATA!

17. Measures of Variability for Continuous data • Range • Variance • Standard deviation

18. Range • Highest score minus lowest score • How accurately will the “range” describe dispersion of the data?

19. Variance Don’t be confused by different formulations : this is also the formula for variance

20. Standard Deviation (the square root of the variance) Why “n” or “n-1?”

21. Find the standard deviation of 4, 9, 11, 12, 17, 5, 8, 12, 14

22. STD Example • Find the standard deviation of 4, 9, 11, 12, 17, 5, 8, 12, 14First work out the mean: 10.222Now, subtract the mean individually from each of the numbers given and square the result. This is equivalent to the (x - )² step. x refers to the values given in the question. • X 4 9 11 12 17 5 8 12 14 • (x - )2 38.7 1.49 0.60 3.16 45.9 27.3 4.94 3.16 14.3 • Now add up these results (this is the 'sigma' in the formula): 139.55 • Divide by n. n is the number of values, so in this case is 9. This gives us: 15.51 • And finally, square root this: 3.94

23. Example • Mean scores for a class on two different tests were: Test 1- 75.5% Test 2- 75.5% Did an average student do better, worse or the same on test 2 vs test 1?

25. Test 1

26. Test 2

27. NOTE*** • When you present a mean, it should always be accompanied by a measure of variability!!

29. Relatedness = correlation • Correlations yield coefficient values • Between +1.0 and -1.0

32. Correlational outcomes can be visualized

35. Relatedness…correlation • Consider scale of data for each variable • Var XVar YTechnique • Nominal Nominal Chi-square • Nominal continuous Rpbs • OrdinalSpearmans rho • Continuous Continuous Pearson’s r

36. Pearsons’ product-moment correlation

37. Further considerations when performing correlation analysis

40. considerations

41. Graphing resultsBar graphs vs line graphs

42. Label axis

43. Use error bars

45. Provide a figure legend!

46. Rough methods section for worry survey • Methods • Materials • The subjects were randomly chosen people with no preference for race, socioeconomic status, appearance, etc. Researchers attempted to avoid recruitment of subjects under the age of eight years old. The subjects were separated into two different groups, child (8 years to 12 years) and adult. Otherwise, a matched stratified random sampling procedure was used across age groups. Adult subjects were classified in one of four subsets: teen (13 years to 19 years), adult (20 years to 40 years), middle-aged adult (41 years to 60 years), and old persons (61 years plus). The subjects were chosen with intent at achieving an equal represent among all four subsets within the adult group. To maintain the objective nature of the experiment the subjects were recruited in a city in southeastern North Carolina at a variety of places including, but not limited to: local restaurants, the local college campus, the local beach, and local parks.

47. Materials • A team of twenty-four researchers devised a survey to examine age, relative anxiety, and risk perception. A survey was created through a collaboration of the twenty-four members of the research team. Members submitted a list of items/events that would cause them to worry. This list was compiled and examined for relevance to adults and children, redundancy, and effectiveness. Items deemed unnecessary or irrelevant were excluded from the survey. The team then decided which of the events/items were inappropriate for children and were thus discarded. • There were two different forms of the survey, one for the adult set of subjects and one for the child group of subjects. The reasoning for this was there were some items on the adult survey that were not appropriate for children. Examples of this would include worry involved with “drunk driving”, “being drugged”, and “getting sexually assaulted”. The survey required some general demographic information

48. including gender, age, highest level of education, and race. The survey then asked the subject to indicate on a scale of 1-7, 1 being not worried at all and 7 being extremely worried, if he or she was a worrier in general. A listing of potentially risky events followed. The adult survey contained 54 items and the child survey contained 42 items. Excluding the examples depicted above, the items on the adult and child surveys were the same. These items included events/activities tat would generally cause one anxiety such as “skydiving”, “holding a snake”, “being outside during a lightning storm”, “swimming in the ocean after reports of a shark attack”, etc. Items were also included to act as controls for biased or inaccurate responding such as “playing putt-putt golf” or “taking a walk”. The survey was also designed to control for those not paying attention / not taking the survey seriously by placing “being lost” on the survey in two separate places. Subjects were to indicate their level of worry if they were to participate in or encounter each of these items on the same 1-7 scale of worry. The survey concluded with a question regarding the interference of worry with the subject's normal routines, work, school, and/or social activities on which the subject gave a score of 1-7, 1 being no interference and 7 being extremely interfering.

49. Procedure • Adult subjects were randomly recruited by walking up to a person and asking it he or she would like to participate in a quick (about five minutes) survey. If the person obliged, he or she was informed that this was a survey inquiring about typical worries. The subject was also informed that partaking tin the survey posed no mental or physical risk, and was assured of the anonymity of his or her responses to the items. Following administration of the survey, the subject was informed of the intent of the survey. • Potential subjects were excluded if they looked to be in either too much of a hurry or too busy. These potential subjects were excluded on the basis of possible contamination of the results. Subject traveling in a group were not approached, as group bias would possibly skew their responses. For the same

50. reason, when surveys were administered to more than one subject at once, the subjects were asked not to speak with one another about the survey until all had completed. • Because only two of the members had ready access to administration of the survey to children, some of the elimination criteria used of adults could not apply. There were two main places children were recruited, at a soccer practice and at a children's museum. At the soccer field, the children arrived in groups of three to five. These subjects were instructed to take the survey quietly without discussion of the survey during administration, but because they were children this was quite difficult to control. The children recruited at the children's museum were directed to a table where the survey was administered on a one by one basis.