1. Statistics Types of Data

2. Types of Data In science (and statistics), evidence is called “data”
(no… not that kind of “Data”)

3. Types of Data
Data!
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4. Science (and Statistics) deals only with things that are
Types of Data
Science (and Statistics)
deals only with things that are
Measurable
Replicable
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5. Types of Data Two levels of measurement for data: counts measurements
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6. Types of Data Two classifications of data: qualitative – a category
quantitative – a number
Qualitative Quantitative

7. Types of Data
We count qualitative data (how many fall into each category) We measure quantitative data

8. Types of Data
IN-CLASS PROBLEMS
Lengths of time three brands of aspirin take to cure headaches Counts or measurements? Qualitative or quantitative?

9. Types of Data
IN-CLASS PROBLEMS
Speed of your car taken by the cop Count or measurement? Qualitative or quantitative?

10. Types of Data
IN-CLASS PROBLEMS
Maximum daily temperatures for Denver Counts or measurements? Qualitative or quantitative?

11. Types of Data
Some numbers are really names! (qualitative, not quantitative)

12. Types of Data
IN-CLASS PROBLEMS
List of social security numbers Count or measurement? Qualitative or quantitative?

13. Types of Data
IN-CLASS PROBLEMS
Your CO driver’s license info Counts or measurements? Qualitative or quantitative?

14. Types of Data
IN-CLASS PROBLEMS
The “Q” Game

15. Questions?

16. Best Descriptor
Traditionally, we split data into quantitative and qualitative types because this determines what statistical descriptors we will calculate to summarize our data and answer our questions

17. Best Descriptor
You use a statistic (descriptive number) called the “mode” for qualitative (categorical) data

18. Best Descriptor
You use a traditional average (arithmetic mean) for quantitative data

19. What type of data are these:
Best Descriptor
IN-CLASS PROBLEMS
What type of data are these:

20. Best Descriptor
IN-CLASS PROBLEMS
What single value would you use for the “typical” response to this survey question:

21. The most commonly occurring response (the mode) is “brown”
Best Descriptor
IN-CLASS PROBLEMS
The most commonly occurring response (the mode) is “brown”

22. What type of data are these:
Best Descriptor
IN-CLASS PROBLEMS
What type of data are these:

23. Best Descriptor
IN-CLASS PROBLEMS
What single value would you use to illustrate the “typical” response to this experimental result:

24. For this, the “average” height of the 12 students would be better
Best Descriptor
IN-CLASS PROBLEMS
For this, the “average” height of the 12 students would be better

25. Questions?

26. Measurement
Scales or number systems used to measure something we want to know

27. Measurement
four levels of scale measurement

28. Qualitative or quantitative?
Measurement
IN-CLASS PROBLEMS
four levels of scale measurement Nominal - assigns a value to an object for identification or classification purposes only – a “name”
Qualitative or quantitative?

29. Measurement
four levels of scale measurement Nominal: What is your hair color? Represents unordered categories

30. Qualitative or quantitative?
Measurement
IN-CLASS PROBLEMS
four levels of scale measurement Nominal Ordinal - things are arranged in order based on how much of some concept they possess – a “rank order”
Qualitative or quantitative?

31. Measurement
four levels of scale measurement Nominal Ordinal:  Disagree  Neutral  Agree an ordered scale of agreement

32. Qualitative or quantitative?
Measurement
IN-CLASS PROBLEMS
four levels of scale measurement Nominal Ordinal Interval - capture information about differences in quantities
Qualitative or quantitative?

33. Measurement
four levels of scale measurement Nominal Ordinal Interval: Temperature! The difference between 32° and 42° is the same as between 400° and 410°

34. Qualitative or quantitative?
Measurement
IN-CLASS PROBLEMS
four levels of scale measurement Nominal Ordinal Interval Ratio - represent absolute quantities – have a true zero
Qualitative or quantitative?

35. Measurement
four levels of scale measurement Nominal Ordinal Interval Ratio: Sam makes twice as much money as Pauline – and Gerry makes zero money!

36. Measurement
True ratio-level data are found by measuring stuff with a piece of measurement equipment or a test of some sort

37. Questions?

38. It’s Not Black and White
It is traditional to teach the levels of measurement in an introductory statistics class

39. It’s Not Black and White
This is because the level of measurement theoretically determines the appropriate statistical analysis to be used

40. It’s Not Black and White
In practice, it is not always clear cut

41. It’s Not Black and White
We are CONSTANTLY changing measurement data to count data…

42. It’s Not Black and White
…and count data are (because they are counts) used like measurements

43. It’s Not Black and White
In practice, ordinal scales containing five or more categories of response are treated as interval When fewer than five categories are used, this is inappropriate

44. It’s Not Black and White
The Likert Scale
Likert scaling is bipolar - it measures either positive
or negative response
to a statement
Rensis Likert
( )

45. It’s Not Black and White
The format of a typical five-level Likert item:  Strongly disagree  Disagree  Neither agree nor disagree  Agree  Strongly agree

46. It’s Not Black and White
Because Likert scale items typically have 5 or more categories, they can be treated as interval-level (you can calculate an “average” response

47. It’s Not Black and White
IN-CLASS PROBLEMS
What level of measurement are these data?

48. It’s Not Black and White
IN-CLASS PROBLEMS
What is the “usual” response for these items?

49. It’s Not Black and White
A calculated weighted average for the responses:
How would you rate your recycling frequency:
Response
Score
Resp x Score
all the time 4 5 20
frequently 13 52
often 15 3 45
sometimes 14 2 28
rarely 1
never 12
Sum 63
150
Average

50. Questions?

51. Measurement Criteria
Three Criteria for Good Measurement: reliability, validity and sensitivity

52. Measurement Criteria
Reliability is an indicator of a measure’s internal consistency A measure is reliable when different attempts at measuring something converge on the same result

53. Measurement Criteria
Is it consistent?

54. Measurement Criteria
Validity is the accuracy of a measure or the extent to which a score truthfully represents a concept

55. Measurement Criteria
Are we accurately measuring what we think we are measuring?
Accurate Precise Accurate
but not precise but not accurate and precise

56. Measurement Criteria
Sensitivity is the ability to accurately measure the subtle variability in a concept

57. Measurement Criteria Which will measure subtle differences better:
 agree  disagree
or:
strongly agree
mildly agree
neither agree nor disagree
mildly disagree
strongly disagree

58. Questions?