1. hss2381A – stats... or whatever
Univariate Analysis, part 1
Descriptive Statistics

2. Evidence-based practice (EBP): Use of best clinical evidence in making patient care decisions
Best source of evidence: Systematic research

3. How reliable is the evidence? What is the magnitude of effects?
Evidence-Based Medicine (EBM) or Evidence-Based Practice (EBP) Questions:
How reliable is the evidence?
What is the magnitude of effects?
How precise is the estimate of effects?
Answering these questions requires an understanding of statistics

4. Data and Data Analysis
In the context of a study, the information gathered to address research questions is data
In quantitative research, data are usually quantitative (numbers)
Quantitative data are subjected to statistical analysis

5. Examples of Independent and Dependent Variables
Independent variable (IV): Smoking
Dependent variable (DV): Lung cancer
IV  DV ?

6. Research Question
Research questions are the queries researchers seek to answer through the collection and analysis of data
Research questions communicate the research variables and the population (the entire group of interest)
Example: In hospitalized children (population) does music (IV) reduce stress (DV)?

7. Defining a Variable
Two phases:
Conceptual
operational

8. Defining a Variable In studies, variables need to be defined
Conceptual definition: The theoretical meaning of the underlying concept
Operational definition: The precise set of operations and procedures used to measure the variable
Example:
Concept = how long have you been on this planet?
Operation = In what age group, by years, are you in?

9. Descriptive Statistics
Researchers collect their data from a sample of study participants—a subset of the population of interest
Descriptive statistics describe and summarize data about the sample
Examples: Percent female in the sample, average weight of participants

10. Inferential Statistics
Researchers obtain data from a sample but often want to draw conclusions about a population
Parameter: A descriptive index for a population
Example: Average daily caloric intake of all 10-year-old children in New York
Statistic: A descriptive index for a sample
Example: Average daily caloric intake of year-old children from three particular NY schools

11. SPSS and Statistical Analysis
SPSS (Statistical Package for the Social Sciences) is among the most popular statistical software packages for analyzing research data
It is user friendly and menu driven
The datasets offered with this textbook are set up as SPSS files

12. The Data Editor in SPSS
The data editor in SPSS offers a convenient spreadsheet-like method of creating, editing, and viewing data
There are two “views” within the data editor:
Data View: Shows the actual data values
Variable View: Shows variable information for all variables

13. Data View in the Data Editor
The columns represent one variable each; unique variable names (no more than eight characters long) are shown at the top of each column
Each row is a case, representing an individual participant
The data view tab is at the bottom

14. Variable View in the Data Editor
Variable View shows a wealth of information about how variables are coded, how they will be labeled in output, level of measurement, and so on
The Variable View tab is at the bottom

15. Versions of SPSS
New versions of SPSS are created regularly, to offer improved options for analysis and presentation
Examples in this book were created in SPSS Version 16.0
The student version of SPSS is available for analyzing relatively small datasets (no more than 50 variables and no more than 1,500 cases)

16. FREQUENCY DISTRIBUTION
What is this?
Same as Histogram?

17. Frequency Distributions
A frequency distribution is a systematic arrangement of data values, with a count of how many times each value occurred in a dataset
You can portray this as a table or as a graph

18. Constructing a Frequency Distribution
List each data value in a sequence (usually, ascending order) 1, 2, 3, 4, 5…
Tally each occurrence of the value
Total the frequencies for each value (f)
The sum of fs for all data values must equal the sample size:
Σf = N

19. Elements of a Typical Frequency Distribution
Data values
Absolute frequencies (counts)
Relative frequencies (percentages)
Cumulative relative frequencies (the percentage for a given score value, combined with percentages for all preceding values)

20. Example... Let’s say we have 10 people of varying ages:
Let’s construct the frequency distribution of the age GROUPS: 0-25 yrs, yrs, >45 yrs
Age group
0-25
26-45
>45
Frequency 4 2
Relative Freq.
4/10 = 40%
2/10 = 20%
Cumulative Freq.
40%
40+40% = 80%
80+20% = 100%

21. Cumulative Percentage
Summary of Our Example
Data Value
Frequency
(f)
Percentage
(%)
Cumulative Percentage
0-25 4
40.0
26-45
80.0
>45 2
20.0
100.0
TOTAL 10

22. Frequency Distributions and Measurement Levels
Remember “measurement levels”?
Nominal, ordinal, interval, ratio...
Frequency distributions can be constructed for variables measured at any level of measurement
BUT…for categorical (nominal-level) variables, cumulative frequencies do not make sense
Also...

23. Frequency Distributions for Variables with Many Values
When a variable has many possible values, a regular frequency distribution may be unwieldy
For example, weight values (here, in pounds)
Weight f 98 1 99
100
101
102 2
103
104
105
106
Etc. to 285 lb …

24. Which is Why We Used “Age Group” instead of “Age”
This is sometimes called a “grouped frequency distribution”
In a grouped frequency distribution contiguous values are grouped into sets (class intervals)
Typically, we use groupings that are psychologically appealing (e.g., years etc, not 7-13 years, etc)

25. Weight f 98 1 99
100
101
102 2
103
104
105
106
Etc. to 285 lb …
This grouping communicates information more conveniently than individual weights
Weight Interval f 6 15 33 26 24 14 9 2

26. Reporting Frequency Information
Can be reported narratively in text (e.g., “83% of study participants were male”)
In a frequency distribution table (multiple variables often presented in a single table)
In a graph: Different graphs used for different types of data

27. Bar Graphs
Bar graphs: Used for nominal (and many ordinal) level variables
Bar graphs have a horizontal dimension (X axis) that specifies categories (i.e., data values)
The vertical dimension (Y axis) specifies either frequencies or percentages
Bars for each category drawn to the height that indicates the frequency or %

28. Bar Graphs Example of a bar graph
Note the bars do not touch each other

29. Pie Chart
Pie Charts: Also used for nominal (and many ordinal) level variables
Circle is divided into pie-shaped wedges corresponding to percentages for a given category or data value
All pieces add up to 100%
Place wedges in order, with biggest wedge starting at “12 o’clock”

30. Pie Chart
Example of a pie chart, for same marital status data

31. Histograms Histograms: Used for interval- and ratio-level data
Similar to a bar graph, with an X and Y axis—but adjacent values are on a continuum so bars touch one another
Data values on X axis are arranged from lowest to highest
Bars are drawn to height to show frequency or percentage (Y axis)

32. Histograms
Example of a histogram: Heart rate data f
Heart rate in bpm

33. Frequency Polygons
Frequency polygons: Also used for interval- and ratio-level data
Similar to histograms, but instead of bars, a dot is used above score values to designate frequency/percentage
Better than histograms for showing shape of distribution of scores, and is usually preferred if variable is continuous

34. Example of a frequency polygon (created in SPSS)
Note that the line is brought down to zero for the score below lowest data point (54) and above highest data point (75)

35. Shapes of Distributions
Distributions of data values can be described in terms of:
Modality
Symmetry
Kurtosis

36. Modality
Modality concerns how many peaks (values with high frequencies) there are
Unimodal = 1 peak
Bimodal = 2 peaks
Multimodal = multiple peaks

37. Unimodal:
Bimodal:

38. How is this useful?

39. Example: Tuberculosis
What is it?
We apply tuberculin skin test (also called PPD – purified protein derivative) test
Positive response is an “induration”
a hard, raised area with clearly defined margins at and around the injection site

40. What type of curve is this?

41. Distribution of systolic blood pressure for men (unimodal distribution)

42. Symmetry
Symmetric Distribution: the two halves of the distribution, folded over in the middle, are identical

43. Symmetry
Asymmetric (Skewed) Distribution: Peaks are “off center” and there is a tail trailing off for data values with low frequency
Positive skew: Longer tail trails off to right (fewer people with high values, like for income)
Negative skew: Longer tail trails off to left (fewer people with low values, like age at death)

44. Direction of Skew
Examples of distributions with different skews:

45. Skewness Index
Indexes have been developed to quantify degree of skewness
One skewness index (e.g., in SPSS) has:
Negative values, for a negative skew
0, for no skew
Positive values, for a positive skew
If skewness index is less than twice the value of its standard error (to be explained later), distribution can be treated as not skewed

46. Skewness Index Examples
Standard error = 0.33
Positive skew
Skewness index = -0.72
Standard error = 0.34
Negative skew

47. Kurtosis
Kurtosis: Degree of pointedness or flatness of the distribution’s peak
Leptokurtic: Very thin, sharp peak
Platykurtic: Flat peak
Mesokurtic: Neither pointy nor flat
Like skewness, there is an index of kurtosis
Positive values: Greater peakedness
Negative values: Greater flatness

48. Kurtosis Examples
Leptokurtic (+ index)
Platykurtic (– index)

49. Normal Distribution
What is this curve called?

50. Normal Distribution
A normal distribution (aka normal curve, bell curve, Gaussian distribution, etc) is:
Unimodal
Symmetric
Neither peaked nor flat
Plays an important role in inferential statistics
We will re-visit the Normal Distribution in more depth in the future

51. Some human characteristics are normally distributed (approximately), like height
1 short person, 3 medium persons, 1 tall person

52. Uses of Frequency Distributions in Data Analysis
First step in understanding your data!
Begin by looking at the frequency distributions for all or most variables, to “get a feel” for the data
Through inspection of frequency distributions, you can begin to assess how “clean” the data are
(will discuss next time)

53. Central Tendency
“Central Tendency” is a characteristic of a distribution
Describes how data is clustered around some value
In other ways, it’s a way of summarizing your data by identifying one value in the set that is the most important
There are several indices of central tendency, but 3 are the most important:
Mode
Median
Mean
Next class, we’ll get into these in more depth

54. Homework!
P.17: A1-A4
P.36: A1-A5