1. Statistics as a Tool in Scientific Research
PY209 Stats Fall 2001, Dr. L. Henkel
Statistics as a Tool in Scientific Research
Types of Research Questions
Descriptive (What does X look like?)
Correlational (Is there an association between X and Y? As X increases, what does Y do?)
Experimental (Do changes in X cause changes in Y?)
Different statistical procedures allow us to answer the different kinds of research questions

2. Statistics as a Tool in Scientific Research
PY209 Stats Fall 2001, Dr. L. Henkel
Statistics as a Tool in Scientific Research
 Start with the science and use statistics as a tool to answer the research question
Get your students to formulate a research question first:
How often does this happen?
Did all plants/people/chemicals act the same?
What happens when I add more sunlight, give more praise, pour in more water?

3. Statistics as a Tool in Scientific Research
PY209 Stats Fall 2001, Dr. L. Henkel
Statistics as a Tool in Scientific Research
Helping students to formulate research question:
* Laura, Should we try to say something more here

4. Types of Statistical Procedures
PY209 Stats Fall 2001, Dr. L. Henkel
Types of Statistical Procedures
Descriptive: Organize and summarize data
Inferential: Draw inferences about the relations between variables; use samples to generalize to population

5. Descriptive Statistics
PY209 Stats Fall 2001, Dr. L. Henkel
Descriptive Statistics
The first step is ALWAYS getting to know your data
 Summarize and visualize your data
It is a big mistake to just throw numbers into the computer and look at the output of a statistical test without any idea what those numbers are trying to tell you

6. Descriptive Statistics
PY209 Stats Fall 2001, Dr. L. Henkel
Descriptive Statistics
Numerical Summaries:
Measures of central tendency
Measures of variability
Frequencies
Contingency tables
Representing numerical summaries in Tables
Graphical Summaries:
Bar graphs
Histograms
Scatterplots
Time series

7. Types of Data: Measurement Scales
PY209 Stats Fall 2001, Dr. L. Henkel
Types of Data: Measurement Scales
In order to choose the appropriate ways to summarize and visualize your data, you have to know what type of data you have
Categorical: male/female, blood type (A, B, AB, O)
Numerical: weight, # of white blood cells

8. Types of Data: Measurement Scales
PY209 Stats Fall 2001, Dr. L. Henkel
Types of Data: Measurement Scales
Categorical:
Nominal (name/label)
Ordinal (rank order)
Numerical:
Interval (equal intervals)
Ratio (equal intervals and absolute zero)

9. Types of Data: Measurement Scales
PY209 Stats Fall 2001, Dr. L. Henkel
Types of Data: Measurement Scales
Nominal: numbers are arbitrary; 1= male, 2 = female
Ordinal: numbers have order (I.e., more or less) but you do not know how much more or less; 1st place runner was faster but you do not know how much faster than 2nd place runner
Interval: numbers have order and equal intervals so you know how much more or less; A temperature of 102 is 2 points higher than one of 100
Ratio: same as interval but because there is an absolute zero you can talk meaningfully about twice as much and half as much; Weighing 200 pounds is twice as heavy as 100 pounds

10. Descriptive Statistics
PY209 Stats Fall 2001, Dr. L. Henkel
Descriptive Statistics
Once you know what type of measurement scale the data were measured on, you can choose the most appropriate statistics to summarize them:
Measures of central tendency: Most representative score
Measures of dispersion: How far spread out scores are

11. Descriptive Statistics
PY209 Stats Fall 2001, Dr. L. Henkel
Descriptive Statistics
LAURA: Do we need to have them look at distribution first – shape of distribution or we will cover that later? I feel like I keep referencing the normal curve when talking about central tendency and variability
Do you have something on excel that visualizes the shape of the distribution? Or maybe this is too much – too in depth. We have slated for issues later to talk about normality and outliers

12. The Normal Curve
Most scores in center, tapering off symmetrically in both tails
Amount of peakedness (kurtosis) can vary

13. Variations to Normal Distribution
Skew = Asymmetrical distribution
Positive skew = greater frequency of low scores than high scores (tail is less pronounced on high end)
Negative skew = greater frequency of high scores than low scores (tail is less pronounced on low end)

14. Examples of Different Skews

15. Variations to Normal Distribution
Bimodal distribution: two peaks
Rectangular: all scores (high and low) occur with equal frequency
Important to determine normality (skewness & kurtosis) so you can choose appropriate measures of central tendency and variability

16. MEASURES OF CENTRAL TENDENCY
PY209 Stats Fall 2001, Dr. L. Henkel
MEASURES OF CENTRAL TENDENCY
Central tendency = Typical or representative value of a group of scores
Mean: Average score
Median: middlemost score; score at 50th percentile; half the scores are above, half are below
Mode: Most frequently occurring score

17. MEASURES OF CENTRAL TENDENCY
PY209 Stats Fall 2001, Dr. L. Henkel
MEASURES OF CENTRAL TENDENCY
Measure
Definition
Takes Every Value Into Account?
When to Use
Mean
M =  X / n
Yes
Interval or ratio data
BUT… Can be heavily influenced by extreme scores (outliers) so can give inaccurate view if distribution is not normal
Median
Middle value No
Ordinal data or for interval/ratio data that are skewed
Mode
Most frequent data value
Nominal data

18. MEASURES OF VARIABILITY
PY209 Stats Fall 2001, Dr. L. Henkel
MEASURES OF VARIABILITY
Knowing what the center of a set of scores is is useful but….
How far spread out are all the scores? Were all scores that exact value, or did they have some variability?
Range, Standard deviation, Interquartile range

19. PY209 Stats Fall 2001, Dr. L. Henkel

20. Variability = extent to which scores in a distribution differ from each other; are spread out

21. The Range as a Measure of Variability
Difference between lowest score in the set and highest score
Ages ranged from years of age
There was a 29-year age range
The number of calories ranged from 256 to 781

22. Sample Standard Deviation
Standard deviation = How far on average do the scores deviate around the mean?
s = SD = (X-M) 2
n-1
In a normal distribution, this is the midmost 68% of the scores
The bigger the SD is, the more spread out the scores are around the mean

23. Variations of the normal curve (larger SD= wider)

24. Interquartile Range: Quartile 1: 25th percentile
Quartile 2: 50th percentile (median)
Quartile 3: 75th percentile
Quartile 4: 100th percentile
Interquartile range =
Score at 75th percentile – score at 25th percentile
So this is the midmost 50% of the scores
LAURA: DO WE NEED THIS? IS IT TOO MUCH?

25. Interquartile range on a positively skewed distribution
IQR is often used for interval or ratio data that are skewed (do not want to consider ALL the scores)

26. MEASURES OF VARIABILITY
PY209 Stats Fall 2001, Dr. L. Henkel
MEASURES OF VARIABILITY
Measure
Definition
Takes Every Value Into Account?
When to Use
Range
Highest score – lowest score
No, only based on two most extreme values
To give crude measure of spread
Standard Deviation
Midmost 68% of scores
Yes but describes majority
For interval or ratio data that are normally distributed
Interquartile Range
Midmost 50% of scores
Yes but describes most
When interval/ratio data are skewed

27. Presenting Measures of Central Tendency and Variability in Text
PY209 Stats Fall 2001, Dr. L. Henkel
Presenting Measures of Central Tendency and Variability in Text
The number of fruit flies observed each day ranged from 0-57 (M = 25.32, SD = 5.08).
Plants exposed to moderate amounts of sunlight were taller (M = 6.75 cm, SD = 1.32) than plants exposed to minimal sunlight (M = 3.45, SD = 0.95).
 Sentences should always be grammatical and sensible. Do not just list a bunch of numbers. Use the statistical information to supplement what you are saying

28. Presenting Measures of Central Tendency and Variability in Tables
PY209 Stats Fall 2001, Dr. L. Henkel
Presenting Measures of Central Tendency and Variability in Tables
Range M SD
Number of Fruit Flies
0-57
25.32
5.08
Weight
160.31
10.97
Speed of Pitch (mph)
25-96
45.37
12.66

29. Presenting Measures of Central Tendency and Variability in Tables
PY209 Stats Fall 2001, Dr. L. Henkel
Presenting Measures of Central Tendency and Variability in Tables
Range
Median
IQR
Number of Fruit Flies
MAKE UP #S
Weight
Speed of Pitch (mph)

30. Describing Your Data: Simple Frequency
 Frequency = number of times each score occurs in a set of data   

31. SIMPLE FREQUENCY TABLE
Score f
A 6
A- 3
B+ 10
B 13
B- 8
C+ 7
C 5
C- 6
D 3
F 2
Total: N = 63

32. GROUPED FREQUENCY TABLE
Score f
A (90-100) 9
B (80-89)
C (70-79) 18
D (60-69) 3
F (0-59) 2
Total: N = 63
 Choose class intervals to maximize informativeness with truthfulness

33. RELATIVE FREQUENCY DISTRIBUTIONS
Considers frequency relative to number of scores
Relative frequency = frequency/number of scores in set
rel f = f/N

34. Score f Rel f
Total: N = 15 Sum = 1.0 (100%)

35. Examples of relative frequency distributions

36. Graphical Representations of Data
STUFF TO COVER AND MAKE SLIDES FOR:
Bar graphs
Histograms
Scatterplots
Time series

37. Simple frequency bar graph for nominal and ordinal data

38. Histogram showing the simple frequency of parking tickets in a sample

39. Simple frequency polygon showing the frequency of parking tickets in a sample

40. Guidelines to Making Graphs
Y axis should be ¾ as tall as X axis
When the number of score values on X axis is large, scores should be collapsed so there are at least 5 intervals but no more than 12
The width of each interval on the X axis should be equal
Frequency on the Y axis must be continuous and regular
Range on the Y axis and X axis must neither unduly compress nor unduly stretch the data
LAURA: Lets add to this from different sources; e.g., unit of measure should be labeled on Y axis…

41. Choosing the Appropriate Type of Graph
Laura: I pilfered this from a book. I think we need to think this out better:
One interval/ratio variable (with frequencies): Histogram or frequency polygon
One interval independent variable and one interval/ration dependent variable: scatterplot or line graph
One nominal independent variable and one interval/ratio dependent variable: bar graph
Two or more nominal independent variables and one interval/ration dependent variable: bar graph

42. Choosing the Appropriate Type of Graph
STUFF TO COVER
Issues:
Use and misuse of graphs
Outliers and normality
Dangers of low n
Association vs. causation