1. Chapter 10

2. Goal
Not only to be able to analyze your own data but to understand the literature that you read.

3. Data Analysis
Statistics
Parameter

4. Reporting your Results
With words….
With numbers….
With Charts/Graphs…

5. Data
Categorical
Quantitative

6. Quantitative In this chapter: Correlation Frequency
distributions
Measures of Central Tendency
Mean
Variability
Standard deviation

7. Distributions Skewed Distributions
Positive – scores trailing to the right with a majority at the lower end
Negative – scores trailing to the left

8. Curve “Skewness”

9. Distributions Normal Large majority of scores in the middle
Symmetrical
Bell-shaped
Mean, median, and mode are identical

10. Types of Curves...
The Normal Curve:

11. Measures of Central Tendency
Mode
Median
Point at which 50% of scores fall above and below
Not necessarily one of the actual scores in the distribution
Most appropriate if you have skewed data

12. Measures of Central Tendency
Mean
Uses all scores in a distribution
Influenced by extreme scores
Mean = sum of scores divided by the number of scores

13. Variability Range Standard Deviation Low to High
Quick and dirty estimate of variability
Standard Deviation

14. Standard Deviation 1. Calculate the mean
2. Subtract the mean from each score
3. Square each of the scores
4. Add up all the squares
5. Divide by the total number of scores = variance
6. Take the square root of the variance.

15. Standard Deviation
The more spread out the scores the larger the standard deviation.
If the distribution is normal then the mean + two standard deviations will encompass about 95% of the scores. (+ three SD = 99% of scores)

16. Normal Curve: By Standard Deviation

17. % of Scores in 1 SD
1 SD = 68% of sample

18. 2 Standard deviations?
2 SD = 95% of sample

19. What can you tell me about these groups?
Group A
30 subjects
Mean = 25
SD = 5
Median = 23
Mode = 24
Group B
30 subjects
Mean = 25
SD = 10
Median = 18
Mode= 13

20. Calculate the Standard Deviation and Average
Use your text (p )
Check your scores with this link.
Scores:
12, 10, 6, 15, 17, 20, 16, 11, 10, 16, 22, 17, 15, 8
Mean = ??
SD = ??

21. Excel Now go to the following web page and click on “class data”:
assignments
Calculate mean, median, mode, SD for the ACT and Writing column data.

22. Standard Scores A method in which to compare scores
Z scores – expressed as deviation scores
Example:
Test 1= 80
Test 2 = 75

23. Example
Test 1: mean = 85, SD = 5
Test 2: mean = 65, SD = 10

24. Probability
We can think of the percentages associated with a normal curve as probabilities.
Stated in a decimal form.
If something occurs 80% of the time it has a probability of .80.

25. Example
We said that 34% of the scores (in a normal distribution) lie between the mean and 1SD.
Since 50% of the scores fall above the mean then about 16% of the scores lie above 1SD

26. Example
The probability of randomly selecting an individual who has a score at least 1SD above the mean?
P=.16
Chances are 16 out of 100.

27. Example Probability of selecting a person that is between the mean and
–2SD?

28. Z-Scores
For any z score we know the probability
Appendix B

29. Z-Scores Can also be calculated for non-normal distributions.
However, cannot get probabilities values if non-normal.
If have chosen a sample randomly many distributions do approximate a normal curve.

30. Determining Relationships Between Scores
Correlation

31. Relationships
We can’t assign blame or cause & effect, rather how one variable influences another.

32. Correlation
Helpful to use scatterplots

33. Plotting the relationship between two variables
Age = 11 Broad Jump = 5.0 feet
Y axis
Age 11
5.0
X axis 5
Feet

34. Plot some more (Age & Broad Jump)y
Do you see a relationship??
Age x
Feet

35. Outliers
Differ by large amounts from the other scores

36. Correlation….
Is a mathematical technique for quantifying the amount of relationship between two variables
Karl Pearson developed a formula known as “Pearson product-moment correlation”

37. Correlation Show direction (of relationship)
Show strength (of relationship)
Range of values is (strength)
0 = no relationship
1 = perfect relationship
Values may be + or - (direction)

38. Correlation
r= 1.0
r = 0
r = -1.0

39. Correlation Strength Very Strong .90 - 1.0 Strong .80 - .89
Moderate
Weak < .50

40. Types of relationships
Curvalinear
Sigmoidal
Linear

41. Test Your Skill
Guess the Correlation

42. Quick Assignment
For the same excel spreadsheet that we opened earlier calculate a correlation coefficient for the ACT vs. Tricep.
Make a scatterplot of tricep vs. ACT.
Scatterplot and correlation for ACT vs. Writing

43. Coefficient of Determination
Determines the amount of variability in a measure that is influenced by another measure
I.e. how much does the broad jump vary due to varied ages?
Calculated as r2 (Corr. Squared)

44. Example: Say that strength and 40yard sprint time have an r = .60
How much does a variation in strength contribute to the variation in sprint speed?

45. Summarizing Data Frequency Table Bar Graphs/Pie Charts
Crossbreak Table
A graphic way to report a relationship between two or more categorical variables.

46. Assignment
Under assignments on my web page there is an excel spreadsheet published entitled “assignment 1”.
Download the spreadsheet by clicking here assignments

47. Assignment
1. Calculate the mean, mode, and median for body density, ACT Score, and Reading Score on sheet 1
2. Calculate the mean and SD for TC, Trig, HDL, and LDL on sheet 2

48. Assignment
3. Calculate a correlation coefficient for body density and age, ACT and Reading Scores, TC and LDL, and Trig and HDL
4. Make a scatterplot for HDL and Trig as well as LDL and Total

49. Assignment
5. Make a bar graph for the mean Total, Trig, LDL, HDL values.