1 / 49

Chapter 10

Chapter 10. http://members.aol.com/johnp71/javastat.html. Goal. Not only to be able to analyze your own data but to understand the literature that you read. Data Analysis. Statistics Parameter. Reporting your Results. With words…. With numbers…. With Charts/Graphs…. Data. Categorical

alice-spence
Download Presentation

Chapter 10

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 10 http://members.aol.com/johnp71/javastat.html

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

  20. Use your text (p. 207-208) Check your scores with this link. Scores: 12, 10, 6, 15, 17, 20, 16, 11, 10, 16, 22, 17, 15, 8 Mean = ?? SD = ?? Calculate the Standard Deviation and Average

  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 0 - 1.0 (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 .50 - .79 • 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.

More Related