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KIN 369 (1)
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KIN 369 Full Course Notes With Diagrams

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Department
Kinesiology
Course
KIN 369
Professor
Alison Harper
Semester
Spring

Description
KIN 369 1/28/13 Intro to Measurement and Evaluation  Test o Instrument, protocol, or technique used to measure a quantity or quality of properties or attributes of interest.  Measurement o Process of collecting data on the property or attribute of interest o Quantitative (Numerical based data) o Qualitative (Non-numerical based data)  Evaluation and Assessment o Process of interpreting the collected measurement and determining some worth or value o Identify deficits and decide how to improve them  Relationship between Test, Measurement and Evaluation? o Tests are specific instruments used to collect data o Administering the test is a process of measurement o Evaluation requires making decisions based on data generated from tests and measurement  Uses of Test, Measurement and Evaluation? o Motivation  Fat loss  Training o Diagnosis  High Cholesterol/Mono/Strep throat, etc o Classification  Athletic categorization  Academic placement o Achievement  Anywhere with reward for doing well o Evaluation of Instruction and Programs  Surveys o Prediction  MCAT/SAT/GRE  Submax Testing o Research Statistics  What are Statistics? o Collection, organization, analysis, interpretation and presentation of data  Why are they important? o Analyze and Interpret Data o Interpret Research o Standardize Test Scores o Determine Validity and Reliability of Tests Measurement Scales and Displays of Data  Nominal o Numbers represent categories o Ex: 1=male, 2=female; 1=brown hair, 2=blond hair, 3=red hair, 4=green hair  Ordinal o Numbers indicate rank but not spacing/intervals o Ex: order of finish in a race  Interval o Numbers represent equally spaced units, but there is no meaningful zero o Ex: temperature, IQ  Ratio o Numbers represent equally space units with an absolute zero point o Ex: height, distance, heart rate, test scores 1/30/13 Frequency Distribution  Used to describe our data set with interval or ratio data  The best score is always on top  Includes the best through the worst scores with all intervals in between  Frequency is occurrence of each score  cf = cumulative frequency o Simply sum the frequencies, start at the bottom and work your way up. The cf of the top row should be equal to the total number of scores. (N = 12 for this example)  c% = cumulative percent o Divide current cf by number of scores and convert it to a percentage. (N = 12 for this example) Score Tally f cf c% 9 XX 2 12 100 8 XX 2 10 83.33333 7 X 1 8 66.66667 6 XXX 3 7 58.33333 5 XXX 3 4 33.33333 4 0 1 8.333333 3 X 1 1 8.333333  Graphing Distributions o Histogram  Type of bar graph  Width of bar represents interval size  Height of bar represents frequency within the interval o Line Graph  X-axis is always some measurement of time o Pie Chart  Displays percentages of a categories pertaining to the whole data set  How often or at which percentage each piece occurs o Scatter Plot  Measures the relationship between two things o Bar Graph  Comparative graph  Can show more than one type of data  How do you make a frequency distribution with a large range? o Aim for approximately 5-10 intervals o Example  Measured sit-ups  Scores ranged from 75 to 12  Far too many for intervals of 1  Break it up into segments or by set intervals Descriptive Statistics 2/4/2013 Descriptive Statistics  Percentiles o Describe the relative position of a data point in more detail than the median o Calculation:  Step 1: Put data in rank order from “worst” to “best” – number the ranks  Step 2: % = rank of data point / N OR (%*N = rank of data point) Measures of Variability Range  Describes how spread out the data set is  Calculation o Range = Highest Score – Lowest Score Quartile Deviation/Inter-Quartile Range  Divides the data into quarters (25%,50%,75%,etc)  Describes the spread of the middle half of the data set  Calculation th th o 25 and 75 percentiles  Several methods for calculation including subtracting and averaging, for this th th class you may simply identify the 25 and 75 percentiles.  Practice Problem o Find the range and inter-quartile range of the following: 82, 93, 76, 85,97, 68, 79, 88  In order: 97, 93, 88, 85, 82, 79, 76, 68  Range = 97 – 68 = 29  25 = (.25 * N) = (.25 * 8) = 2 [76] th  75 = (.75 * N) = (.75 * 8) = 6 [88] Variance  Describes the scatter of the scores around the mean  Calculation: ( )  o s is the variance o X is whatever data point you’re looking at o x1 is the mean 2 X X-x1 (X-x1) 4 -1 1 Variance = (6/4) = 1.5 5 0 0 4 -1 1 7 2 4 x1=5 Total=0 Total=6 Standard Deviation  Describes the scatter of scores around the mean  Calculation: ( )  √  Symbols to remember o s is standard deviation o x1 is the mean Practice Problems 1. If the variance of a data set is 100, what is the standard deviation? a. Sqrt(100) = 10 2. If the standard deviation of a data set is 5, what is the variance? 2 a. 5 = 25 3. Find the variance and standard deviation of the following: 12, 15, 10, 9, 18, 20. 2 X X-x (X-x) 9 -5 25 10 -4 16 12 -2 4 15 1 1 Variance = 98/6 =16.34 18 4 16 20 6 36 Std Dev = sqrt(16.34) =4.04 x=14 Total=-8 Total=98 4. Find the variance and standard deviation of the following: 4, 5, 5, 6, 7, 8, 8, 9, 11. Standard Scores Z-Scores  Express how far away a number is from the mean, in terms of standard deviations  Positive z-scores indicate our number is better than the mean  Negative z-scores indicate our number is worse than the mean  A z-score of 0 indicates our number is equal to the mean  Calculation: o If larger numbers are better o o If smaller numbers are better  Practice problems o Top 6 golf scores: 70, 74, 80, 82, 86, 88 [mean=80] o Find z-scores for 70, 80, and 88  70: 2 X X-x (X-x) 70 -10 100 Variance = 0 74 -6 36 Std dev = 0 80 0 0 82 2 4 86 6 36 88 8 64 x=80 Total=0 Total=240 T-Scores  Express how far away a number is from the mean, in positive numbers between 0 and 100 o A T-Score above 50 indicates our number is better than the mean o A T-Score below 50 indicates our number is worse than the mean o A T-Score of 50 indicates our number is equal to the mean  Calculation o If larger numbers are better ( ) o If smaller numbers are better ( )  Alternate calculation  Example o You are given a set of data in which higher numbers are better, the mean is 20, and the standard deviation is 4. Find the t-score of 12. ( ) [ ] [ ] Finding Probabilities and Percentiles 2/6/13  If we know the z-score of a data point, we can calculate that point’s percentile or the probability of achieving that score or worse.  Percentiles are written with %, probabilities are written as decimals.  Percentiles describe the relative position of a data point in more detail than the median. For example, being in the 76 percentile means the score was better than or equal to 76% of all scores.  Calculation o Step 1: put the data in order from “worst” to “best” and rank them so that the “worst” score is 1 and the “best” score is equal to N o Step 2: % = rank of data point/N --or-- % * N = rank of data point  Value from table gives probability area under the standard normal curve between 0 and z.  Example Bench Press o You have a set of 8 bench press max’s. (N=8) Max Rank o 88 1 o 1) Find the percentile of the person whos max was 109 92 2  Formula: %ile = rank/N 109 3  Calculation: %ile = 3/8 117 4  Answer: 37.5 percentile 135 5 o Find the max of the person in the 75 percentile 144 6  Formula %ile * N = rank of data 163 7  Calculation: rank = 0.75 * 8 181 8  Rank of answer: 6  Answer: 144 Drawing Probability Diagrams  Total Probability = 1.0  Probability of each half = 0.5  Graph your z-score and shade the area you are interested in  Then decide which area you can look up on a table  Examples: 1. What is the probability of a given number having a z-score of 1.82 or less? P = 0.5 + 0.4686 = .9686 2. What percentile is associated with a z-score of 2.9 P= .4981 + .5 = .9981 x 100 = 99.81% 3. A z-score of -0.55 is _________ percent below the mean? This same z-score is in what percentile? P= .2088 x100 = 20.88% = .5 - .2088 = .2912 (29.12%) percentile 4. What is the probability of achieving a z-score between -3.04 and -2.94 P= .4988 - .4984 = .0004 2/13/13 Correlation and Regression Correlation  Correlation – relationship between 2 variables  Correlation Coefficient – statistic that represents the relationship between variables o Range from -1 to 1, 0 = no correlation  What kind of graph? o Scatter Plot  If the dots go up from left to right, that is a Strong Positive correlation (very close to a value of 1)  If the dots go down from left to right, that is a Strong Negative correlation (very close to a value of -1)  If there is no uniform pattern to the dots, then there is no correlation (very close to a value of 0) Correlation Strength  +/- .80 - 1.00 High  +/- .60 - .79 Moderately High  +/- .40 - .59 Moderate  +/- .20 - .39 Low  +/- .00 - .19 No relationship Significance  “Significant” is a statistical term that determines if we can believe our result. It is determined by a judgment call we can make ourselves. The answer to “Is your result significant?” will be either yes or no.  If a statistic is significant, we trust that the result can be replicated and that it did not occur by coincidence.  To determine significance you will need the following: correlation coefficient, degrees of freedom, alpha level, and correlation significance table. Degrees of Freedom  Degrees of Freedom (abbreviated df) describes the sample size, or number of people tested.  This is important because a coincidence that changes our results is more likely to occur in a smaller group.  When you start using the correlation significance table you will see that smaller groups require a larger correlation coefficient to be deemed significant.  For Pearson Correlations df = N-2. Therefore if you tested a group of 12 people, you would calculate df = 12-2 = 10. Alpha Level  The alpha (α) level we choose is based on the confidence we want to have in our result.  For this class we will always use an α of 0.05. This level is very common, but you will see others from time to time, such as 0.01.  An α of 0.05 means that there is a 5% chance we will say two variables were not related (95% confidence) when they really were. An α of 0.01 would reduce that to a 1% chance, but would increase the chances of making the opposite error—saying the variables were related when they really were not. For our purposes, choosing 0.05 is a good compromise between these two types of error. Using Correlation Significance Chart 1. Locate the appropriate df on the left column 2. If your value falls between numbers, be conservative and use the lower number (i.e. for 23 degrees of freedom, select 20) 3. Using the appropriate df, locate the corresponding score in the 0.05 column—this number is called the “Critical Value” 4. If your correlation coefficient is greater than or equal to the critical value (ignoring the sign), the correlation is significant 5. If your correlation coefficient is less than critical value, the correlation is not significant 6. If we had 6 degrees of freedom and a correlation coefficient of -0.39, we would find that our result is non-significant. However, with 40 degrees of freedom a correlation coefficient of -0.39 is significant. This highlights the importance of N in determining significance. Example  You have just calculated a correlation coefficient of -0.84 for a set of data in which N = 6 o What is your df?  df = 6-2 = 4 o What is your critical value?  0.811 o Is your result significant? Why?  Yes; 0.84 is greater than 0.811  You have just calculated a correlation coefficient of 0.25 for a set of data in which N = 6 o What is your df?  58 o What df will you use from the chart?
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