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Kinesiology
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KIN 369
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Alison Harper
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Lecture

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Kinesiology

KIN 369

Alison Harper

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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