2. Organizing Data:
A) Simple Frequency Distribution
1) Open the data
2) On the toolbar, click Analyze.
3) From the dropdown menu, highlight Descriptive Statistics.
4) From the dropdown menu, highlight Frequencies…
5) Move the variables of interest from the list of variables in the left box into the box labeled
Variable(s).
6) Ensure that the Display Frequency Tables is checked.
7) Click OK.
The output should appear as:
Statistics
Age
N Valid 23
Missing 0
Age
Frequency Percent Valid Percent
Cumulative
Percent
Valid 20 2 8.7 8.7 8.7
21 2 8.7 8.7 17.4
22 2 8.7 8.7 26.1
23 2 8.7 8.7 34.8
24 6 26.1 26.1 60.9
25 2 8.7 8.7 69.6
26 1 4.3 4.3 73.9
27 3 13.0 13.0 87.0
29 1 4.3 4.3 91.3
30 1 4.3 4.3 95.7
35 1 4.3 4.3 100.0
Total 23 100.0 100.0
3. The first column represents all of the possible raw scores from the data set (which in this data set
is age in years). The frequency column displays the amount of times each score (age) appeared.
The total number of subjects (N) is listed at the bottom of the frequency column. The percent
column equals the frequency of each raw score divided by the total number of subjects N
multiplied by 100 ([frequency (ƒ) / N] *100) . The cumulative percent column represents the
percentage of total subjects who had scores at or above the given row.
B) Histogram
1) Open the data
2) On the toolbar, click Graphs.
3) From the dropdown menu, highlight Chart Builder…
4) A dialog box will appear. Press OK.
5) Select Histogram from the Gallery tab on the lower left hand side.
6) Click on the histogram of your choice and drag it to the white Chart preview space.
7) Drag the variable from the Variables box to the x-axis of the histogram.
8) Click OK.
The output should appear as:
4. The value or range of values described by a bar is represented on the x-axis under its base. The
height of each bar is associated with its frequency (# of times occurred) whose numerical value is
found on the y-axis.
C) Frequency Polygon
1) Open the data
2) On the toolbar, click Graphs.
3) From the dropdown menu, highlight Chart Builder…
4) A dialog box will appear. Press OK.
5) Select Area or Line from the Gallery tab on the lower left hand side.
6) Click on the graph of your choice and drag it to the white chart preview space.
7) Drag the variable from the Variables box to the x-axis of the histogram.
8) Click OK.
The output should appear as:
The raw data values are represented on the x-axis. The frequency each X-coordinate value
occurs is represented by the height, or Y-coordinate, that is associated with it. Frequency
polygons can be deceiving, however, as straight lines connect data points and can create the
allusion of a frequency for an x-coordinate for which the score does not actually exist. For
example, in this frequency polygon a frequency of 1 is given for every age from 29-35 years old.
In reality there is one 29 year old, one 30 year old, and one 35 year old in the data set and none
for the other ages. Cross validation of data may be important when using frequency polygons.
5. Central Tendency:
A) Mode
1) Open the data.
2) On the toolbar, click Analyze.
3) From the dropdown menu, highlight Descriptive Statistics.
4) From the dropdown menu, highlight Frequencies...
5) Move the variables of interest from the list of variables in the left box into the box labeled
Variables.
6) Select Statistics.
7) Check Mode under Central Tendency.
8) Click Continue.
9) Uncheck Display Frequency Tables.
10) Click OK.
The output should appear as:
Statistics
X
N Valid 15
Missing 0
Mode 8
The mode is the value that appears most frequently. In this case, there are 15 scores (N) and the
mode is 8. If there are two scores that have the same frequency then the data is bimodal. If all of
the individual scores occur only once or more than two scores occur the same number of times
then the data is multimodal. The data will appear as:
Statistics
X2
N Valid 15
Missing 0
Mode 1a
a. Multiple modes exist.The
smallestvalue is shown
Here multiple modes exist and the lowest mode score is shown.
6. B) Median
1) Open the data.
2) On the toolbar, click Analyze.
3) From the dropdown menu, highlight Descriptive Statistics.
4) From the dropdown menu, highlight Frequencies…
5) Move the variables of interest from the list of variables in the left box into the box labeled
Variables.
6) Select Statistics.
7) Check Median under Central Tendency.
8) Click Continue.
9) Uncheck Display Frequency Tables.
10) Click OK.
The output should appear as:
Statistics
X
N Valid 15
Missing 0
Median 9.00
The median is highlighted in green. In this case there are 15 scores (N) and the median is 173.
C) Mean
1) Open the data.
2) On the toolbar, click Analyze.
3) From the dropdown menu, highlight Descriptive Statistics.
4) From the dropdown menu, highlight Frequencies…
5) Move the variables of interest from the list of variables in the left box into the box labeled
Variables.
6) Select Statistics.
7) Check Meanunder Central Tendency.
8) Click Continue.
9) Uncheck Display Frequency Tables.
10) Click OK.
The output should appear as:
7. Statistics
X
N Valid 15
Missing 0
Mean 9.13
The mean is highlighted in green. In this case, there are 15 subjects (N) and the mean is 173.
The mean is the best measure of central tendency as it gives equal weight to all scores. It is also
the only measure of central tendency that is used in further calculations.
D) Standard Error of the Mean
1) Open the data.
2) On the toolbar, click Analyze.
3) From the dropdown menu, highlight Descriptive Statistics.
4) From the dropdown menu, highlight Frequencies…
5) Move the variables of interest from the list of variables in the left box into the box labeled
Variables.
6) Select Statistics…
7) Check S.E. Meanunder Dispersion.
8) Click Continue.
9) Uncheck Display Frequency Tables.
10) Click OK.
The output should appear as:
Statistics
X
N Valid 15
Missing 0
Std. Error of Mean 1.162
The standard error of the mean numerically estimates sampling error. Sampling error occurs
when a sample of a population is measured instead of the entire population. The standard error
of the mean is highlighted in yellow. If a score is within ±1 SE mean from the sample mean, then
there is a 68% chance that this score is correct. If a score is within ± 2 SE mean from the sample
mean, then there is a 95% chance that this score is correct. If a score is within ±3 SE mean from
the sample mean, then there is a 99% chance that this score is correct.
8. The equation for Standard error of the mean is √SD/n. An increase in Standard Deviation results
in a larger Standard Error of the Mean. Increase the number of subjects decreases the Standard
Error of the Mean.
Variability:
A) Range
1) Open the data.
2) On the toolbar, click Analyze.
3) From the dropdown menu, highlight Descriptive Statistics.
4) From the dropdown menu, highlight Frequencies...
5) Move the variables of interest from the list of variables in the left box into the box labeled
Variable(s).
6) Click the box labeled Statistics…
7) Check Range under Dispersion.
8) Click Continue.
9) Uncheck Display Frequency Tables.
10) Click OK.
The output should appear as:
Statistics
measure
N Valid 9
Missing 0
Range 14
The range is the difference between the highest and lowest raw scores in a data set. It is very
unstable because the range is based on only two values. It is best used to double check work.
B) Variance
1) Open the data.
2) On the toolbar, click Analyze.
3) From the dropdown menu, highlight Descriptive Statistics.
4) From the dropdown menu, highlight Frequencies...
5) Move the variables of interest from the list of variables in the left box into the box labeled
Variable(s).
6) Click the box labeled Statistics…
7) Check Variance under Dispersion.
8) Click Continue.
9) Uncheck Display Frequency Tables.
9. 10) Click OK.
The output should appear as:
Statistics
measure
N Valid 9
Missing 0
Variance 20.750
Variance (s2) is the average of the squared deviation of each score from the mean. It is not
directly useful in the analysis of data though it is used as a precursor in the calculation of
Standard Deviation.
C) Standard Deviation
1) Open the data.
2) On the toolbar, click Analyze.
3) From the dropdown menu, highlight Descriptive Statistics.
4) From the dropdown menu, highlight Frequencies...
5) Move the variables of interest from the list of variables in the left box into the box labeled
Variable(s).
6) Click the box labeled Statistics…
7) Check Standard Deviation under Dispersion.
8) Click Continue.
9) Uncheck Display Frequency Tables.
10) Click OK.
The output should appear as:
Statistics
measure
N Valid 9
Missing 0
Std. Deviation 4.555
Standard Deviation is the square root of variance. It describes variability in the original units of a
data set. The data is typically reported as mean ±SD.
eg. Bulls scoring = 20 ± 28 points. SD = 28
Cavs scoring = 20 ± 10 points. SD = 10
10. Standard Scores:
A) Z-scores
A Z-score is a raw score expressed in standard deviation units. Z-scores eliminate test-specific
units allowing comparisons between tests.
1) Open the Data.
2) On the toolbar, click Analyze.
3) From the dropdown menu, highlight Descriptive Statistics…
4) Move the variables of interest from the list of variables in the left box into the box labeled
Variable(s).
5) Ensure the box labeled Save standardized values as variables is selected
6) Click OK.
The output should appear as:
The Z-scores will be listed in the SPSS data output screen as another column. Here it is shown at
the right of the screen (Zheight).
B) T-scores
A T-score is a derivative of the z-score that produces user-friendly numbers.
T = 50 + 10z
For normally distributed data, ~99% of all T-scores range between 20 and 80.
1) Open the data.
2) On the toolbar, click Transform.
3) From the dropdown menu, highlight Compute Variable.
4) Create a label in the box on the top right labeled Target Variable: (i.e. Tunit).
11. 5) From the box on the top right labeled Numeric Expression type in 50+10*ZScores(make sure that it is
typed identical to the Z score label from the data view)
6) Click OK
The output should appear as:
Here the T-scores are listed in a column adjacent to the corresponding Z-scores.
Assessing Normality:
Data is said to be normal if it passes two conditions:
1) It cannot be skewed:
-2≤ (skewness/SEs)≤2
2) It cannot be kurtosed:
-2≤ (kurtosis/SEk)≤2
A) Skewness
Skewness is the degree to which a curve is not bilaterally symmetrical. Characterized as
positively skewed or negatively skewed.
Negatively Skewed curves look like the curve is being pulled to the right. The data is more
concentrated on positive side of the range.
Positively Skewed curves look like the curve is being pulled to the left. The data is more
concentrated on negative side of the range.
1) Open the data.
2) On the toolbar, click Analyze.
3) From the dropdown menu, highlight Descriptive Statistics.
4) From the dropdown menu, highlight Frequencies...
12. 5) Move the variables of interest from the list of variables in the left box into the box labeled
Variable(s).
6) Click the box labeled Statistics…
7) Check Skewness under Distribution.
8) Click Continue.
9) Uncheck Display Frequency Tables.
10) Click OK.
The output should appear as:
Statistics
measure
N Valid 20
Missing 0
Skewness 1.513
Std. Error of Skewness .512
B) Kurtosis
Kurtosis is the degree of peakedness or flatness to a curve.
Leptokurtic curves have a narrow but tall spike that represents a large frequency over a small
range.
Platykurtic curves are flat and broad in nature. Low frequencies occur over a large range.
1) Open the data.
2) On the toolbar, click Analyze.
3) From the dropdown menu, highlight Descriptive Statistics.
4) From the dropdown menu, highlight Frequencies...
5) Move the variables of interest from the list of variables in the left box into the box labeled
Variable(s).
6) Click the box labeled Statistics…
7) Check Kurtosis under Dispersion.
8) Click Continue.
9) Uncheck Display Frequency Tables.
10) Click OK.
The output should appear as:
13. Statistics
measure
N Valid 20
Missing 0
Kurtosis 3.515
Std. Error of Kurtosis .992
Relationships Between/Among Variables:
A) Simple Correlation
Correlation is a numerical value that describes the direction and strength of the linear
relationship between two variables.
- Pearson Product Moment Correlation (r)
Ranges from a perfect relationship (±1) to no relationship (0)
-1 0 1
(complete relationship) (no relationship) (complete relationship)
Correlation can be used to:
- Examine to see if two variables share a relationship
- To evaluate the validity of a new measure
- As the basis for prediction
Correlation should NOT be used to assess reliability.
Steps:
1) Open the data.
2) On the toolbar, click Analyze.
3) From the dropdown menu, highlight Correlate.
4) From the dropdown menu, click Bivariate...
5) Move the variables of interest from the list of variables in the left box into the box labeled
Variables.
6) Ensure that Pearson is selected in the Correlation Coefficient box.
7) Ensure that Two-tailed is selected in the Test of Significance box.
8) Ensure that the box labeled Flag significant correlations is checked.
9) Click OK.
14. The output should appear as:
Correlations
Simple Reaction
Time (ms)
Movement Time
for Linear Arm
Movement (ms)
Simple Reaction Time (ms) Pearson Correlation 1 -.034
Sig. (2-tailed) .925
N 10 10
Movement Time for Linear
Arm Movement (ms)
Pearson Correlation -.034 1
Sig. (2-tailed) .925
N 10 10
Conclusion statements:
1) Written in past tense.
2) Use a word that describes strength
3) Use actual r-value.
4) Must have the words “statistically significant”
5) The actual r-value.
If p > 0.05 (regardless of r), the conclusion statement reads:
o “There is no significant relationship (p>0.05) between X and Y
If p≤0.05 and r is between ±0.10 and ±0.30, the conclusion statement reads:
o “A weak (r=0.XXX) statistically significant relationship (p≤0.05) existed between
X and Y.”
If p≤0.05 and r is between ±0.30 and ±0.50, the conclusion statement reads:
o “A moderate (r=0.XXX) statistically significant relationship (p≤0.05) existed
between X and Y.”
If p≤0.05 and r is greater than ±0.50, the conclusion statement reads:
o “A strong (r=0.XXX) statistically significant relationship (p≤0.05) existed
between X and Y.
The conclusion statement for this output reads as:
15. There is no significant relationship (p>0.05) between Simple Reaction Time and Movement
Time for Linear Arm Movement.
B) Coefficient of determination
Area of overlap represents common variance (how much X explains the variability of Y or vice
versa). Can calculate this area by squaring r (r2).
1) Open the data.
2) On the toolbar, click Analyze.
3) From the dropdown menu, highlight Correlate.
4) From the dropdown menu, click Bivariate...
5) Move the variables of interest from the list of variables in the left box into the box labeled
Variables.
6) Ensure that Pearson is selected in the Correlation Coefficient box.
7) Ensure that Two-tailed is selected in the Test of Significance box.
8) Ensure that the box labeled Flag significant correlations is checked.
9) Click OK.
The output should appear as:
Model Summary
Model R R Square
Adjusted R
Square
Std. Error of the
Estimate
1 .940a
.884 .876 3.6261
a. Predictors:(Constant),mile walk/run time (s)
eg. Body weight (Variable 1) explains 11% of the variability in Body Fat % (Variable 2)
C) Simple Regression
The line of best fit (regression line) best describes the relationship between two variables.
Allows for the prediction of a dependent variable (predicted variable) from an
independent variable (predictor variable).
Equation of the line:
Y = bX + C
Y = score in y variable, b = slope, X = score in x variable, and c = y-intercept.
16. Example:
Using Y = 0.7353X + 7.9852 to describe the relationship between right grip strength and left grip
strength, what is the prediction for the left grip strength of a person with a right grip strength =
40kg?
Y = 0.7353X + 7.9852
Y’ = 0.7353 (40kg) + 7.9852
Y’ = 37.4kg
Y’ = 37kg
Y’ = 37kg is the predicted left grip strength of a person with a right grip strength of 40kg.
The prime (‘) in Y’ denotes that this value is the predicted value and is an estimate. The
original regression equation represents the actual value and becomes the predicted value once
values are inserted and a prediction is made.
Steps:
1) Open the data.
2) On the toolbar, click Analyze.
3) From the dropdown menu, highlight Regression.
4) From the dropdown menu, click Linear…
5) Select the variable that you want to predict and move it to the Dependent box.
6) Select the predictor variable and move it to the Independent box.
7) Click OK.
The output should appear as:
Coefficientsa
Model
Unstandardized Coefficients
Standardized
Coefficients
t Sig.B Std. Error Beta
1 (Constant) 80.167 3.633 22.068 .000
mile walk/run time (s) -.073 .007 -.940 -11.021 .000
a. DependentVariable:VO2 max (ml/kg/min)
Slope of the regression line = -0.073
Y-intercept = 80.167
D) Multiple Regression
17. Equation of the line:
Y’ = b1X1 + b2X2 + b3X3 + C
Steps:
1) Open the data.
2) On the toolbar, click Analyze.
3) From the dropdown menu, highlight Regression.
4) From the dropdown menu, click Linear…
5) Select the variable that you want to predict and move it to the Dependent box.
6) Move the variable of interest (more than one variable) (Predictor Variables(X)) from the list
of variables in the left box into the box labeled Independent.
7) Click OK.
The output should appear as:
Model Summary
Model R R Square
Adjusted R
Square
Std. Error of the
Estimate
1 .636a
.405 .364 5.3735
a. Predictors:(Constant),Body Weight (lbs),Body Height(cm)
Coefficientsa
Model
Unstandardized Coefficients
Standardized
Coefficients
t Sig.B Std. Error Beta
1 (Constant) 88.346 21.620 4.086 .000
Body Height(cm) -.546 .144 -.711 -3.791 .001
Body Weight(lbs) .146 .035 .792 4.219 .000
a. DependentVariable:Body Fat (%)
Body Height:
Slope of the regression line = -0.546
Y-intercept = 88.346
Body Weight:
Slope of the regression line = 0.146
Y-intercept = 88.346
18. Multiple RegressionEquation:
Y’ = -0.546X1 + 0.146X2 + 88.346
E) Standard Error of the Estimate
The standard error of the estimate (SEE) estimates the error in prediction.
Fundamentally, SEE is the average of the squared residuals of each score.
o Interpreted like a standard deviation (or standard error of the mean), allowing the
determination of ranges and probabilities for each score.
Example: The previously determined left grip strength of a person with a right grip strength of
40kg was 37kg. If the SEE = 5kg, we are ~95% confident the actual score will be between what
two values?
~95% = 2(SEE)
o Y’ - 2(SEE) < actual < Y’ + 2(SEE)
o 37kg – 2(5kg) < actual < 37kg + 2(5kg)
o 37kg – 10kg < actual < 37kg +10kg
o 27kg < actual < 47kg
Steps:
1) Open the data.
2) On the toolbar, click Analyze.
3) From the dropdown menu, highlight Regression.
4) From the dropdown menu, click Linear…
5) Select the variable that you want to predict and move it to the Dependent box.
6) Select the predictor variable and move it to the Independent box.
7) Click OK.
The output should appear as:
Model Summary
Model R R Square
Adjusted R
Square
Std. Error of the
Estimate
1 .940a
.884 .876 3.6261
a. Predictors:(Constant),mile walk/run time (s)
Differences Between/Among Sample Means:
A) t-tests
19. A t-test is a statistical analysis that determines whether the difference between two means is
“real” or the result of random chance.
t = Sample 1 Mean – Sample 2 Mean
Difference due to Random Chance (SEDiff)
Probability:
If p >0.05, accept H0 and conclude:
o “There was no significant difference (p>0.05) between levels of the independent
variable in the dependent variable.”
o “There was no significant difference (p>0.05) between males and females in
height.”
If p≤0.05, reject H0 and conclude:
o “Independent variable level 1 was significantly (p<0.05) greater than independent
variable 2 in the dependent variable.”
o “Males were significantly greater (p<0.05) than females in height.”
o “Males were significantly taller (p<0.05) than females.”
Conclusion statements must include:
1) p-value.
2) The word “significant”.
3) Written in past tense (was, were…).
4) If there was a difference than it must have directionality (Males were taller than females).
One sample t-test
Compares the mean of one sample against a known standard.
1) Open the data.
2) On the toolbar, click Analyze.
3) From the dropdown menu, highlight Compare Means.
4) From the dropdown menu, click One-sample T-Test…
5) Select the variable that you want to compare and move it to the Test Variable(s) box.
6) Select the measurement standard you want to compare against and move it to the Test Value
box.
7) Click OK.
The output should appear as:
One-Sample Statistics
N Mean Std. Deviation Std. Error Mean
Body Fat (%) 32 18.519 6.7380 1.1911
20. One-Sample Test
Test Value = 20
t df Sig. (2-tailed) Mean Difference
95% Confidence Interval of the
Difference
Lower Upper
Body Fat (%) -1.244 31 .223 -1.4813 -3.911 .948
P>0.05
Conclusion Statement:
There was no significant difference in body fat percentage (p>0.05) between the sample mean
and the standard for body fat %.
Independent t-test (between subjects)
Compares the means of two samples composed of different people.
1) Open the data.
2) On the toolbar, click Analyze.
3) From the dropdown menu, highlight Compare Means.
4) From the dropdown menu, click Independent-Samples T Test…
5) Select the dependent variable and move it to the Test Variable(s) box.
6) Select the independent variable and move it to the Grouping Variable box.
7) The Grouping Variable box should say “(Group? ?)”. Click on Define Groups. Designate
the levels of the independent variable using the same labels used in the data. Eg. Men =1 or M;
Women =2 or W. Ensure that the same labels are used for both.
7) Click OK.
The output should appear as:
Group Statistics
Active or
Passive N Mean Std. Deviation Std. Error Mean
Arm positioning Active 10 2.2820 1.24438 .39351
Passive 10 1.9660 1.50606 .47626
Independent Samples Test
21. Levene's Test for
Equality of Variances t-test for Equality of Means
F Sig. t df
Sig. (2-
tailed)
Mean
Difference
Std. Error
Difference
95% Confidence
Interval of the
Difference
Lower Upper
Arm
positioning
Equal variances
assumed
.513 .483 .511 18 .615 .31600 .61780 -.98194 1.61394
Equal variances
not assumed
.511 17.382 .615 .31600 .61780 -.98526 1.61726
What to look for:
Independent Samples Test Box:
Levene’s Test for Equality of Variances:
If Levene’s Test has p<0.05 then there are not equal variances in both samples. Use the p-
value from the bottom row (equal variances not assumed).
If Levene’s Test has a p>0.05 then equal variance is assumed. Use the p-value from the
top row (equal variances assumed).
Conclusion Statement for this output:
Levene’s Test = p>0.05 (equal variance assumed)
p-value >0.05 (0.615). Accept the H0.
There were no significant differences in the errors made by the active group versus the passive
group (p>0.05) in arm positioning.
Dependent (paired samples)t-test (within subjects)
Compares the means of two samples composed of the same people.
1) Open the data.
2) On the toolbar, click Analyze.
3) From the dropdown menu, highlight Compare Means.
4) From the dropdown menu, click Paired Samples T Test...
5) Select the first sample mean from the variable you want to compare and move it to the
Variable 1 box.
22. 6) Select the second sample mean from the variable you want to compare and move it to the
Variable 2 box.
7) Click OK.
The output should appear as:
Paired Samples Statistics
Mean N Std. Deviation Std. Error Mean
Pair 1 Not Motivated V02 max test 39.80 10 11.858 3.750
Motivated VO2 max test 47.80 10 9.830 3.108
Paired Samples Test
Paired Differences
t df
Sig. (2-
tailed)Mean
Std.
Deviation
Std. Error
Mean
95% Confidence Interval of
the Difference
Lower Upper
Pair 1 Not Motivated V02
max test - Motivated
VO2 max test
-8.000 4.738 1.498 -11.389 -4.611 -5.340 9 .000
What to look for:
Paired Samples Test Box:
Sig. (2-tailed) = p-value <0.0005
Paired Samples Statistics Box:
Compare means to determine which Sample Mean is larger. Determines directionality with
p<0.05.
Conclusion Statement for this output:
p-value <0.05. Reject the H0. Accept HA.
VO2 max scores were significantly greater with motivation than without motivation (p<0.05).
B) ANOVA
The analysis of variance (ANOVA) compares any number of sample means to determine if
significant differences exist or if the differences are due to random chance.
H0 = There is no significant difference among sample means.
HA = There is a significant difference among sample means.
23. If p>0.05 accept H0 and reject HA
If p<0.05, reject H0 and accept HA
o There is a significant difference among the means.
o Analyze Post hoc tests.
Post Hoc tests are statistical analyses calculated after ANOVA that
determine which pair(s) of means significantly differ.
Make Pairwise Comparisons between Sample means and evaluate as
normal (conclusion statements are like t-tests).
Simple ANOVA
Simple ANOVA is an extension of the independent t-test. It is a “between” comparison
comparing sample means taken from groups of different people.
o It is a 1-way ANOVA comparing sample means of 1 Independent Variable.
Steps:
1) Open the data.
2) On the toolbar, click Analyze.
3) From the dropdown menu, highlight General Linear Model.
4) From the dropdown menu, click Univariate…
5) Select the dependent variable and move it to the Dependent Variable box.
6) Select the independent variable and move it to the Fixed Factor(s) box.
7) Click Post Hoc button and move Independent Variable into Post Hoc Tests For box.
8) Select Scheffé, Tukey, or LSD Post Hoc Tests depending on preference. Tukey is the most
neutral Post Hoc Test.
9) Click Options and move all variables over to Display Means For box.
10) Check Descriptive Statistics.
11) Click Continue.
The output should appear as:
Descriptive Statistics
DependentVariable:FootSpeed
Groups Mean Std. Deviation N
Good 6.00 1.414 6
Average 7.83 1.472 6
Poor 11.00 1.789 6
Total 8.28 2.585 18
24. Tests of Between-Subjects Effects
DependentVariable:FootSpeed
Source
Type III Sum of
Squares df Mean Square F Sig.
Corrected Model 76.778a
2 38.389 15.633 .000
Intercept 1233.389 1 1233.389 502.285 .000
Groups 76.778 2 38.389 15.633 .000
Error 36.833 15 2.456
Total 1347.000 18
Corrected Total 113.611 17
What to look for:
Tests of Between Subjects Effects Box:
p-value on “Groups” row represents p-value for entire group and determines if a Post Hoc Test is
required.
p-value <0.05 is significant.
There was a significant difference (p<0.05) among the sample means.
Post Hoc tests are required for further evaluations.
Post Hoc:
Multiple Comparisons
DependentVariable:FootSpeed
(I) Groups (J) Groups
Mean Difference
(I-J) Std. Error Sig.
95% Confidence Interval
Lower Bound Upper Bound
Tukey HSD Good Average -1.83 .905 .140 -4.18 .52
25. Poor -5.00*
.905 .000 -7.35 -2.65
Average Good 1.83 .905 .140 -.52 4.18
Poor -3.17*
.905 .009 -5.52 -.82
Poor Good 5.00*
.905 .000 2.65 7.35
Average 3.17*
.905 .009 .82 5.52
Scheffe Good Average -1.83 .905 .163 -4.29 .62
Poor -5.00*
.905 .000 -7.46 -2.54
Average Good 1.83 .905 .163 -.62 4.29
Poor -3.17*
.905 .011 -5.62 -.71
Poor Good 5.00*
.905 .000 2.54 7.46
Average 3.17*
.905 .011 .71 5.62
What to look for:
Evaluate all pairwise comparisons in Post Hoc Test and make conclusion statements for
each.
If a significant difference is found between a pairwise comparison, look in Descriptive
Statistics Box to determine which sample mean is larger to determine directionality.
Conclusion Statements:
There was a significant difference in the means between Good Sprinters v. Poor Sprinters
(p<0.0005) and Average sprinters v. poor sprinters (p=0.011)
Good sprint group sample mean = 6
Average sprint group sample mean = 8
Poor sprint group sample mean = 11
Good sprinters had a significantly lower horizontal foot speed at touchdown (p<0.05)
than poor sprinters.
26. Average sprinters had a significantly lower horizontal foot speed at touchdown (p<0.05)
than poor sprinters.
Repeatedmeasures ANOVA (with post hocs)
Repeated measures ANOVA is an extension of the dependent t-test. It is a “within”
comparison typically comparing the same subjects on the same test completed on
multiple occasions.
o It is a 1-way ANOVA comparing sample means of 1 Independent Variable.
Steps:
1) Open the data.
2) On the toolbar, click Analyze.
3) From the dropdown menu, highlight General Linear Model.
4) From the dropdown menu, click RepeatedMeasures…
5) In the Within-Subject Factor Name box, rename (set as factor1) the Within-variable (time is
always a within variable).
6) In the Number of Levels box enter the number of levels of the independent variable.
7) Click Add.
8) Move the appropriate variables from the left column into the Within-Subjects Variables box.
9) Click on Options.
10) In the Display Means for box move all variables into Factor(s) and Factor Interactions
box.
11) In the Repeated Measures Options, click on Compare main effects box.
12) Under Confidence interval adjustment ensure LSD is selected.
13) In the Repeated Measures Options, click on descriptive statistics (optional).
14) Click Continue.
15) Click OK.
The output should appear as:
Descriptive Statistics
Mean Std. Deviation N
minute 2 16.60 3.209 5
minute 4 20.80 3.564 5
minute 6 25.00 3.742 5
minute 8 30.60 3.507 5
minute 10 35.40 4.159 5
Minute 2 = 17 ml/kg/min
Minute 4 = 21 ml/kg/min
Minute 6 = 25 ml/kg/min
27. Minute 8 = 31 ml/kg/min
Minute 10 = 35 ml/kg/min
Mauchly's Test of Sphericityb
Measure:MEASURE_1
Within
Subjects
Effect Mauchly's W
Approx. Chi-
Square df Sig.
Epsilona
Greenhouse-
Geisser Huynh-Feldt Lower-bound
time .000 19.748 9 .046 .351 .484 .250
What to look for:
Mauchly’s Test of Sphericity box:
Mauchly’s Test of Sphericity is equivalent to Levene’s test of variance.
If p>0.05 then the assumption of sphericity (variance) is valid.
Use top line of Tests of Within-Subjects Effects box to evaluate p-value for overall H0.
If p<0.05 then the assumption of sphericity (variance) is violated.
Use second line (Greenhouse – Geisser) of Tests of Within-Subjects Effects box to
evaluate p-value for overall H0.
Tests of Within-Subjects Effects
Measure:MEASURE_1
Source
Type III Sum of
Squares df Mean Square F Sig.
time Sphericity Assumed 1127.040 4 281.760 98.517 .000
Greenhouse-Geisser 1127.040 1.405 802.122 98.517 .000
Huynh-Feldt 1127.040 1.937 581.965 98.517 .000
Lower-bound 1127.040 1.000 1127.040 98.517 .001
Error(time) Sphericity Assumed 45.760 16 2.860
Greenhouse-Geisser 45.760 5.620 8.142
Huynh-Feldt 45.760 7.746 5.907
Lower-bound 45.760 4.000 11.440
Post Hoc Required?
p <0.05 = There is a significant difference (p<0.05) among the means.
Yes, Post Hoc Tests are required for pairwise comparisons.
29. What to look for:
Evaluate all pairwise comparisons in Post Hoc Test and make conclusion
statements for each.
If a significant difference is found between a pairwise comparison, look in
Descriptive Statistics Box to determine which sample mean is larger to
determine directionality.
Minute 2 = 17 ml/kg/min
Minute 4 = 21 ml/kg/min
Minute 6 = 25 ml/kg/min
Minute 8 = 31 ml/kg/min
Minute 10 = 35 ml/kg/min
Conclusion Statements:
Minute 2 was significantly lower (p < 0.05) than Minute 4.
Minute 2 was significantly lower (p < 0.05) than Minute 6.
Minute 2 was significantly lower (p < 0.05) than Minute 8.
Minute 2 was significantly lower (p < 0.05) than Minute 10.
Minute 4 was significantly lower (p < 0.05) than Minute 6.
Minute 4 was significantly lower (p < 0.05) than Minute 8.
Minute 4 was significantly lower (p < 0.05) than Minute 10.
Minute 6 was significantly lower (p < 0.05) than Minute 8.
Minute 6 was significantly lower (p < 0.05) than Minute 10.
Minute 8 was significantly lower (p < 0.05) than Minute 10.
Intraclass correlation
Intraclass correlation (ICC) solves the two problems associated with using Pearson’s r for
reliability:
1) Controls for systematic bias.
2) Can evaluate more than two trials.
30. Steps:
1) Open the data.
2) On the toolbar, click Analyze.
3) From the dropdown menu, highlight Scale.
4) From the dropdown menu, click Reliability Analysis…
5) Move variables to be tested into Items: box.
6) Click on Statistics box.
7) Check Intraclass Correlation Coefficient box.
8) Click Continue.
9) Click OK.
The output shout appear as:
Intraclass Correlation Coefficient
Intraclass
Correlationa
95% Confidence Interval F Test with True Value 0
Lower Bound Upper Bound Value df1 df2 Sig
Single Measures .908b
.714 .989 50.272 4 16 .000
Average Measures .980c
.926 .998 50.272 4 16 .000
What to look for:
In the Intraclass Correlation Coefficient box the coefficient is in the Single Measures row.
Conclusion:
R =0.908
The pilot data is reliable with R>0.8
Between-within(mixed model) factorial ANOVA (with post hocs)
A 2-way ANOVA that analyzes 2 Independent variables:
o within IV
o between IV
Three p-values are obtained:
o p-value for Main Effect 1 (between IV)
o p-value for Main Effect 2 (within IV)
o p-value for Interaction effect (Effect of main effect 1 on main effect 2 and 2 on 1)
31. Steps:
1)Open the data..
2) On the toolbar, click Analyze.
3)From the dropdown menu, highlight General Linear Model.
4)From the dropdown menu, click Repeated Measures.
5) In the Within-Subject Factor Name box, define within-subject factor (ex. Pre-anger, post-
anger).
6) In the Number of Levels box enter the number of levels (ex 2)
7) In the Between-Subject Factor(s) box, assign the between-subject variable(s) (mass-loss
group/(group)). (Image 5).
8) Click Options.
9) From the Factor(s) and Factor Interactions box: move variables: overall, group (group
effect on anger), time (time effect on anger), group*time (group-time interaction)) into the
Display Means for box. (Image 6)
10) Click Compare main effects box.
11) Click Display Means under the Display box.
12) Click Continue.
13) Click OK.
The output should appear as:
For Pre and Post Anger:
Tests of Within-Subjects Effects
Measure:MEASURE_1
Source Type III Sum of
Squares df Mean Square F Sig.
time Sphericity Assumed 93.006 1 93.006 8.670 .011
Greenhouse-Geisser 93.006 1.000 93.006 8.670 .011
Huynh-Feldt 93.006 1.000 93.006 8.670 .011
Lower-bound 93.006 1.000 93.006 8.670 .011
time * group Sphericity Assumed 17.042 2 8.521 .794 .473
Greenhouse-Geisser 17.042 2.000 8.521 .794 .473
Huynh-Feldt 17.042 2.000 8.521 .794 .473
Lower-bound 17.042 2.000 8.521 .794 .473
Error(time) Sphericity Assumed 139.458 13 10.728
Greenhouse-Geisser 139.458 13.000 10.728
Huynh-Feldt 139.458 13.000 10.728
Lower-bound 139.458 13.000 10.728
32. Estimates
Measure:MEASURE_1
time
Mean Std. Error
95% Confidence Interval
Lower Bound Upper Bound
1 1.333 .505 .242 2.424
2 4.806 1.167 2.285 7.326
What to look for:
Tests of Within Subjects Effects:
Use this box for p-value evaluating Main Effect (within).
Conclusion Statement:
Post-anger was significantly greater than pre-anger (p<0.05)
___
For Group Effect on Anger:
Tests of Between-Subjects Effects
Measure:MEASURE_1
Transformed Variable:Average
Source Type III Sum of
Squares df Mean Square F Sig.
Intercept 290.720 1 290.720 20.452 .001
group 13.083 2 6.542 .460 .641
Error 184.792 13 14.215
What to look for:
Tests of Between Subjects Effects:
Use this box for p-value evaluating Main Effect (between).
There was no significant effect on group on anger (p>0.05).
___
For Time and Anger Interaction
Tests of Within-Subjects Effects
Measure:MEASURE_1
33. Source Type III Sum of
Squares df Mean Square F Sig.
time Sphericity Assumed 93.006 1 93.006 8.670 .011
Greenhouse-Geisser 93.006 1.000 93.006 8.670 .011
Huynh-Feldt 93.006 1.000 93.006 8.670 .011
Lower-bound 93.006 1.000 93.006 8.670 .011
time * group Sphericity Assumed 17.042 2 8.521 .794 .473
Greenhouse-Geisser 17.042 2.000 8.521 .794 .473
Huynh-Feldt 17.042 2.000 8.521 .794 .473
Lower-bound 17.042 2.000 8.521 .794 .473
Error(time) Sphericity Assumed 139.458 13 10.728
Greenhouse-Geisser 139.458 13.000 10.728
Huynh-Feldt 139.458 13.000 10.728
Lower-bound 139.458 13.000 10.728
What to look for:
Tests of Within Subjects Effects:
Use this box for p-value evaluating time and anger interaction effect.
Conclusion Statement:
There was no significant time by group interaction p > 0.05.
Steps for evaluating Between-Within ANOVA output:
1. Evaluate p for main effect 1.
If p < 0.05, evaluate pairwise comparisons.
If p > 0.05, stop.
2. Evaluate p for main effect 2.
If p <0.05, evaluate pairwise comparisons.
If p > 0.05, stop.
3. Evaluate p for main effect 3.
If p <0.05, evaluate pairwise comparisons.
If p > 0.05, stop.
34. Decision Tree:
1) Normal? Interval or Ratio?
A) No Non Parametric
B)Yes Question 2
2) Relationship, Difference, or Prediction?
A) Relationship = Correlation
B) Difference = Question 3
C) Predictions = Regression
1 Predictor – Simple Regression
2 Predictor – Multiple Regression
3) How many Sample Means?
A) 2 Sample Means
Are samples composed of Same or Different People?
Same people – Dependent T-Test
Different people – Independent T-Test
B) 3 or more Sample Means = Question 4
4) How many IVs?
A) 1 IV
Are Samples Composed of Same or Different People?
Same – 1-Way Repeated Measures ANOVA
Different – 1-Way Simple ANOVA
B) 2 IVs = Question 5
5) IVs between or within?
A) Between –Within (Mixed Model)
B) Between – Between
C) Within – Within (Repeated Measures)
