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Statistical Methods and SPSS Physical Therapy 34.616 Research Methods Robert Karasek and Sean Collins

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Title: Statistical Methods and SPSS Physical Therapy 34.616 Research Methods Robert Karasek and Sean Collins


1
Statistical Methods and SPSSPhysical Therapy
34.616Research MethodsRobert Karasek and Sean
Collins
  • Robert Karasek, PhD
  • Department of Work Environment, University of
    Massachusetts Lowell

2
Statistical Methods and SPSS
  • 34.616 Course Module Goal
  • To develop hands-on proficiency and scientific
    understanding of basic statistical data analysis,
    using the SPSS statistical analysis program
    available in the UML Computer Laboratory.
  • SPSS Basic Text J. Pallant, SPSS Survival
    Manual, 3rd or 4th Ed, McGraw Hill
  • 34.616 Main Text Portnoy LG and Watkins MP,
    Foundations.. (Part IV Data Analysis - selected
    sections)
  • http//www.umass.edu/statdata/software/handouts/SP
    SS20Syntax.pdf
  • http//www.vassarstats.net/textbook/toc.html

3
Lecture Topics / order - dates
  • Lecture 1 Running SPSS and Descriptive
    Statistics
  • April 5, 2012
  • Lecture 2 Bivariate Relations and Correlation
  • April 10, 2012
  • Lecture 3 Multiple Regression and Factor
    Analysis
  • April 12, 2011
  • Lecture 4 Categorical Variable Statistics and
    T-tests
  • April 17, 2012
  • Lecture 5 Analysis of Variance (ANOVA)
  • April 19, 2012

4
Research Methods 34.616Statistical
Methods/SPSSLecture 1Using the SPSS
programand Descriptive Statistics
5
Research Methods 34.616Statistical
Methods/SPSSLecture 1APreliminary
Task Getting SPSS data analysis program /
dataset up and running in UML Computer Lab
6
Using SPSS for Data Analysisw/ Pallant, SPSS
Survival Manual (SSM) Using a typical SPSS
Datafile (3ED.sav/4ED.sav)
  • Download data set from web http//www.allena
    ndunwin.com/spss/data_files.html
  • Download Datafile (Survey3ED.sav /
    Survey4ED.sav)
  • Open UML Computer Lab SPSS Statistical program
    (it maybe called PASW Stat. 18).
  • Double click on dataset (above) icon. (SPSS
    should open - or... )
  • SPSS is Menu-driven and Syntax-driven (SSM, Chap
    2). So
  • Go to SPSS Menu File icon on far left - find
    the dataset.

7
SPSS Syntax
  • Syntax Editor Window
  • SPSS statistical commands can be written in
    two-ways
  • 1. Personal input (using book examples, SPSS
    manuals)
  • 2. Auto-written from Menu click processes (and
    saved in Syntax Window).
  • The SYNTAX NEEDS TO BE SAVED so it can be
    modified as you adjust your scientific questions
    for analysis (there is no other record of how you
    generated your output from the Menu analysis).
  • Syntax in SPSS is further discussed in the U Mass
    Amherst Memo (and the memo gives you access to
    other interesting downloadable datasets).

8
Research Methods 34.616Statistical
Methods/SPSSLecture 1BDescriptive Statistics
9
Lecture 1B Descriptive Statistics
  • I. Goals
  • 1. Describe the sample
  • 2. Check variables
  • 3. Research tests
  • II. SPSS Procedures
  • 1. FREQUENCIES
  • 2. DESCRIPTIVES
  • 3. EXPLORE

10
A Data Base - Typical (SPSS Survival Manual
3ED.sav / 4ED.sav) Cases 429, Variables 139
- ID Sex Age Marital ....
1 419 2 24 4 ....
2 9 1 39 3 ....
3 425 1 48 4 ....
4 301 1 41 5 ....
.... .... .... .... .... ....
11
FREQUENCIES (preliminary examination
categorical variables)
12
DESCRIPTIVES (continuous variables)Output/Statist
ics for Age in SPSS
  • SYNTAX
  • DESCRIPTIVES VARIABLESage
  • /NTILES4
  • /STATISTICS
  • STDDEV
  • VARIANCE
  • MINIMUM
  • MAXIMUM
  • MEAN
  • MEDIAN
  • SKEWNESS
  • KURTOSIS
  • /ORDERANALYSIS

13
Sample Population Descriptive Statistics
  • STDDEV ------- Distribution Parameters
  • VARIANCE (Normal)
  • MINIMUM ------ Range
  • MAXIMUM
  • MEAN ------- Central Tendency
  • MEDIAN
  • (MODE)
  • SKEWNESS ------- Distribution Shape
  • KURTOSIS

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Formula for variance, standard deviation
  • s2 v?(Xi - MX)2 /N

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Boxplot
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EXAMINE contd
20
Modifying Variables and Creating Scales - Compute
/ Recode
21
Modifying Variables and Creating Scales - Recode
/ Compute - (Labels, Missing Values)
22
Research Methods 34.616Statistical
Methods/SPSSLecture 2Bivariate Relationship
Analysis and Correlation
23
Choosing the Right Statistics/Methods I.
Exploring Relationships Between Multiple
Variables
  • 1. Correlation
  • a. Biavarite relationships (ordinal data) -
    Assess strength of association.
  • b. Continuous variable and ordinal categorical
    variable statistics.
  • 2. Partial Correlation
  • a. Use a second continuous to control for the
    effects of the first in a bivariate relationship
    (ordinal data).
  • 3. Multiple Regression
  • a. Explore the association of one or more
    continuous (ordinal) variable on a third variable
    - the dependent variable (also a continuous
    variable). The technique apportions relative
    strength of association among variables.
  • b. A variant is logistic multiple regression,
    where the dependent variable may be dichotomous
    (case/ non-case).
  • 4. Factor Analysis
  • Data reduction technique find a small set of
    primary directions of variability among a large
    set of interrelated variables. Used for creating
    scales based on multiple variables.
  • 5. Categorical variables (non-ordinal)
  • For categorical variables (no clear ordering or
    interval relationship between categories), use
    the Chi-square or Kappa statistic.

24
Choosing the Right Statistics/Methods I.
Exploring Differences Between Groups
  • 5. T-tests
  • Used to determine whether the mean values of an
    independent variable measured in two samples are
    statistically different from each other, based on
    parameters of each sample distribution.
  • 6. One-way Analysis of Variance
  • Used to determine whether the mean values of a
    continuous independent variable measured in many
    samples are statistically different from each
    other. Determines how much of the variation in
    the samples is within the compared groups and how
    much is between the groups.
  • 7. Two -way Analysis of Variance
  • Used to determine whether the mean values of a
    continuous independent variable measured in
    multiple samples, different on two dimensions,
    are statistically different from each other.
    Determines how much of the variation in the
    samples is within the compared groups and how
    much is between the groups. It can be used to
    determine whether the association between the
    independent variable and the first co-variate
    depends on the level of the second co-variate
    an Interaction Effect.

25
Boxplots Two-variables
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Examples of correlations
  • 3.2c and 3.2e represent perfect correlation,
    the maximum degree of linear correlation,
    positive or negative, that could possibly exist
    between two variables.

28
Examples of correlation coefficients
29
Calculating the correlation coefficient r
SCXY / v SSX x SSY
30
Calculating the correlation coefficient
  • Pair a b c d e f
  • Xi 1 2 3 4 5 6
  • Yi 6 2 4 10 12 8
  • Xi2 1 4 9 16 25 36
  • Yi2 36 4 16 100 144 64
  • XiYi 6 4 12 40 60 48
  • For any particular item in a set of measures of
    the variable Y,deviateYYi-MeanY
  • Similarly, calculate the deviate for X

31
Calculating the correlation coefficient
  • SSX 17.5,
  • SSY 70.0, and SCXY 23.0 you can then easily
    calculate the correlation coefficient as
  • r 23.0 / v17.5 x 70.0 0.66
  • r2 (0.66)2 0.44

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Matrix of Correlation coefficients
34
Research Methods 34.616Statistical
Methods/SPSSLecture 3Partial
CorrelationMultiple Regression and Factor
Analysis
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Partial Correlation
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From Correlation to Regression
40
Regression Coefficients
  • Slope
  • b SCXY/SSX23.0/17.5 1.31
  • Intercept
  • a MeanY - bMeanX 7.0 - 1.31(3.5) 2.4
  • the point at which the line crosses the Y?axis
    (the 'intercept')

41
Regression line (slope)
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Multiple Regression
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Multiple Regression - Stepwise
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Factor Analysis
47
Number of Factors Cut-off Suggestions
(eigenvaluesgt 1.0) / 4 factors
48
Oblique Factor Pattern (Often Varimax Method)
49
A Two-Factor solution (vs. 4 factors)
  • More factors explain more variance, but are more
    complex to theoretically interpret
  • - 4 Factors 68 of variance
  • - 2 Factors 40 of variance

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Asssessing Scale ReliabilityCronbacks Alpha
51
Asssessing Scale ReliabilityCronbacks Alpha
52
Research Methods 34.616Statistical
Methods/SPSSLecture 4Categorical Variable
Statistical Tests and T-Tests
53
CROSSTABULATIONS Investigating Data
54
Categorical Comparison Statistics
55
Investigating Data MEANS
  • Additional Commands
  • /CELLS(...Mean, Std. dev.) / STATs- ANOVA
  • /CROSSBREAK Variables... BY Variables... BY
    Variables...

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T-Test Significant Differences in Means
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T-test assessing significance
59
T-test Assessing significance a. Calculating
est. Std.dev M-M 1.19b. Calculating t
60
T-test assessing significance Sampling
Distribution of t for df 28
61
T-test Assessing significance
  • If our observed value of t had ended up smaller
    than 1.70, the result of the experiment would be
    non-significant vis-a-vis the conventional
    criterion that the mere-chance probability of a
    result must be equal to or less than .05.
  • If it had come out at precisely 1.70, we would
    conclude that the result is significant at the
    .05 level.
  • As it happens, the observed t meets and somewhat
    exceeds the 1.70 critical value, so we conclude
    that our result is significant somewhat beyond
    the .05 level.
  • If the observed t had been equal to or greater
    than 2.05, we would have been able to regard the
    result as significant at or beyond the .025 level

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Research Methods 34.616Statistical
Methods/SPSSLecture 5Analysis of Variance
(ANOVA)
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T-Test Significant Differences in Means
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Two-Way Analysis of Variance for Independent
Samples - Interaction Effects (no interaction)
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Two-Way Analysis of Variance for Independent
Samples - Interaction Effects (no interaction
- but, linear A B effects)
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Two-Way Analysis of Variance for Independent
Samples - Interaction Effects I (synergistic)
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Two-Way Analysis of Variance for Independent
Samples - Interaction Effects II (reversal)
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Dosage Level and Mean Pull
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