We will cover:
Types of
Statistics
Descriptive &
Graphical
Inferential
Variable
Relationships
Modeling a
Response
Factor
Analysis
Nonparametric
Methods
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Data Types
General speaking, statistical techniques are
determined by the type of data. A basic understanding about the data types is helpful for
choosing statistical procedures. In SPSS, a column is for a variable and a row is for a
case. There are, generally speaking, two major types of data:
 | Qualitative variables: The data values are
non-numeric categories.
Examples: Blood type, Gender.
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| Quantitative variables: The data values are
counts or numerical measurements. A quantitative variable can be either discrete such as #
of students receiving an 'A' in a class, or continuous such as GPA, salary and so on.
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Another way of classifying data is by the
measurement scales. In statistics, there are four generally used measurement scales:
| Nominal data: data values are non-numeric
group labels. For example, Gender variable can be defined as male = 0 and female =1.
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| Ordinal data (we sometimes call 'Discrete
Data'): data values are categorical and may be ranked in some numerically meaningful way.
For example, strongly disagree to strong agree may be defined as 1 to 5.
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| Continuous data:
 | Interval data : data values are ranged in a
real interval, which can be as large as from negative infinity to positive infinity. The
difference between two values are meaningful, however, the ratio of two interval data is
not meaningful. For example temperature, IQ. Today is 1.2 times hotter than yesterday is
not much useful nor meaningful.
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| Ratio data: Both difference and ratio of
two values are meaningful. For example, salary, weight.
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NOTE: The statistical procedures
mentioned below are demonstrated using movie clips in the Statistical
Procedures Page.
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In this on-line
workshop, you will find many movie clips. Each movie clip will demonstrate some specific
usage of SPSS.
Statistics can
be divided into these main areas:
| Descriptive statistics:
| Summary statistics:
 | mean |
| median |
| standard deviation |
| percentile |
| frequency |
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| Summary graphic tools
| pie charts |
| histograms |
| boxplots |
| scatterplots |
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| Inferential statistics: used to make comparisons between
two or more groups or study relationships
| Estimation |
| Confidence interval |
| Hypothesis testing |
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Descriptive and Graphical Analysis
| For nominal data: Frequency,
Crosstabs, bar charts and pie charts are common tools.
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| For ordinal data: Frequency,
Crosstabs, and descriptive statistics, bar charts, pie charts, stem-leaf plots are common
tools.
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| For continuous data: Descriptive
statistics, histograms, boxplots, and scatterplots for two variables are common tools.
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Inferential
Analysis
If you are interested in comparing
group effects.
| For Nominal or ordinal data: Use
crosstabs.
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| For continuous data:
| First, check to see if the variable
is normal. To check Normality, go to 'Analyze' then to 'Descriptive Statistics' then
choose 'Explore' procedure.
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| Second, if you compare two or more
groups, check the homogeneity of the variances among groups. To do so, you also use
the 'Explore' procedure.
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| For two group comparison, use
Independent t-test.
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| For three or more group comparison,
use one-way analysis of variance.
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| For two or more factors, use
multiway analysis of variance.
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| If there are factors and
covariates, use analysis of covariance.
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| If the same subject is measured
more than one time, it is a repeated measure problem.
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If you are
interested in the relationship between two
variables:
| For nominal data, use crosstabs,
and choose proper tests for nominal data.
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| For ordinal data, use crosstabs,
bivariate correlation such as Spearman correlation coefficient..
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| For continuous data, use bivariate
correlation such as Pearson correlation.
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If you are
interested in modeling a response (also called dependent
variable) using predictor variables (also called independent variables):
| For nominal data, if the response
is a binary variable (that is only two possible values such as graduate in four years or
not), then, use Logistic regression model. If the response has more than two
categories, use multinomial logistic regression.
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| For ordinal data, if the response
follows Poisson distribution, use Poisson regression model. In general, one can use
log-linear models for ordinal data.
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| For continuous response, check the
normality and homogeneity of variance, take appropriate data transformation as needed and
use regression model.
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If you are
interested in reducing the data dimension, a
typical procedure is the Factor Analysis.
Factor analysis combines similar
variables together into a dimension that can be interpreted from the qualitative aspects
of the study. In many survey studies, one may collect many variables. It is difficult to
understand the overall meaning of these variables. Factor analysis helps to combine
similar variables into the same dimension, and results to only a few dimensions (factors)
that are meaningful for explaining the problem.
| For example, in the technology
survey, we collect 16 variables related to the difficulty faced by faculty when using
classroom technology. Using Factor Analysis, we are able to combine these 16 different
types of difficulties into four general groups of difficulty (factors). These are
difficulties related to:
(1) Computer hardware and software,
(2) Media technology,
(3) Instructor's technology need in office, and
(4) Classroom instructional technology need.
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Nonparametric Methods are another alternative:
If assumptions are violated for the
statistical procedure that is chosen, there are many nonparametric statistical procedures
that can do similar analysis that are less sensitive to the assumptions. The corresponding
nonparametric procedures in SPSS include:
| Chi-square
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| Two Independent Samples Comparison:
The similar parametric procedure is independent t-test.
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| K Independent Samples Comparison :
The similar parametric procedure is Analysis of Variance.
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| Two Related Samples: The similar
parametric procedure is the paired t-test.
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| K Related Samples: The similar
parametric procedure is the Repeated Measure Analysis.
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To perform nonparametric statistical
procedure in SPSS,
Go to 'Analyze', go down to
'Nonparametric Tests', then select the appropriate nonparametric procedure.
There are many more statistical procedures in SPSS. For
example, Multivariate procedures, Survival Analysis, Discriminant Analysis, and so on. We
are not able to cover all of these procedures in this workshop. The bottom line is, when
you have questions about your design and analysis, contact a statistical consultant for
help.