2. Creation & Description of a Data Set
Four Levels of Measurement
• Nominal, ordinal, interval, ratio
Variable Types
• Independent Variables (IV), Dependent Variables (DV)
• Moderator variables
• Discrete Variables
• Finite answers, limited by measurement e.g. test scores,
• Continuous variables
• All values possible (GPA not exceed 5.0)
• Dichotomous variable
• Only 2 values, yes or no, male or female
• Binary variable
• Assign a 0 (yes) or 1 (no) to indicate presence or absence of something
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3. Categories of Analysis
Number of Variables Analyzed
Univariate analyses
Examine the distribution of value
categories (nominal/ordinal) or values
(interval or ratio)
Bivariate analyses
Examine the relationship between two
variables
Multivariate analyses
Simultaneously examine the relationship
among three or more variables
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4. Purpose of Analysis
Descriptive
Summaries of population studied
(parameters)
Preliminary to further analysis
Inferential
Used with sample from total
population and how well can results
be generalized to total population
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5. Parametric vs. Non-Parametric
Parametric Tests require:
One variable (usually the DV) is at the interval or
ratio level of measurement
DV is normally distributed in the population;
independent samples should have equal or near
equal variances
Cases selected independently (random selection or
random assignment)
Robustness how many and which assumptions
above can be violated without affecting the result
(delineated in advanced texts).
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6. Parametric vs. Non-Parametric
Nonparametric Tests involve nominal or ordinal level
data when:
Samples complied form different populations and
we want to compare the distribution of a single
variable within each of them
Variables are nominal or can only be rank
ordered
Very small samples: e.g. only 6 or 7 are available
Statistical power is low, increases with sample
size (as with parametric tests)
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7. Creation & Description of a Data Set
Frequency Distributions:
An array is an arrangement of data from smallest to
highest
Absolute/simple frequency distribution displays
number of times a value occurs (all levels of
measurement)
Cumulative frequency distribution adds cases
together so that it last number in distribution is the
total number of cases observed
Percentage distribution adds the percent of
occurrence in the table
Cumulative Percentage
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8. Example of an Array
Initial Age Frequency
Cumulative
Frequency %
Cumulative
%
A + T 21 2 2 10 10
B+G+C 26 3 5 15 25
R+W+S 27 3 8 15 40
K+V+R+
D
31 4 12 20 60
Q+F 32 2 14 10 70
S+O+P 37 3 17 10 95
M+A 49 2 19 10 95
B 69 1 20 5 100
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9. Graphical Representations
Bar Graph/Histogram (bars touch)
Line Graph/Frequency Polygon
Pie Chart
Keep graphs simple.
Limit to salient information info.
Collapse categories/distributions when
possible.
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10. Measures of Central Tendency
Typical representation of data, e.g. find a number
or groups of numbers that is most representative
of a dataset. The three types include:
Mode
Values within a dataset that occur most frequently, if two occur
equally then bimodal distribution, etc.
Median
The value in the exact middle of a linear array, mean between
2 values if even number of values.
Mean: arithmetic mean
Trimmed mean (outliers removed) minimize effect of extreme
outliers
Weighted mean: compute an average for values that are not
equally weighted (proportionate / disproportionate sampling)
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11. Measures of Central Tendency
Variability/Dispersion
Nominal or Ordinal use a frequency distribution
or graph (bar chart)
Interval or ratio use range
Range = maximum value – minimum value +1
Informs about the number of values that exist
between the ends of the distribution e.g. 31 to 46 --
there are potentially 16 values possible. The larger
the range, the greater the variability. However,
outliers make the range misleading. Therefore use
median, or mean and standard deviation whenever
possible for interval & ratio data.
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12. Errors
Our Decision
Real World Reject Null (-1)
Does work =
difference
Accept Null (1)
Doesn’t work =
no difference
Null Hypothesis
False (-1) Does
work =
difference
No Error (+1) Type II (-1)
Null Hypothesis
True (+1) Does
n’t work = no
difference
Type I (-1) No Error (+1)
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13. Errors (continued)
The smaller the p value, the less likelihood
of committing a type I, the greater the p
value, the greater the chance of a type II
error. p values range from 0 (total
significance) to 1.0 (least significance).
Generally p values less than .05 are
considered significant, while those more
than .05 are not.
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14. How to Select a Statistical Test
Sampling Method Used
How was the sample selected?
What is the size of the sample?
Were the samples related?
Was probability sampling used?
What type of variables were used
Variable Distribution among Population
Evenly distributed?
Judgment call
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15. How to Select a Statistical Test
Level of Measurement of the
Independent & Dependent Variables
Inclusionary/ exclusionary criteria
(screening mechanisms)
Variable measurement levels (nominal,
ordinal, etc.)
Measurement precision (best measurement
level used). Use of low level measurement
reduces the availability of stronger
statistical techniques.
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16. How to Select a Statistical Test
Statistical Power (Reduction in Type II error)
True relationship between variables is strong not weak
Variability of variables is small rather than large
A higher p value is used (e.g. .1 vs .05) thereby increases
risk of Type I error
Directional hypothesis used (one tailed)
Large sample versus a small sample (power analysis)
Cost effective sample just right for analysis
Avoid too small a sample since even if the IV is
effective, it would not yield a statistically significant
relationship
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17. Introduction to SPSS
Originally it was an acronym of Statistical
Package for the Social Science but now it
stands for Statistical Product and Service
Solutions
SPSS is one of the most popular statistical
packages which can perform highly complex
data manipulation and analysis with simple
instructions
17
18. How to Open SPSS
Go to START
Click on PROGRAMS
Click on SPSS INC
Click on SPSS 19 or 20
18
19. Basic Structure of SPSS
There are two different windows in SPSS
1st
– Data Editor Window - shows data in
two forms
Data view
Variable view
2nd
– Output viewer Window – shows
results of data analysis
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20. Data View vs. Variable View
Data view
Rows are cases
Columns are variables
Variable view
Rows define the variables
Name, Type, Width, Decimals, Label, Missing,
etc.
Scale – age, weight, income
Nominal – categories that cannot be ranked
(ID number)
Ordinal – categories that can be ranked (level
of satisfaction)
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21. Videos about Statistics and SPSS
The Basics: Descriptive and Inferential Statistics – 2.51 minutes:
http://www.youtube.com/watch?v=oHGr0M3TIcA
SPSS Video Tutor – 11.20 minutes:
http://blip.tv/spssvideotutor/spss-video-tutorial-introduction-to-spss-4014884
Intro to SPSS – 9.57 minutes:
http://www.youtube.com/watch?v=eTHvlEzS7qQ
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