Concepts and Variables, Descriptive Statistics, Measuring Relationships, Significance of Differences, Statistical Software Demonstration

1. Statistical Analysis and
Interpretation
Concepts and Variables
Descriptive Statistics
Measuring Relationships
Significance of Differences
Statistical Software Demonstration

2. Why you
need to use
statistics
in your
research?

3. Why you need to use statistics
in your research?
 measure things;
 examine relationships;
 make predictions;
 test hypotheses;
 construct concepts and
develop theories;
 explore issues;
 explain activities or
attitudes;
 describe what is happening;
 present information;
 make comparisons to find
similarities and differences;
 draw conclusions about
populations based only on
sample results.

4. - is a range of procedures for gathering,
organizing, analyzing and presenting
quantitative
What is statistics?
‘Data’ is the term for
facts that have been
obtained and
subsequently
recorded, and, for
statisticians, ‘data’
usually refers to
quantitative data that
are numbers
a scientific approach to
analyzing numerical
data.
in order to enable us to
maximize our
interpretation,
understanding and use
data.

5. What is statistics?
is the systematic
collection and analysis
of numerical data

6. Objectives
To
summarize
and describe
sets of
observations
Descriptive
To make an
inference
(determine
significant
differences,
relationships
between sets
of
observations)
Inferential
Artificial
classification
of sets of
observations
Exploratory

7. Variables
–Ex:
• Sex
(male, female);
• marital status
(single,
married,
divorced,
widowed)
is a concept that
can take two or
more values
is the thing that
is measured or
counted; the
thing of interest.

8. Variables
Independent Variables
* causes changes in
another
Dependent Variables
* a variable that is
affected or explained
by another variable
Ex:
• “family status and
scholastic
achievement”
• Independent: family
status
• Dependent: scholastic

9. Variables
Discrete
* measurement uses
whole units or
numbers, with no
possible values
between adjacent
units
* counted not
measured
Ex: family size: 2, 4, 7
Continuous
* are measured, not
counted
* measurement uses
smaller increments of
units
Ex: height, distance,
time, age,
temperature etc
if sample size is < 40,
the data set is not
normally distributed
(non-parametric test)
has the tendency to
assume a normal
distribution
(parametric tests)
The type of data set is one of
the determinants in choosing
the appropriate analysis.

10. Levels of Measurement
Nominal
-Male / female
-Black / white
-Young / old
-Single / married /
widowed
-Nationality
-Type of shoes
-Skin color
-Type of music
Ordinal
-Status (low,
middle, high)
-Size (smallest,
small, big, biggest)
-Quality (poor,
good, very good,
excellent)
Interval
-Degrees of
temperature
-Calendar
time
-Attitude
scales
-IQ scores
Ratio
-Interval level
with 0
-Number of
family members
-Weight
-Length
-Distance
-Number of
books

11. Important items to consider in
choosing a particular analysis
 The problem or the specific objective
If the problem requires for the data to be
summarized and described
If the problem requires for an inference to
be made
If the problem requires for data to be
classified or pattern determined
Descriptive
Statistics
Inferential
Statistics
Exploratory
Statistics

12. Important items to consider in
choosing a particular analysis
 The type of data set
Discrete Data (counts, ranks)
Non-Parametric Tests
Continuous Data (ratio, interval)
Parametric Tests

13. Important items to consider in
choosing a particular analysis
 Number of Variables
There are different tests for 2 variables and > 2 variables

14. Important items to consider in
choosing a particular analysis
 The population where the samples were
taken
Dependent Population
data of variables to be compared were taken from the same
population (e.g. before and after experiment measurements)
Independent Population
data of variables to be compared were taken from two separate
and distinct population

15. Important items to consider in
choosing a particular analysis
 The population where the samples were
taken
Dependent Population
data of variables to be compared were taken from the same
population (e.g. before and after experiment measurements)
Independent Population
data of variables to be compared were taken from two separate
and distinct population

16. Structure of Statistical Analysis

17. Structure of Statistical Analysis
Descriptive Statistics
• Summarizing Data
• Frequency (For discrete data
sets usually but there are also
instances wherein continuous
data sets are summarized into
frequency tables)
• Central Tendencies
• Mean
• Median
• Mode

18. Structure of Statistical Analysis
Descriptive Statistics
• Summarizing Data
• Measures of Dispersion
(variations among the
data)
• Range (minimum
and maximum
values)
• Standard Deviation
(measure of
precision: “how close
are your
measurements”)
• Confidence Interval
(measure of accuracy:
“how close are you to
the true value”)

19. Structure of Statistical Analysis
Inferential Statistics
Significant relationships
are determined by rejecting
the null hypothesis and
accepting the alternative
hypothesis
Ho: Variable A =
Variable B
H1: Variable A =
Variable B

20. Structure of Statistical Analysis
Inferential Statistics
Null hypothesis are
rejected if:
computed statistics is
greater than the table
(critical) value at a
(for manual
computation)
probability value is less
than a
(computer generated)
a is the confidence level
(usually set at 95% or 0.05)

21. Structure of Statistical Analysis

22. Structure of Statistical Analysis
Inferential Statistics
Comparing Frequency
Tables
Observed Frequency
Table vs Theoretical
Distribution
Chi Square Test (X2):
Goodness of Fit Test
2 or more Observed
Frequency Tables
Chi Square Test (X2):
Contingency Table
Chi Square Test for
Independence

23. Structure of Statistical Analysis

24. Structure of Statistical Analysis
Inferential Statistics
Relationship between two
variables
Continuous Data
Pearson Product Moment
Correlation (r)
Scatter plot
Rank Data Set
Spearman Rank Correlation (r)
If r approaches 1 : the
relationship is directly
proportional
If r approaches 0 : there is no
relationship
If r approaches -1: the
The Spearman rank-order correlation is used when
both variables are at least ordinal scales of
measurement, but one is not sure that both would
qualify as interval or ratio scales of measurement.
Remember that a Pearson product-moment
correlation is an index of the degree
of linear relationship between two variables.
That is, the correlation gives an indication of how
closely the points in a scatter plot cluster around
a straight line. But the relationship between two
variables is not always linear.

25. Structure of Statistical Analysis

26. Structure of Statistical Analysis
Inferential Statistics
 To predict values for Y variable given a value for X variable
Regression analysis
For a simple linear regression (y = a + bX), the analysis will determine the a and b values in
the equation
In principle, the regression analysis can only predict values with the range of the values
of the samples used in the correlation.

27. Structure of Statistical Analysis

28. Structure of Statistical Analysis

29. Structure of Statistical Analysis
Independent - Correlated

30. Structure of Statistical Analysis

31. Structure of Statistical Analysis

32. Structure of Statistical Analysis
Exploratory Statistics
Cluster Analysis
Cluster Analysis develops artificial groupings based on an
index of dissimilarity generated from the occurrence or
weight of attributes in the variables being studied.

33. Structure of Statistical Analysis
Exploratory Statistics
Cluster Analysis
Cluster Analysis develops artificial groupings based on an
index of dissimilarity generated from the occurrence or
weight of attributes in the variables being studied.

34. Structure of Statistical Analysis
Exploratory Statistics
Cluster Analysis
Cluster Analysis develops artificial groupings based on an
index of dissimilarity generated from the occurrence or
weight of attributes in the variables being studied.

35. Structure of
Statistical
Analysis

36. Use of Statistical Package for
Social Science

37. e-Statistical Tool (open source)

38. e-Statistical Tool (open source)

39. e-Statistical Tool (free)

40. e-Statistical Tool (proprietary)

41. e-Statistical Tool (proprietary)

42. SPSS Demonstration
• Basic Descriptive Statistics
– Descriptive Statistics for Categorical Data
– Doing a Cross-Tabulation
– Descriptive Statistics for Score Data
• Pearson Product-Moment Correlation
• Spearman Rank-Order Correlation
• Linear Regression
• Reliability
– Test-Retest or Interrater Reliability Analyses
– Internal Consistency Reliability

43. SPSS Demonstration
• Independent Samples t-Test
• Correlated Samples t-Test
• One-Way ANOVA
• Chi Square Goodness-of-Fit Test
• Chi Square Test for Independence

44. Demonstration
(Measuring Dependency of Two
Variables from Categorized Data)
Online Chi-Square Calculator

45. • Sample Data:

46. References
• De Leon, R.O. Introduction to Statistics. Slides Presentation. Silliman
University
• http://www.mheducation.co.uk/openup/chapters/9780335227242.
pdf
• Calderon, J. F. and Gonzales, E. C. (1993). Methods of Research and
Thesis Writing
• http://wps.prenhall.com/hss_salkind_exploring_5/4/1035/265001.cw/ind
ex.html
• http://experientia.com/services/understanding/ethonographic-
research/
• The Role and Importance of Research.
http://wps.prenhall.com/hss_salkind_exploring_5/4/1035/265001.
cw/index.html
• The Foundations of Research.
http://www.socialresearchmethods.net/kb/intres.php