The document outlines various statistical techniques used for data analysis, including descriptive and inferential statistics, central tendency measures (mean, median, mode), data variability, and normality tests. It discusses advanced methods such as correlation, regression, factor analysis, and ANOVA, providing insights on how to choose appropriate statistical methods based on data characteristics. Additionally, it emphasizes the importance of hypothesis testing and the role of statistical software in analyzing results.

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Bodhiya Wijaya Mulya, S.Sos., M.M.
Research aims to discover phenomenon that we
assume actually exist
Whatever the phenomenon we desire to explain, we
collect data from the real world to test our hypotheses
about the phenomenon
Hypotheses testing must involve statistical technique

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Descriptive
Statistics
Inferential
Statistics
• collecting
• organizing
• Summarizing
• presenting data
• making inferences
• hypothesis testing
• determining
relationships
• making predictions
Statistical
Techniques

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Statistic that describe numerical data
Frequency Distribution
Central Tendency
Variation
Data Shape
 Easiest way to describe numerical data
 Can present in table or graph
Poor
Below Average
Average
Above Average
Excellent
2
3
5
9
1
Total 20
Rating Frequency
PoorPoor Below
Average
Below
Average
AverageAverageAbove
Average
Above
Average
ExcellentExcellent
FrequencyFrequency
RatingRating
11
22
33
44
55
66
77
88
99
1010
Toyota Quality Ratings

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Mode:
 The most common or frequently occurring number
 Can be used with nominal, ordinal, interval and
ratio
Median:
 The middle point of data. Also known as 50th
Percentile or Second Quartile
 Can be used with ordinal, interval, and ratio
Mean:
 Arithmetic average
 The most widely used measure of central tendency
 Can be used with interval and ratio

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Measuring how data spread and vary
Range
 Substraction between Maximum Value with Minimun
Value
 Easiest way to measure variability
 Very sensitive with outlier
Percentile
 Divided data into 10 part
 Tell us the score at a specific position within
distribution
 Calculation of percentile is similar with median

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Standard Deviation
 Gives “average distance” between all data and the
mean
 The most comprehensive and widely used
 Can be used only with interval/ratio data
 Tell us the score at a specific position within
distribution
Skewness
Kurtosis

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An important measure of the shape of a distribution
Pearson coefficient of Skewness (sk)
sk = 3(Mean-Median)
Standard Dev.
Symmetric:
 The mean and median are equal and the data values are evenly spread around
these values
 Value of Pearson skewness is zero
 Value in software skewness is near zero
Right-SkewedLeft-Skewed Symmetric
Mean = Median = ModeMean Median Mode Mode Median Mean

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Positive/Right Skewed:
 Mean will usually be more than the median Value of Pearson
skewness 0 < sk < 3
 Value in software skewness is positive
Right-SkewedLeft-Skewed Symmetric
Mean = Median = ModeMean Median Mode Mode Median Mean
Negative/Left Skewed:
 Median will usually be more than the mean
 Value of Pearson skewness -3 < sk < 0
 Value in software skewness is negative
Right-SkewedLeft-Skewed Symmetric
Mean = Median = ModeMean Median Mode Mode Median Mean

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Measure provides information about the peakedness
of the distribution
Zero or near zero kurtosis values indicate that the
distribution is normal
Sometimes it’s called mesokurtic

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Positive kurtosis values indicate that the distribution is
rather peaked because many cases clustered in the
centre)
Sometimes it’s called leptokurtic
Negative kurtosis values indicate that the distribution
is a distribution that is relatively flat because too many
cases in the extremes)
Sometimes it’s called platykurtic

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In large sample skewness and kurtosis could be
inaccurate
inspecting the shape of the distribution using a
histogram
Introduction to Social Science Statistics
Normality tests are used to determine if a data set is
well-modeled by a normal distribution
Normality test help us to determine what statistics
technique we should use
Most of Inferential technique require normal
distribution
Introduction to Social Science Statistics

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Test of Relationship
Test of Difference

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Correlation
 Pearson or Spearman Correlation can be used to explore the
strength of relationship between two continuous variable
 Pearson for normal distribution, while Spearman for not
 This test will give us direction and strength of relationship
 Positive correlations: If one variable increase, the other
would also increase
 Negative correlations: If one variable increase, the other
would decrease
Correlation
 Lind, Marchal, and Wathen (2012, p. 465)
0 = No Correlation
0,10 – 0,49 = Weak Correlation
0,5 = Medium Correlation
0,51 – 0,99 = Strong Correlation
1 = Perfect Correlation

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Correlation
 Cohen (1988, p. 79-81) in Pallant (2007, p. 132)
0.10 – 0.29 = Weak Correlation
0,30 – 0,49 = Medium Correlation
0,50 – 1 = Strong Corellation
Partial Correlation
 Extension of Correlation that allows us to control another
variable
 This test allows us to get more accurate picture about
relationship between two variable

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Simple/Multiple Regression
 Sophisticated extension of correlation
 These test is used when we want to predict ability of a set of
independent variable(s) on one continuous dependent
variable
Logistic Regression
 Similar with multiple regression but use categorical dependent
variable
 Dependent variable better to be dichotomous
 It doesn’t have the requirements of the independent
variables to be normally distributed, linearly related, nor
equal variance within each group
 Minimum 50 sample per one independent variable

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Factor Analysis
 Not designed to test hypotheses
 This teqhnique is used extensively by researcher to develop
and evaluate test or scales
 Reduce and refine large number of question items into
smaller and more manageable
 Example:What is the factor that makes people religious
Discriminant Analysis
 Explore predictive ability of a set of independent variables
on one categorical dependent variable
 Used to differentiate group based on several
predictors/Independent variables
 Can have more than two groups on dependent variable
 Example: Differentiate student failure/passed/standout
based on Mid-Exam and Paper score

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Canonical Correlation
 This test is used when we want to analyze two sets of
variable
 Usually used for exploratory research
 Example: a set of variables measuring medical compliance
(willingness to buy drugs, to make return office visits, to use
drugs, to restrict activity) and a set of demographic
characteristics (educational level, religious affiliation,
income, medical insurance)
Structural Equation Modeling
 Very sophisticated technique
 Combine multiple regression with factor analysis
 Evaluate model fit with our data

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T-Test
 Test to comparing mean score difference between two
group
 Consist of Independent, Paired, and One-sample with
different situation
Mann-Whitney U Test and Wilcoxon Signed Rank Test
 Non-parametric version of T-Test
One Way Analysis of Variance (One Way ANOVA)
 Test to comparing mean score difference between two or
more group
 In ANOVA, independent variable is “group” and dependent
variable is score
 Can be used for same group or different group
Kruskal-Wallis Test and Friedman Test
 Non-parametric version of One Way ANOVA

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Two Way Analysis of Variance (Two Way ANOVA)
 Test to comparing mean score difference from two
independent variables (group)
 Independent variables are categorical such as comparing
GPA between student enrollment group and gender
 Can be used for same group or different group
Multivariate Analysis of Variance (MANOVA)
 Test to comparing mean score difference with several
dependent variables
 Can be one way or two way
 Example: Comparing leadership skills and GPA based on
Religion and Gender of student

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Analysis of Covariance (ANCOVA)
 Test to comparing mean score difference with “controlled”
covariate variable to minimize error
 Similar with partial correlation
 Can be one way, two way, or multivariate
 Example: Comparing leadership skills based on gender
with controlled GPA
Research questions that you want to address
Find the questionnaire items and scales that you will
use to address these questions
Identify the nature of each of your variables
Draw diagram for each of your research questions (if
Possible)
Decide wheter a parametric or a non-parametric
statistical technique is appropriate

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 Field, A. (2009). Discovering statistics using SPSS (3rd ed.). London: Sage Publications
Ltd.
 Lind, D.A., Marchal,W.G., and Wathen, S.A. (2012). Statistical techniques in business
and economics. New York: McGraw-Hill.
 Pallant, J. (2007). SPSS survival manual. Berkshire: McGraw-Hill Open University
Press.
 Tabachnick, B.G. and Fidell, L.S. (2013). Using Multivariate Statistics (6th ed.). Boston:
Pearson Education.