Appendix I

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Appendix I A Refresher on some Statistical Terms
and Tests
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Chapter Objectives

• Provide a refresher of some statistical terms
  and tests
• Explain what types of analysis are appropriate,
  under what conditions and for what objectives
• Give examples of SPSS computer output
• Explain descriptive statistics, including
  frequencies, means, standard deviations, and
  variance
• Present a process for statistical hypothesis
  testing using a computer package
• Demonstrate how inferential statistics can be
  used to test hypotheses

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Statistics

• Descriptive Statistics
• Help to describe the phenomena of interest
• Inferential Statistics
• Help to draw conclusions from the analysis of
  data
• Parametric
• Assumes sample drawn from normal population
• Non-parametric
• Assumes sample drawn from a non-normal population

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Properties of the Four Measurement Scales
Note The interval scale has 1 as an arbitrary
starting point. The ratio scale has the natural
origin 0, which is meaningful.
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Sample Questionnaire for Data Analysis
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Variable Names, Labels and Values for Sample Data
Set
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Example of SPSS Data Editor Input Data Data View
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Example of SPSS Data Editor Input Data Variable
View
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Descriptive Statistics

• Frequencies
• Measures of central tendencies
• mean, median, mode
• Measures of dispersion
• range, variance, standard deviation
• other measures
• standard error of the mean

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Example Responses to the statement Statistics
is interesting
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The Mean
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Range

• Represents the difference between the highest
  and lowest values of a variable of interest.
• Eg, max 50, min 30, range 20

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Variance Formula

• Note This formula is correct. The formula in
  the book is incorrect

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Area under the Normal Curve
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Box and Whisker Plots
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Normal, Skewed and Sampling Distributions
Source Adapted from Zikmund (2000381).
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Standard Error of the Mean

• When a number of samples are taken from the
  population, the sample means form a distribution
• The standard deviation of these sample means is
  called the standard error of the mean
• As the sample size increases, the standard error
  gets smaller

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Standard Error of the Mean - Formula
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Example of SPSS output of Descriptive Statistics
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Inferential Statistics

• Helps to draw inferences or conclusions from the
  analysis of the data, such as
• The relationships between two variables
• Differences in variables among different
  subgroups
• How several independent variables might explain
  the variance in an independent variable

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Inferential Statistics

• Statistical hypothesis testing
• The null and alternate hypotheses
• Choosing a statistical test
• Significance level
• Correlations

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Process for Statistical Hypothesis Testing using
a Computer
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The null and alternate hypotheses

• Null hypothesis
• the conjecture that postulates no differences or
  no relationship between or among variables
• Alternate hypothesis
• an educated conjecture that sets the parameters
  one expects to find

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Choosing a Statistical Test

• Parametric tests can be applied to interval and
  ratio data (and also ordinal data where they are
  expressed in numeric form and interval features
  are present).
• Non-parametric tests are applied to categorical
  data ie, nominal and most ordinal data

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Classification of Statistical Tests
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Significance level

• the probability of rejecting the null hypothesis
  when it is true
• also called the critical value
• the probability of this occurring is called a
  (alpha)
• Significance level 1 confidence level
• Eg significance level a 0.05, indicates
  confidence level 0.95 (or 95)

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Hypothesis Testing and Statistical Decision Making
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Relationship between Type I and II Errors
Source D. A. Aaker, V. Kumar and G. S. Day 1995,
Marketing Research, 5th edition. New York John
Wiley Sons, p. 473
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Pearson Correlation

• indicates the direction, strength and
  significance of the bivariate relationships
  between interval or ratio variables, eg
• HO Role overload and performance are not related
  to each other. r 0
• HA the two are significantly negatively
  correlated. r lt 0
• r -0.1735 p 0.083
• r -0.29 p 0.054
• r -0.33 p 0.049

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Scatter Diagrams of two Variables with different
Correlation Coefficients
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Procedure for Chi-square Test with SPSS

• Step 1 Formulating the hypotheses
• Step 2 Decision criterion
• Step 3 Analyse data with computer package
• Step 4 Make a statistical decision
• Step 5 Interpret the decision

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Example of SPSS Output for Crosstabs and
Chi-square tests36
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Example of SPSS Output for Crosstabs and
Chi-square tests36 (cont)
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t distribution

• is suitable for analysing the means of small
  samples
• drawn from a population that is normally
  distributed
• shape of the t distribution depends on the
  degrees of freedom (df )

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t distribution formula
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Comparison of t distribution normal curve
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Example of SPSS output for single sample tests
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Example of SPSS output for two independent
samples t-tests
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Example of SPSS output for one-way between groups
ANOVA
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Regression Analysis

• Explains the variance in the dependent variable
  by a set of predictors
• R-square (R2) is the explained variance
• Step-wise regression will indicate the order of
  importance of the significant preditors in the
  regression model
• The Beta weight of the predictors and their
  significance indicates the weight each predictor
  (independent variable) exerts in explaining the
  variance in the dependent variable.

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A Simple Regression Model
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General Form of Simple Regression Line

• Y a bX
• where
• Y is the dependent variable
• X is the independent variable
• a is the intercept of the regression line on the
  Y (vertical) axis
• b is the slope of the regression line

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Assumptions of Regression Analysis
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Example of SPSS output for simple regression
analysis
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Example of SPSS output for simple regression
analysis (cont.)
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Factor Analysis

• helps to reduce a vast number of variables (for
  example all the questions tapping several
  variables of interest in a questionnaire) to a
  meaningful, interpretable and manageable set of
  factors

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Output of a Factor Analysis for the Evaluation
Questionnaire
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Items under each Factor for the Evaluation
Questionnaire
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Items under each Factor for the Evaluation
Questionnaire (cont.)
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Multivariate Analysis

• examines several variables and their
  relationships simultaneously
• Multivariate techniques include
• MANOVA
• Discriminant analysis
• Canonical correlation
• Factor analysis
• Cluster analysis
• Multidimensional analysis

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