Statistical Analysis and InterpretationConcepts and VariablesDescriptive StatisticsMeasuring RelationshipsSignificance of DifferencesStatistical Software Demonstration

Dave E. Marcial, Ph.D.

Why you need to use

statistics in your

research?

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.

- 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.

What is statistics?is the systematic

collection and analysis of numerical data

in order to investigate or discover relationships

among phenomena

so as to explain, predict and

control their occurrence.

Objectives

To summarize and describe sets of observations

DescriptiveTo make an inference (determine significant differences, relationships between sets of observations)

InferentialArtificial classification of sets of observations

Exploratory

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.

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

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.

Levels of MeasurementNominal

-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

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

Important items to consider in choosing a particular analysis

· The type of data set ÞDiscrete Data (counts, ranks)

Non-Parametric Tests

ÞContinuous Data (ratio, interval)Parametric Tests

Important items to consider in choosing a particular analysis

· Number of VariablesThere are different tests for 2 variables and > 2 variables

Important items to consider in choosing a particular analysis

· The population where the samples were takenÞDependent Population

data of variables to be compared were taken from the same population (e.g. before and after experiment measurements)

ÞIndependent Populationdata of variables to be compared were taken from two

separate and distinct population

Important items to consider in choosing a particular analysis

· The population where the samples were takenÞDependent Population

data of variables to be compared were taken from the same population (e.g. before and after experiment measurements)

ÞIndependent Populationdata of variables to be compared were taken from two

separate and distinct population

Structure of Statistical Analysis

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

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”)

Structure of Statistical Analysis

Inferential Statistics·Significant relationships are determined by rejecting the null hypothesis and accepting the alternative hypothesis

ÞHo: Variable A = Variable B

ÞH1: Variable A = Variable B

Structure of Statistical Analysis

Inferential Statistics·Null hypothesis are rejected if:

Þ computed statistics is greater than the table (critical) value at a

(for manual computation)

Þ probability value is less than a

(computer generated)

a is the confidence level (usually set at 95% or 0.05)

Structure of Statistical Analysis

Structure of Statistical AnalysisInferential Statistics

·Comparing Frequency Tables

ÞObserved Frequency Table vs Theoretical Distribution

Chi Square Test (X2): Goodness of Fit Test

Þ2 or more Observed Frequency Tables

Chi Square Test (X2): Contingency Table

Chi Square Test for Independence

Structure of Statistical Analysis

Structure of Statistical AnalysisInferential Statistics

·Relationship between two variables

ÞContinuous Data

Pearson Product Moment Correlation (r)

Scatter plotÞRank 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 relationship is inversely

proportional

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.

Structure of Statistical Analysis

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

Þ In principle, the regression analysis can only predict values with the range of the values of the samples used in the correlation.

Structure of Statistical Analysis

Structure of Statistical Analysis

Structure of Statistical Analysis

Independent - Correlated

Structure of Statistical Analysis

Structure of Statistical Analysis

Structure of Statistical Analysis

Exploratory StatisticsCluster AnalysisÞCluster Analysis develops artificial groupings based on an index of dissimilarity generated from the occurrence or weight of attributes in the variables being studied.

Structure of Statistical Analysis

Exploratory StatisticsCluster AnalysisÞCluster Analysis develops artificial groupings based on an index of dissimilarity generated from the occurrence or weight of attributes in the variables being studied.

Structure of Statistical Analysis

Exploratory StatisticsCluster AnalysisÞCluster Analysis develops artificial groupings based on an index of dissimilarity generated from the occurrence or weight of attributes in the variables being studied.

Structure of Statistical Analysis

Use of Statistical Package for Social Science

e-Statistical Tool (open source)

e-Statistical Tool (open source)

e-Statistical Tool (free)

e-Statistical Tool (proprietary)

e-Statistical Tool (proprietary)

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

SPSS Demonstration

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

Demonstration(Measuring Dependency of Two

Variables from Categorized Data)Online Chi-Square Calculator

• Sample Data:

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/index.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