Level of Measurement, Frequency Distribution,Stem & Leaf
“MULTIVARIATE DATA ANALYSIS”
1- Faiza Batool
2- Faisal Hafeez
LIST OF TOPICS
1-Qualitative and Quantitative Data
2- Level of Measurement
4- Stem and Leaf Plot
5- SPSS demonstration and interpretation
6- What are Multivariate data analysis and multivariate technique?
7- Why the knowledge of level of measurement is important?
DATA is a collection of facts and figures. It can be numbers,
words, measurements, observations or even just descriptions of
Qualitative data can be arranged into categories that are not
numerical. These categories can be physical traits, gender, colours or
anything that does not have a number associated to it.
Example: case studies and interviews. They provide a more in
depth and rich description.
The term quantitative data is used to describe a type of
information that can be counted or expressed numerically. This
type of data is often collected in experiments, manipulated and
Quantitative methods are those which focus on numbers and
frequencies rather than on meaning and experience.
These data may be represented by interval or ratio scales.
Examples of quantitative data are scores on achievement tests,
number of hours of study, or weight of a subject.
LEVEL OF MEASUREMENT
Scale Type Qualitative/quant
Nominal Qualitative Non-metric Gender, Nationality
Ordinal Qualitative Non-metric Class ranking
Interval Quantitative Metric Temperature, dress size
Ratio Quantitative Metric Age, Income, weight
A method of showing the number of occurrences of observational data
in order from least to greatest.
When a data set with a variable that has numerical values, to make a
frequency distribution or more likely, a histogram of the data from that
variable in order to explore the shape of the data center, skew, gaps,
unusually high or low values, etc.
The frequencies command(SPSS) can be used to determine measures
of central tendency (mean, median, and mode), measures of dispersion
(standard deviation, variance, minimum and maximum), measures of
skewness and kurtosis and create histograms.
Frequency analysis to answer research question. Frequency analysis
is a descriptive statistical method that shows the number of
occurrences of each response chosen by the respondents.
STEM AND LEAF PLOT
Stem-and-Leaf Plots: A convenient method to display every piece
of data by showing the digits of each number.
A table in which data values are divided into either a "leaf" or a
In a stem and leaf plot, the stem values appear on the vertical axis
and the leaf values are listed on the horizontal axis.
Stem: The digit or digits that remain when the leaf is dropped.
Leaf: The last digit on the right of the number.
SPSS DEMONSTRATION AND INTERPRETATION
1-Execution of frequency distribution
2-Executing stem and leaf plot
When there is analysis of two variables at which statistical
techniques are applied on objects under investigation.
Multivariate refers to all statistical techniques that
simultaneously analyze multiple measurements on the
individual or objects under investigation.
It is to examine relationships between
or among more than two variables.
KNOWLEDGE OF LEVEL OF MEASUREMENT
There is metric and non metric data and both treatment
can’t be same so important is to identify the level of
measurement for correct treatment.
Example: Country names ( Canada, Japan, Africa) a non-
metric data and if it is used as metric and mean is taken it
will be wrong.
The measurement scale is also critical in determining
which multivariate techniques are most applicable to the
data, with consideration made for both independent and
Simple regression is that there is one predictor variable and one dependent
Multiple regression When there are several predictor variables and one
Some Multivariate techniques e.g. factor analysis, the variates that represent
the best represent the patterns of variables (like factor analysis is use to develop
questionnaire). Discriminant analysis which differentiates among groups based
on the variables.
Multivariate analysis of variance (MANOVA) is a statistical test procedure
for comparing multivariate (population) means of several groups.
Multivariate analysis of covariance (MANCOVA) is a method to cover
cases where there is more then one dependent variable and where the control of
continuous independent variable.
Multidimensional scaling (MDS) is a set of related statistical techniques
often used in information visualization for exploring similarities or
dissimilarities in data.
Cluster analysis is an exploratory data analysis tool for solving
classification problems. Its object is to sort cases (people, things, events,
etc) into groups, or clusters, so that the degree of association is strong
between members of the same cluster and weak between members of
In non-metric MDS, only the rank order of entries in the data matrix (not
the actual dissimilarities) is assumed to contain the significant information.
Dummy variables is one that takes the value 0 or 1 to indicate the
absence or presence of some categorical effect that may be expected to shift
Canonical correlation analysis is used to identify and measure the
associations among two sets of variables. Canonical correlation is
appropriate in the same situations where multiple regression would be, but
where are there are multiple inter correlated outcome variables.
LEVEL OF MEASUREMENT
Nominal Scales - A type of categorical data in which objects
fall into unordered categories.
Ordinal scales -provide no measure of the actual magnitude in
absolute terms ,only the order of values.
Interval scale- provides meaningful difference to value.
Ratio Scales - captures the properties of the other types of
scales, but also contains a true zero