Descriptive Statistics Analysis and
Visualization With IBM SPSS
By Md. Sharif Hossain
What Are Descriptive Statistics?
Brief informative coefficients known as descriptive
statistics are used to sum up a particular data set, which may be a sample of a
population or a representation of the complete population. In a nutshell, descriptive
statistics provide brief summaries of the sample and data measurements to aid
in describing and understanding the characteristics of a particular data set.
The mean, median, and mode, which are utilized at
practically all math and statistics levels, are the most well-known types of
descriptive statistics. Measurements of central tendency and measures of
variability make up descriptive statistics (spread). The mean, median, and mode
are measurements of central tendency, while the standard deviation, variance,
minimum and maximum variables, kurtosis, and skewness are measures of
variability.
What Is the Main
Purpose of Descriptive Statistics?
Descriptive statistics are mostly used to provide details
about a data set. The large amount of data is condensed into numerous helpful
facts using descriptive statistics.
Types of
Descriptive Statistics
Measure
of Central Tendency
Measure
of Variance
Measure
of Variability
What are the Measure of central Tendency?
A summary measure called a measure of central tendency,
also known as a measure of center or a measure of central placement, aims to
characterize the entirety of a set of data with a single number that
corresponds to the middle or center of its distribution.
The mode, the median, and the mean are the three primary
indicators of central tendency. The typical or core value in the distribution
is indicated differently by each of these metrics.
What is the mean?
A dataset's mean is calculated by dividing the total value of all observations
by the total number of observations. The arithmetic average is another name for
this concept.
Taking another look at
the distribution of retirement ages: 54, 54, 54, 55, 56, 57, 57, 58, 58, 60,
60,
When all of the values
are added up (54+54+55+56+57+57+58+58+60+60 = 623) and divided by the number of
observations (11), the mean is obtained as 56.6 years.
What is the
median?
When values are organized in ascending or descending order,
the median is the value that falls in the middle of the distribution.
There are 50% of observations on either side of the median
value, which divides the distribution in half. The median value is the midpoint
of a distribution with an odd number of observations.
The median, or middle value, is 57 years when examining the
retirement age distribution, which comprises 11 observations: 54, 54, 54, 55,
56, 57, 57, 58, 58, 60, 60,
The median value is the mean of the two middle values when
there are an equal number of observations in the distribution. The two middle
values in the following distribution are 56 and 57, making the median age 56.5
years: 52, 54, 54, 54, 55, 56, 57, 57, 58, 58, 60, 60,
What is the mode?
In a distribution, the mode is the value that appears the
most frequently. Take a look at this dataset, which displays the age at
retirement in entire years for 11 people: 54, 54, 54, 55, 56, 57, 57, 58, 58,
60, 60,
Age
|
Frequency
|
54
|
3
|
55
|
1
|
56
|
1
|
57
|
2
|
58
|
2
|
60
|
2
|
The median age in this distribution is 54 years, which is
also the value that occurs most frequently.
Measures of
Variability
A collection of data's distribution's dispersion can be
determined using measures of variability (also known as spread). For instance,
while the central tendency measurements can provide a person with the average
of a group of data, they cannot represent the distribution of the data within
the set.
Range
We'll start with the range since it is the easiest to
compute and comprehend of all the measures of variability. The difference
between a dataset's largest and smallest values is known as its range. In the
two datasets below, for instance, dataset 1's range is 20–38, or 18, and
dataset 2's range is 11–52, or 41. Dataset 2 is more variable than Dataset 1
since it covers a wider range.
Dataset 1
|
Dataset 2
|
20
|
11
|
21
|
16
|
22
|
19
|
25
|
23
|
26
|
25
|
29
|
32
|
33
|
39
|
34
|
46
|
38
|
52
|
The range is simple to understand, but it is highly prone
to outliers because it is based simply on the two most extreme values in the
dataset. Even if it is out of the ordinary, if one of those values is extremely
high or low, it has an impact on the entire range.
The range is also impacted by the amount of the dataset.
Extreme values are often less likely to be seen. However, there are more
chances to get these high results as the sample size grows.
Variance
Because the range is based just on the two most extreme
values in the dataset, it is easy to interpret but very susceptible to
outliers. Even though it is unusual, the entire range is affected if one of
those numbers is very high or low.
The size of the dataset also affects the range. Extreme
values are frequently harder to find. As the sample size increases, there are
more opportunities to achieve extremely high outcomes.
Standard
Deviation
The normal or average difference between each data point
and the mean is known as the standard deviation. You have a reduced standard
deviation when the values in a dataset are clustered more closely together.
Conversely, when values are more dispersed, the standard deviation is higher because
the standard deviation is higher.
The standard deviation conveniently uses the original units
of the data, which simplifies interpretation. The standard deviation is
therefore the most frequently employed measure of variability.
Distribution
The frequency distribution of a data point describes how
frequently a data point appears. In contrast, it is the measurement of a data
point not happening.
Univariate
vs. Bivariate
Univariate data analysis in descriptive statistics uses
just one variable. It does not evaluate any relationships or causes; rather, it
is used to pinpoint traits that make up a single trait.
On the other hand, bivariate data makes an effort to link
two variables together by looking for correlation. The relationship between the
two forms of data is studied after they have both been acquired. This method
may also be referred to as multivariate because several variables are examined.
Summary Statistics
Summary statistics are the most typical technique for
carrying out univariate analysis. The degree of measurement or the type of data
that the variables hold determines the relevant statistics. The two most
popular kinds of summary statistics are as follows:
Measures of Dispersion
These figures show the degree to which values in a dataset
are uniformly distributed. Examples include the variance, interquartile range,
range, and standard deviation.
Range is the space between a dataset's highest and lowest
values.
Standard Deviation: A typical way to gauge the spread
The range of values in the middle 50% is known as the
interquartile range.
Frequency distribution table
Frequency refers to how frequently something occurs. The
number of times an event occurs is revealed by the observation frequency.
Variables that are categorical, qualitative, numerical, or quantitative may be
displayed in the frequency distribution table. The distribution provides a
snapshot of the data and enables pattern discovery.
Bar chart
Rectangular bars are used to depict the bar chart. Various categories
will be compared in the graph. The graph might be displayed either vertically
or horizontally. The bar will often be plotted vertically. The category will be
represented by the horizontal or x-axis, and the category's value by the
vertical or y-axis. The bar graph examines and contrasts the data set. It might
be used, for instance, to determine which component consumes the most
expenditure.
Histogram
The analysis of the data is important since the histogram
functions similarly to a bar chart. The histogram divides the categories into
bins, and the bar graph counts against the categories. The bin can display the
range, the interval, or the number of data points.
Frequency Polygon
The histogram and the frequency polygon are quite similar.
These can be utilized, nevertheless, to contrast the data sets or to show the
cumulative frequency distribution. A line graph will serve as the
representation for the frequency polygon.
Pie Chart
The data is shown in a circular layout on the pie chart.
The graph is broken up into sections, each of which is proportional to the
percentage of the entire category. Each pie slice in the pie chart is thus
compared to the size of the category. Since the entire pie is 100 percent,
adding up all of the pie slices should also result in a total of 100.
Pie charts are used to visualize how a group is divided
into smaller components.
Classification Chart of Multivariate Techniques
Various factors determine which multivariate technique is
most appropriate.
a) Do
the variables fit into the independent and dependent categories?
b) If so, how many variables in a single analysis are
regarded as dependents?
c) What measurements are made for the dependent and
independent variables?
Dependent and non-dependent categories can be used to group
this multivariate analysis technique. The classification is based on whether or
not the relevant variables are interdependent.
We have dependent techniques if the response is affirmative.
We have interdependence methods if the response is no.
Techniques for multivariate analysis that are employed when
one or more of the variables can be classified as dependent variables and the
other variables can be classified as independent are known as dependency
techniques.
Multiple Regression
Analysis Using Multiple Regression: Multiple regression is
a simple linear regression extension. When predicting the value of a variable
based on the values of two or more other variables, this technique is employed.
The dependent variable is the one we're trying to forecast (or sometimes, the
outcome, target, or criterion variable). For each independent variable,
multiple "x" variables are used in multiple regression: (x1)1, (x2)1,
(x3)1, Y1)
Conjoint analysis
‘Conjoint analysis ‘is a survey-based statistical technique
used in market research that helps determine how people value different
attributes (feature, function, benefits) that make up an individual product or
service. The objective of conjoint analysis is to determine the choices or
decisions of the end-user, which drives the policy/product/service.
Multiple Discriminant Analysis
By identifying linear combinations of the variables that
maximize the differences between the variables under study, discriminant
analysis aims to determine the group membership of samples from a set of
predictors. This method creates a model that accurately sorts objects into the
proper populations.
A linear probability model:
A regression model called a linear probability model (LPM)
uses one or more explanatory factors to make predictions about a binary outcome
variable. Explanatory variables themselves can be continuous or binary. It is
advisable to employ a linear probability model when the dependent variable is a
yes/no decision and some of the independent variables are not metric.
Multivariate Analysis of Variance and Covariance
A variation of the conventional analysis of variance is the
multivariate analysis of variance (MANOVA) (ANOVA). ANOVA compares differences
in group means for a single response variable.
Canonical Correlation Analysis
The study of the linear relationships between two sets of
variables is known as canonical correlation analysis. It is the correlation
analysis's multivariate extension.
There are two typical uses for CCA:
Data compression
Interpreting data
Structural Equation Modelling
A multivariate statistical analytic method called
structural equation modeling is employed to examine structural relationships.
It is a very comprehensive and adaptable framework for data analysis, and it
may be more useful to think of it as a group of connected techniques than as a
single one.
Interdependence Technique
When variables are related, they cannot be categorized as
dependent or independent, which is the case with interdependence approaches.
Without making any explicit assumptions about the
distributions of the variables, it seeks to reveal relationships between
variables and/or people. Without making (very) firm assumptions about the
variables, the goal is to describe the patterns in the data.
Factor Analysis
Factor analysis is a method for reducing the amount of data
in numerous variables to only a few. It also goes by the name "dimension
reduction" for this reason. It results in a highly correlated set of
variables.
Cluster analysis
Objects or cases are categorized into relative groupings
called clusters using a range of techniques known as cluster analysis. In a
cluster analysis, none of the objects have any prior knowledge of their group
or cluster membership.
Multidimensional Scaling
A map showing the
relative positions of various objects is produced using the multidimensional
scaling (MDS) approach using simply a table of their respective distances.
There could be one, two, three, or even more dimensions in the map.
Correspondence analysis
In correspondence
analysis, the rows and columns of a table of non-negative data are represented
as points on a map to give them a specific spatial interpretation.
Cross-tabulations typically count the data, but many other types of data can
now be included as well with the proper data transformations.
For More Details watch the Video.
Channel Link: https://www.youtube.com/channel/UCNphyzKdQKOu02VjLQ-N7Fg
You could Follow me on social media.
Facebook Page Link: https://www.facebook.com/ResearchHacks
References
Statistical analysis in Psychology & Education,
George A. Ferguson (6th edition)
Statistical Techniques in Business & Economics,
Douglas Lind (18th edition)
https://www.investopedia.com/terms/d/descriptive_statistics.asp
https://statisticsbyjim.com/basics/variability-range-interquartile-variance-standard-deviation/
https://www.jigsawacademy.com/blogs/business-analytics/univariate-analysis/
https://www.mygreatlearning.com/blog/introduction-to-multivariate-analysis/
