STA 204. 200 level university of Ibadan statistics department

Statistics for 200 level

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GENERAL STATISTICS II
Dr S.O. OYAMAKIN
STA 201/202/204
June 24, 2024
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Introduction
Statistical methods play a crucial role in various fields, including biology,
agriculture, physical sciences, and engineering. Here are some examples
of the scope of statistical methods in each of these fields.
BIOLOGY
(a.)Ecology and Evolutionary Biology:Statistical methods are
used to analyze population dynamics, species distribution, and
evolutionary patterns.
(b.)Genetics and Molecular Biology:Statistics are employed to
study gene expression, genetic variation and protein structure.
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INTRODUCTION
BIOLOGY
(c.)
datasets of biological information, such as gene sequences, to
identify patterns and relationships. Statistical methods are used
to analyze large datasets of biological information, such as gene
sequences, to identify patterns and relationships.
(d.)Neuroscience:Statistical techniques are applied to investigate
brain function, neural networks, and behavior.
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Introduction Cont’D
AGRICULTURE
(a.)Plant Breeding:Statistical methods are used to analyze genetic
variation in crops, identify breeding lines and predict crop perfor-
mance.
(b.)Agricultural Economics:Statistics are employed to study market
trends, crop yields, and the impact of environmental factors on
crop production.
(c.)Animal Science:Statistical techniques are used to analyze animal
behavior, nutrition, and disease prevalence.
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Introduction Cont’D
PHYSICAL SCIENCES
(a.)Physics:Statistical methods are used to analyze data from particle
colliders, cosmic rays, and other physical experiments.
(b.)Chemistry:Statistics are employed to study chemical reactions,
reaction kinetics, and materials science.
(c.)Earth and Environmental Sciences:Statistical techniques are
used to analyze climate data, geological processes, and environ-
mental pollutants.
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Introduction Cont’D
ENGINEERING
(a.)Civil Engineering:Statistical methods are used to analyze struc-
tural dynamics, material properties, and construction management.
(b.)Mechanical Engineering:Statistics are employed to study me-
chanical systems, thermal dynamics, and fluid mechanics.
(c.)Electrical Engineering:Statistical techniques are used to analyze
circuit performance, signal processing, and power systems.
(d.)Computer Science and Engineering:Statistical methods are
used to study software engineering, data mining, and machine
learning.
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SUMMARY
In summary, statistical methods have a wide range of applications
across various fields, from biology to engineering. They are essential
for analyzing and interpreting data, making predictions and drawing
meaningful conclusions.
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VARIABLES
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Variables
a.
on different values.
b.
between two variables for a specific group of individuals.
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Population
a.
b.
class size (variable 1) and academic performance (variable 2) for
the population of third-grade children.
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Samples
Usually populations are so large that a researcher cannot examine the
entire group. Therefore, a sample is selected to represent the population
in a research study. The goal is to use the results obtained from the
sample to help answer questions about the population.
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Types of Variables
Variables can be classified as discrete or continuous.
Discrete variables(such as class size) consist of indivisible cat-
egories, andContinuous variables(such as time or weight) are
infinitely divisible into whatever units a researcher may choose. For
example, time can be measured to the nearest minute, second,
half-second, etc.
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Real Limits
To define the units for a continuous variable, a researcher must use real
limits which are boundaries located exactly halfway between adjacent
categories.
Measuring Variables
To establish relationships between variables, researchers must
observe the variables and record their observations. This requires
that the variables be measured.
The process of measuring a variable requires a set of categories
called a scale of measurement and a process that classifies each
individual into one category.
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Four (4) Types of Measurement Scales
1
Anominal scaleis an unordered set of categories identified only
by name. Nominal measurements only permit you to determine
whether two individuals are the same or different.
2
Anordinal scaleis an ordered set of categories. It tell you the
direction of difference between two individuals.
3
Aninterval scaleis an ordered series of equalsized categories.
Interval measurements identify the direction and magnitude of a
difference. The zero point is located arbitrarily on an interval scale.
4
Aratio scaleis an interval scale where a value of zero indicates
none of the variable. Ratio measurements identify the direction
and magnitude of differences and allow ratio comparisons of mea-
surements.
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Correlational Studies
The goal of a correlational study is to determine whether there is a
relationship between two variables and to describe the relationship.
A correlational study simply observes the two variables as they exist
naturally.
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Example
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Line Graph
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Experiment
The goal of an experiment is to demonstrate a cause-and-effect relation-
ship between two variables; that is, to show that changing the value of
one variable causes changes to occur in a second variable.
In an experiment, one variable is manipulated to create treatment con-
ditions. A second variable is observed and measured to obtain scores
for a group of individuals in each of the treatment conditions. The
measurements are then compared to see if there are differences between
treatment conditions. All other variables are controlled to prevent them
from influencing the results.
The manipulated variable is called the independent variable and the ob-
served variable is the dependent variable.
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Other Types of Studies
Other types of research studies, know as non-experimental or
quasiexperimental, are similar to experiments because they also
compare groups of scores.
These studies do not use a manipulated variable to differentiate
the groups. Instead, the variable that differentiates the groups is
usually a pre-existing participant variable (such as male/female) or
a time variable (such as before/after).
Because these studies do not use the manipulation and control
of true experiments, they cannot demonstrate cause and effect
relationships. As a result, they are similar to correlational research
because they simply demonstrate and describe relationships.
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DATA
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Data
The measurements obtained in a research study are called the data. The
goal of statistics is to help researchers organize and interpret the data.
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Descriptive Statistics
Descriptive statistics are methods for organizing and summarizing data.
For example, tables or graphs are used to organize data, and descriptive
values such as the average score are used to summarize data.•A
descriptive value for a population is called a parameter and a descriptive
value for a sample is called a statistic.
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Inferential Statistics
Inferential statistics are methods for using sample data to make general
conclusions (inferences) about populations. Because a sample is typically
only a part of the whole population, sample data provide only limited
information about the population. As a result, sample statistics are
generally imperfect representatives of the corresponding population
parameters.
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Sampling Error
The discrepancy between a sample statistic and its population parameter
is called sampling error. Defining and measuring sampling error is a large
part of inferential statistics.
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Notation
The individual measurements or scores obtained for a research participant
will be identified by the letter X (or X and Y if there are multiple scores
for each individual). The number of scores in a data set will be identified
by N for a population or n for a sample. Summing a set of values is a
common operation in statistics and has its own notation. The Greek
letter sigma, E, will be used to stand for ”the sum of.” For example, EX
identifies the sum of the scores.
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Order of Operations
All calculations within parentheses are done first.
Squaring or raising to other exponents is done second.
Multiplying, and dividing are done third, and should be completed
in order from left to right.
Summation with the E notation is done next.
Any additional adding and subtracting is done last and should be
completed in order from left to right.
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Practical Question 1
Obtain the Mean, Median and Mode for the groups above.
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