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Chapter 1: Getting Started Section:1'1 What is statistics

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Title: Chapter 1: Getting Started Section:1'1 What is statistics

1
Chapter 1 Getting Started Section1.1 What is
statistics?

Statistics is the study of how to collect ,
organize , analyze, and interpret numerical
information from data.
Individual is people or object included in a
study.
Variable is a characteristic of the individual to
be measured or observed.

2
Section1.1 What is statistics?

Quantitative Variable has a value or numerical
measurement.
----example height of a person.
Qualitative Variable (categorical) places an
individual in a category or group.
-----example gender of a person.

3
Section1.1 What is statistics?

Population data Variable is from every
individual of interest.
-----example Income of all the residents of a
county.
Sample data Variable is from only some of the
individual of interest.
-----example Income of selected residents.

4
Section1.1 What is statistics?

Example 1 Television station QUE wants to know
the proportion of TV owners in Virginia who watch
the stations new program at least one a week.
The station asked a group of 1000 TV owners in
Virginia if they watch the program at least once
a week.
Identify the individuals of the study and the
variable?
Do the data comprise a sample? If so, what is the
underlying population?
Is the variable quantitative or qualitative?
Identify a quantitative variable that might be of
interest?

5
Section1.1 What is statistics?

Level of Measurement

6
Section1.1 What is statistics?

Branches of Statistics
Descriptive methods of organizing, picturing,
and summarizing information.
Inferential methods of using information from a
sample to draw conclusions regarding the
population.

7
Section1.2 Random Samples?

Methods of Producing Data
Sampling drawing subsets from the population
Experimentation impose a change and measure the
result
Simulation arithmetic imitation of real
phenomena
Census using measurements from entire population
Survey asking questions

8
Section1.2 Random Samples?

Simple Random Sample of n measurements
(a) every sample of size n from the
population has an equal chance of being selected
and
(b) every member of the population has an
equal chance of being included in the sample.

9
Section1.2 Random Samples?

Example 1 Suppose you pay one dollar and choose
any six different numbers from the group of
numbers 1 through 42. If your group of six
numbers matches the winning group of six numbers
selected by simple random sampling, then you are
a winner of a grad prize of at least 1.5 million
dollars.
Is the number 25 as likely to be selected in the
winning group of six numbers as the number 5?
Could all the wining numbers be even?
Your friend always plays the numbers
1 2 3 4 5 6
Could she ever win?

10
Section1.2 Random Samples?

Not Random Sampling
Examples (a) Ask for volunteers to
respond to a survey
(b) choosing the first
five customers in a store.
How do you get random Samples?
drawing names from from a hat
using a random number table to select sample
using a random number generator

11
Section1.2 Random Samples?

Example 2 Use a random table to pick a
(simple )random sample of 30 cars from a
population of 500 cars.
Solution We assign each car a different number
between 1 and 500, inclusive. Then we use the
random number table (Table 1 in Appendix II) to
choose the sample. Table 1 in Appendix II has 50
rows and 10 blocks of five digits each it can be
thought of as a solid mass of digits that has
been broken up into rows and blocks for user
convenience.
You read the digits by beginning
anywhere in the table. We dropped a pin on the
table, and the head of the pin landed in raw 18,
block 3. We will begin there and list all the
digits in that row. If we need more digits, we
will move on to the raw 19. The digits we begin
with are
67967 07835 11314 01545 48535
17142 etc
Since the highest number assigned to a car is
500, this number has three digits, we regroup the
digits into blocks of three
679 670 783 511 314
015 454 853 517 142
etc

12
Section1.2 Random Samples?

Note Another important use random number tables
is in simulation.
Examples 3 Use a random-number table to
simulate the outcomes of tossing a balanced (that
is, fair) penny 10 times.
(a) How many outcomes are possible when you
toss a coin once? Two heads or tails
(b) There are several ways to assign a fair
coin, assign an even digit to the outcome heads
and an odd digit to the outcome tails. 7 1
5 4 9 4 4 8 4 3
(c) What are the outcomes associated with 10
digits? T T T H T H H H H T
(d) If you start in a different block and
row of Table 1 in Appendix II, will you get the
same sequence of outcomes. It is possible, but
not very likely.

13
Section1.2 Random Samples?

Note Sampling with replacement means
that although a number is selected for the
sample, it is not removed from the population.
Therefore, the same number may be selected for
the sample more than once. If you need to sample
without replacement, generate more items than you
need for the sample. Then sort the sample and
remove duplicate values.

14
Section1.2 Random Samples?

Other Sampling Techniques
Stratified sampling
Systematic sampling
Cluster sampling
Convenience sampling

15
Section1.3 Introduction to Experimental Design

Planning a Statistical Study and gathering
data are essential components for obtaining
reliable information.

16
Section1.3 Introduction to Experimental Design

Basic Guidelines for planning a statistical
study
First, identify the individuals or objects of
interest.
Specify the variables as well as the protocols
for taking measurements or making observations.
Determine if you will use an entire population
or a representative sample. If using a sample,
decide on a viable sampling method.
In your data collection plane, address the issues
of ethics, subject confidentiality, and privacy.
If you are collecting data at a business, store,
college, or other institution, be sure to be
courteous and to obtain permission as necessary.
Collect the data
Use appropriate descriptive statistics methods
and make decisions using appropriate statistical
methods.
Finally, note any concerns you might have your
data collection methods and list any
recommendations for the future studies.

17
Section1.3 Introduction to Experimental Design

Types of Studies
When gathering data for statistical
study, we want to distinguish between
observational studies and experiments.
In an observational study, observations
and measurements of individuals are conducted in
a way that doesnt change the response or the
variable being measured.
In an experiment, a treatment is
deliberately imposed on the individuals in order
to observe a possible change in the response or
variable being measured.

18
Section1.3 Introduction to Experimental Design

Statistical experiments are commonly used to
determine the effect of a treatment. However, the
design of the experiment needs to control for
other possible causes of the effect. For
instance, in medical experiments the placebo
effect is the improvement or change that is the
result of patients just believing in the
treatment, whether or not the treatment itself is
effective,

19
Section1.3 Introduction to Experimental Design

The placebo effect occurs when a subject
receives no treatment, but (incorrectly) believes
he or she is in fact receiving treatment and
responds favorably.
To account for the placebo effect,
patients are divided into two groups. One group,
is called treatment group, receives the
prescribed treatment. The other group, called
the control group, receives a dummy or placebo
treatment that is disguised to look the real
treatment.

20
Section1.3 Introduction to Experimental Design

In general, a control group is used to
account for the influence of other known or
unknown variables that might be an underlying
cause of a change in response in the treatment
or experimental group. Such variables are called
lurking or confounding variable.
A common way to assign patients to the
treatment and control groups is by using a random
process. This is the essence of a randomized
two-treatment experiment.
Many experiments are also double-blind.
This means that neither the individuals in the
study nor the observers know which subjects are
receiving the treatment. Double-blind experiment
help control for subtle biases that a doctor
might pass to a patient.