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# BYU-I - MATH 221 - MATH 221A - Class Notes

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Lesson 2: The Statistical Process & Design of Studies    Step 1:  Design the study   Step 2:  Collect data   Step 3:  Describe the data   Step 4:  Make inferences   Step 5:  Take action     3.1 Step 1: Design the Study    An important step in scientific inquiry or problem solving can be to state a research question
such as:
Will internet advertising increase a company's revenue?    Does expressing gratitude increase a person’s satisfaction with life in general?    Does a newly developed vaccine prevent the spread of disease?  Researchers also investigate the background of the situation. What have other people discovered
do? What is the population (or total collection of all individuals) under consideration? What
kind of data need to be collected?
Before collecting data, researchers make a hypothesis, or an educated guess about the outcome of
their research. A hypothesis is a statement such as the following:
Using internet advertising will increase the company’s sales revenue.    People who express gratitude will be more satisfied with life than those who do not.    A newly-developed vaccine is effective at preventing tuberculosis.        3.2 Step 2: Collect Data    When designing a study, much attention is given to the process by which data are observed. When
examining data, it is also important to understand the data collection procedures. A sample is a subset
(a portion) of a population. How is this sample obtained? How are the observations made?
3.3 Step 3: Describe the Data
When we describe data, we use any tools appropriate to the situation. This can include creating
graphs or calculating statistics to help understand or visualize the data.
3.4 Step 4: Make Inferences  Inference is the process of using the information contained in a sample from a population to
make a general statement (i.e. to infer something) about the entire population. Later in the course
we will learn techniques that make this type of analysis possible.
.5 Step 5: Take Action  The goal of a statistical analysis is to determine which action to take in a particular situation.
Actions can include many things: launching an internet ad campaign (or not), expressing
gratitude (or not), getting vaccinated (or not), etc.
Design of Studies  Most research projects can be classified into one of two basic categories: observational studies or
designed experiments. In an experiment, researchers control (to some extent) the conditions
under which measurements are made. In an observational study, researchers simply observe
what happens, without controlling the conditions under which measurements are made. Both
types of study follow the five steps of the Statistical Process.
4.1 Designed Experiments  In a designed experiment, researchers manipulate the conditions that the participants
experience. They often do this by randomly assigning subjects to one of two groups, a
"treatment" group and a "control" group. The experiment is conducted by applying some kind of
treatment to the subjects in the treatment group, and observing the effect of the treatment. Those
in the control group do not receive the treatment and are also observed. In this way researchers
can determine the effects of the treatment. The following example illustrates the use of these two
groups.
4.2 Observational Studies  In an observational study researchers observe the responses of the individuals, without
controlling the conditions experienced by the individuals. Therefore, they do not assign the
participants to treatment or control groups.
Observational studies commonly occur in business settings. One example is a financial audit.
The purpose of a financial audit is to assess the accuracy of a company’s financial business
practices. ImmunAvance Ltd., a non-government health care organization, hired the Accounting
Office at Global Optimization Unlimited to perform an independent audit of their financial
practices. Immun Avance provides inoculation and other preventative health care services in
rural African communities.
Imagine you are assigned to serve as a member of the team that will perform this audit. The audit
illustrates the five steps of the Research Process.
Step 1: Design the study   The volume of financial transactions conducted by ImmunAvance makes it impossible to
conduct a census or an examination of the entire collection of ImmunAvance’s financial
documents. Instead, you will collect a manageable group of items (called the sample) from the
entire collection of financial documents (called the population.) A sample is a subset or a
portion of a population. The information gained from the sample is used to make an inference
Auditors typically cannot consider every item in a population, because there are too many. When
it is not possible to conduct a census, auditors face sampling risk. Sampling risk is the risk
affiliated with not auditing every item in the population. It is the risk that the sample may not
adequately reflect the population. The only way to eliminate sampling risk is to conduct a
census, which is usually not practical. Auditors can reduce sampling risk by obtaining a sample
randomly. This is called random selection. Another way to reduce sampling risk is to increase
the sample size, the number of items sampled.
4.3 Sampling Methods  Step 2: Collect data   There are several procedures that can be used to select a random sample from a
population, including: simple random sampling (SRS), systematic sampling, cluster
sampling, stratified sampling, and convenience sampling (or, haphazard sampling).
These are examples of sampling methods
simple random sampling (SRS) is the best method for obtaining a random sample. If
there is a list of all items in the population and they are all accessible, a SRS can be
collected. For example, suppose there are 2,000 accounts receivable items in the
population. Auditors can use a random number generator to choose values between 1 and
2,000 to identify which items are to be audited. Software can be used to create a list of
random numbers corresponding to items for the audit. In Excel, the command to obtain a
random number between 1 and 2,000 is =RANDBETWEEN(1,2000). Sometimes it is
necessary for auditors to renumber the items (1 to 2000) to help create random sample. A
simple random sample can be obtained any time there is a complete list of the items to be
sampled and they are all assessible. All the statistical procedures in this course assume
that simple random sampling has been used.
systematic sample is where auditors select every
k th

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