Probability and Statistics Chapter 1 Notes. Probability and Statistics Chapter 1 Notes I. Section 1-1 A.Definition of Statistics 1.Statistics is the science.

Probability and Statistics

Chapter 1 Notes

Probability and StatisticsChapter 1 Notes I. Section 1-1 A. Definition of Statistics

1. Statistics is the science of collecting, organizing, analyzing,

and interpreting data in order to make decisions.a. Data –

Information coming from observations, counts, measurements,

or responses.1)

There are 2 types of data sets.

a) Population – the collection of all outcomes,

responses, measurements, or counts that are of

interest.

1. In other words, the set of all possible

measurements, counts or observations that are

of interest in a particular study.

Probability and StatisticsChapter 1 Notes I. Section 1-1

b) Sample – A subset of the population.

1. Since it is usually impractical or even impossible

in terms of time or money to obtain every

possible response, we must often rely on

information obtained from a sample.

1. Random Sample: -- A sample in which every

member of the population has an equal

chance of belonging.2) A

central theme, in the study of statistics, is that of

using information obtained from a sample to

make decisions or inferences concerning an entire

population from which the sample has been

drawn.

1. We will study techniques which will enable us

to do this with a high level of reliability.

Probability and StatisticsChapter 1 Notes I. Section 1-1

3)There are 2 types of numerical descriptions

a) Parameter – A numerical description of a

population characteristic.

b) Statistic – A numerical description of a sample

characteristic.B. Branches of Statistics

1. Descriptive Statisticsa. The branch of

statistics that involves the organization, summarization, and

display of data.2. Inferential Statistics.

a. The branch of statistics that involves using a sample to

draw conclusions about a population.

1) A basic tool in the study of inferential statistics is

probability.

Probability and StatisticsChapter 1 NotesII. Section 1-2

A. Types of Data1. Qualitative Data

a. Attributes, labels or nonnumerical entries.

2. Quantitative Dataa. Numerical

measurements or counts.B. Levels of Measurement

1. Nominal Dataa. Consists of

names, categories, qualities, or labels.

Example: type of car you drive.b. Can put data into

categories, but we are unable to determine if one

piece of data is better or higher than another.c. When numbers

are used as labels, such as on an athletic jersey, they are classified as nominal

data.


1) It is of no use whatsoever to know the average of all

jersey numbers of the King’s Fork field hockey team.

2. Ordinal Dataa. Designations or

numerical rankings which can be arranged

in ascending or descending order. 1) TV

ratings for #1 show, #2 show, etc.b. We can compare

rankings as to which is higher, however it does not make sense to subtract one

rank value from another.

1)Differences in rankings are not meaningful

computations.

a) If there are three candidates for a job, they can be

ranked 1, 2, and 3, but there is no way to tell how

far ahead of the second candidate the first

candidate is.


3. Interval Data a. Can be

subtracted to find the difference between two values, put in

order, and put into categories.b. Data is

numerical; 0 can be used to indicate a position in time or space, however, the

zero at this level does not correspond to “none” of the specific

variable being measured.

1)The position on the thermometer of zero degrees

does not indicate that is absolutely no heat present.c. Differences

between data values are meaningful but it does not make sense to

compare one data value as being twice (or any multiple of) another.

1) A temperature of 2 degrees is not twice as warm as a

temperature of 1 degree.


4. Ratio Dataa. The highest level

of measurement. 1)

The number of gallons of gasoline you put into your

car today.b. There is a zero on

this scale which is interpreted as “none” of the

variable in question.1) It

is possible to put zero gallons of gas into your tank today.2)

This is called an “inherent” zero.c. It is meaningful

to say one measure is two times, or three times, as much as another.

1)You may have put twice as much gas in your car today

than you did last week.


5. How to tell Interval data from Ratio data.

a. Does the expression “twice as much” have any meaning in

the context of the data?1) $2

is twice as much as $1, so these data points are at the ratio level.

2) A temperature of 2 degrees is NOT twice as warm as 1

degree is, so these data points are at the interval level.

Probability and StatisticsChapter 1 NotesIII. Section 1-3

A. Design of a Statistical Study1. Identify the variable(s) of

interest (the focus) and the population of the study.2. Develop a detailed plan for

collecting data.3. Collect the data.4. Describe the data, using

descriptive statistics techniques.5. Interpret the data and make

decisions about the population using inferential statistics.

6. Identify any possible errors.B. Data Collection

1. Do an Observational Studya. Observe and

measure characteristics of interest of part of a population, but do NOT

change existing conditions.


B. Data Collection2. Do an Experiment

a. Apply a treatment to part of a population and observe

responses or results.b. Observe another part

of the population as a control group.

1)May use a placebo in place of the treatment being

tested.


B. Data Collection3. Use a simulation

a. Use a mathematical or physical model to reproduce the

conditions of a situation or process.

1) Simulations allow us to study situations that are

impractical or even dangerous to create in real life.

a) Testing the effects of alcohol on a pilot’s ability to

fly is best done in a flight simulator2)

Simulations often save time and/or money.4. Use a survey (census)

a. A survey is an investigation of one or more

characteristics of a population.1) Usually

carried out on people by asking them to

respond to questions.


B. Data Collectionb. It’s important to

word the questions so that they do not lead to biased results.

C. Experimental Design1. Experiments must be carefully

designed in order to produce meaningful, unbiased, results.

a. The Hawthorne effect occurs in an experiment when

subjects change their behavior simply because they know

they are participating in an experiment.2. Three key elements of a well-

designed experiment are control, randomization, and replication.


C. Experimental Designa. Control

1) It is important to control as many influential factors as

possible in a study.

2)When an experimenter cannot tell the difference

between the effects of different factors in an

experiment, a confounding variable has occurred.

3)Placebo effect occurs when a subject reacts favorably

to a placebo when in fact they have been given no

medical treatment at all.

a) Blinding is a technique used in which the subject

does not know whether he or she is receiving a real

treatment or a placebo.


C. Experimental Design

b) Double-blind experiments occur when neither the

subjects nor the experimenter know which

individual subjects are receiving a treatment or a

placebo.

1. The experimenter only finds out which subjects

are which after all the data have been collected.

b. Randomization is a process of randomly assigning

subjects to different treatment groups.

1)Randomized block design – Divide subjects with

similar characteristics into blocks, and then randomly

split each block up into different treatment groups.


C. Experimental Design2)

Matched-pairs design – Subjects are paired up

according to a similarity.

a) One subject in each pair is randomly selected to

receive one treatment, while the other one gets

another, different treatment.

c. Replication is the repetition of an experiment using a

large group of subjects.1)

The larger the sample size, the better.D. Sampling Techniques

1. Census – a count or measure of an entire population.

a. Provides complete information, but is often too costly or

difficult to perform.


D. Sampling Techniques2. Sampling – a count or measure

of part of a population.a. Researcher must

ensure that the sample is

representative of the population.1)

This is necessary to ensure that inferences about a

population are valid.

a) Sampling error – the difference between the

results of a sample and those of the population.

b. Random sample – a sample in which every member of

the population has an equal chance of being selected.

1)Methods of sampling randomly


D. Sampling Techniques

a) Simple Random Sample – assign each member of

the population a number and then randomly select

the numbers that you will survey.

1. Random number table (Appendix B of the book)

a. Randomly pick a starting point

b. Count off digits in groups that match how

many digits your population has.

c. Record the numbers, ignoring those that are

larger than the population size.



2. Calculator

a. Press Math, select PRB, press 5(randInt)

b. Enter the number that you started with when

assigning labels to your population, then a

comma, then the last number you assigned,

comma, and the sample size you wish to use.

1) The calculator will generate the requested

quantity of random numbers.

3. If you do not want to have any member of the

population included in the sample twice, the

sampling process is said to be without

replacement.



4. If you don’t care if a member of the population

is included twice, the sampling process is said to

be with replacement.

b) Stratified Sample

1. Separate population into two or more subsets,

called strata, using some similar characteristic.

a. Randomly select members of each strata to

make up your sample.

c) Cluster Sample

1. When the population is already divided into

subsets that are very similar to each other, you

could randomly select a number of entire

groups (not all the groups) and do your data

collection on those groups.



a. We call these groups clusters.

d) Systematic Sample

1) Each member of the population is assigned a

number.

a. Put the members of the population in order

somehow.

b. Randomly select a starting point.

c. Randomly select an interval.

d. Survey every nth member of the population

from your starting point.



e) Convenience Sample

1) NOT RECOMMENDED!!

a. Simply select those members of the

population who are readily available.

QUIZ on Chapter 1 Sections 1 and 2 during next class block

Friday (ODD) and Monday (EVEN)

TEST on Chapter 1 next weekTuesday (ODD) and Wednesday (EVEN)

Probability and Statistics Chapter 1 Notes. Probability and Statistics Chapter 1 Notes I. Section 1-1 A.Definition of Statistics 1.Statistics is the science.

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