Section 1.1:Introduction

to the practice of Statistics

Objectives Learn the definition of statistics and

its two branches.

How to distinguish between population/sample and parameter/statistic

Learn different ways to classify data- Qualitative vs. Quantitative- Discrete vs. Continuous- The four levels of measurement

Definition of Statistics

Statistics is the science of collecting, organizing, summarizing, and analyzing information to draw conclusions or answer questions

Important VocabularyAn individual is a person or object that is a

member of the population being studied.

A population is the group of individuals to be studied.

A sample is a subject of the population being studied.

A parameter is a numerical summary of a population

A statistic is a numerical summary of a sample

Two branches of StatisticsDescriptive

statistics consists of organizing and summarizing data, such as numerical summaries, tables, and graphs.

Inferential statistics uses methods that take a result from a sample, extend it to the population, and measure the reliability of the result.

ExampleA drug manufacturer is interested in the proportion of persons who have hypertension whose condition can be controlled by a new drug. A study involving 5000 individuals with hypertension is conducted, and it is found that 80% of the individuals are able to control their hypertension with the drug.

a) The individual isb) The population isc) The sample isd) The parameter ise) The statistic isf) What can we infer?

ExampleA drug manufacturer is interested in the proportion of persons who have hypertension whose condition can be controlled by a new drug. A study involving 5000 individuals with hypertension is conducted, and it is found that 80% of the individuals are able to control their hypertension with the drug.

a) The individual is a person with hypertensionb) The population is all people with hypertensionc) The sample is the 5000 people in this studyd) The parameter is not given in this examplee) The statistic is 80%f) What can we infer? This drug is 80% effective in

controlling hypertension.

Your TurnA statistics student is interested in finding out something about the average dollar value of cars owned by the faculty members at Dover High School. He takes a random sample of 100 cars in the faculty lots and finds that their average dollar value is $11,200.

a) The individual isb) The population isc) The sample isd) The parameter ise) The statistic isf) What can we infer?

What is Data?Data is a collection of values

or measurements. (Numbers, words, measurements, descriptions, etc.)

Data can be qualitative or quantitative. ◦ Qualitative data is descriptive information (words)◦ Quantitative data, is numerical information

(numbers)

Quantitative data can also be discrete or continuous◦ Discrete data can only take on a finite or countable

number of possible outcomes◦ Continuous data can take on an infinite number of

possible outcomes, represented by an interval on the number line.

Data PracticeDetermine if the data is Qualitative or

Quantitative. If it is Quantitative determine if it is

discrete or continuous.

a) Type of wood used to build a kitchen table.b) Number of times your phone rings todayc) Amount of time students do homeworkd) Way of getting to school (walk, bus, drive)e) Money you make at work each weekf) Shoe sizeg) Social security number

Levels of Measurement1. Nominal: Names, labels, or qualities.

Cannot perform meaningful operations on this data. (Type of car, Eye Color, Zip codes)

2. Ordinal: Data can be arranged in order, but differences are not meaningful.(Hotel Ratings, poor/fair/good, low/medium/high)

3. Interval: Data can be ordered and differences can be calculated. There is no inherent zero. (Temperature, Year of birth)

4. Ratio: There is an inherent zero. Data can be ordered, differences can be found, and a ratio can be formed so you can say one data value is a multiple of another. (Height, weight, age)

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Practice

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State the Level of Measurement:

1. The average daily temperature (°F) in Dover, NH during the month of August.

2. The height, in centimeters, of an NFL player.

3. The hair color of every female in Dover High School.

Practice

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State the Level of Measurement:

1. The average daily temperature (°F) in Dover, NH during the month of August.

Interval2. The height, in centimeters, of an NFL

player.Ratio

3. The hair color of every female in Dover High School.

Nominal

Section 1.2: Data

Collection & Sampling methods

Objectives Learn about the different methods

of collecting data.

Identify the method used in creating a sample: random, stratified, cluster, systematic, or convenience sampling.

Be able to identify a biased sample.

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Methods of Data Collection

1. Observational Study: researcher observes characteristics of interest but does not change existing conditions.

2. Experiment: Apply a treatment to a part of the population and responses are observed

3. Simulation: Use a mathematical or physical model to reproduce conditions of a situation or process

4. Survey: An investigation of one or more characteristics of a population. This can be done by taking a census or a sample.

Observational Study, Experiment, Simulation, or Survey (census or sample)

1. A study of the effect of changing flight patterns on the number of airplane accidents.

2. A study of the effects of aspirin on preventing heart attacks.

3. A study of how fourth grade students solve a problem

4. A study of the weights of all linemen in the National Football League.

5. A study of U.S. residents’ approval rating of the U.S. presidents.

Identify the Method of Collection

Observational Study, Experiment, Simulation, or Survey (census or sample)

1. A study of the effect of changing flight patterns on the number of airplane accidents.

2. A study of the effects of aspirin on preventing heart attacks.

3. A study of how fourth grade students solve a problem

4. A study of the weights of all linemen in the National Football League.

5. A study of U.S. residents’ approval rating of the U.S. presidents.

Identify the Method of Collection

Simulation

Experiment

Observational Study

Survey – Census

Survey – Sample

Sampling Techniques

1. Random/Simple Random - All samples of the same size are equally likely

2. Stratified - Divide the population into groups (strata) and select a random sample from each group. Strata could be age groups, genders or levels of education

3. Cluster - Divide the population into clusters (subgroups) and randomly select one or more clusters to sample.

4. Systematic - Choose a starting value at random. Then choose sample members at regular intervals.

5. Convenience - Choose readily available members of the population for your sample.

Cluster, Random, Stratified, Systematic, or Convenience?

1. You select a class at random and question each student in the class.

2. You divide the student population with respect to majors and randomly select and question some students in each major

3. You assign each student a number and generate random numbers. You then question each student whose number is randomly selected.

1. You select a class at random and question each student in the class.

2. You divide the student population with respect to majors and randomly select and question some students in each major

3. You assign each student a number and generate random numbers. You then question each student whose number is randomly selected.

1. Cluster 2. Stratified 3. Random

Cluster, Random, Stratified, Systematic, or Convenience?

WARNING! Beware of Bias

Biased samples are not representative of the populationThere are 3 types of bias:

1. Sampling Bias – the technique used to obtain the individuals to be in the sample tends to favor one part of the population over another.

Convenience Samples Not having a full list of population members to draw from

2. Nonresponse Bias – exists when individuals selected do not respond to the survey have different opinions from those who do respond.

Mail in surveys, phone calls, etc

3. Response Bias – exists when the answers do not reflect the true feelings of the respondent.

Wording of questions – written in a way that lead to biased answers.

Section 1.3:Observational

Studies & Experiments

Objectives Understand the difference

between observational studies and experiments

Learn about and be able to discuss the concepts of experiments using appropriate vocabulary.

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Observational Studies In an observational study, researchers

don’t assign choices.◦ Example: the relationship between music

education and grades.◦ Researchers do not assign students to get music

education and simply observed students “in the wild”

Observational studies are valuable for discovering trends and possible relationships.

However, it is not possible for observational studies to demonstrate cause and effect

Experiments

In an experiment, the experimenter must identify at least one explanatory variable (factor) to manipulate and at least one response variable to measure.

An experiment is a study design that allows us to prove a cause-and-effect relationship.

The three key elements of a well-designed experiment are control, randomization, and replication.

Experiment Vocabulary

In general, the individuals on whom or which we experiment are called experimental units. ◦ When humans are involved, they are

commonly called subjects or participants.

The specific values that the experimenter chooses for a factor are called the levels of the factor.

A treatment is a combination of specific levels from all the factors that an experimental unit receives.

ExampleIs diet or exercise effective in combating insomnia? Forty volunteers suffering from insomnia agreed to participate in a month long study. Half were randomly assigned to a special no dessert diet and the other half ate dessert as usual. Half of the people in each group were randomly assigned to an exercise program, while the others did not exercise. Those who ate no desserts and engaged in exercise showed the most improvement.(a) What subjects were studied?

(b) What are the factors in this experiment and how many levels are in each factor?

(c) What is the number of treatments?

(d) What is the response variable that is measured?

SolutionIs diet or exercise effective in combating insomnia? Forty volunteers suffering from insomnia agreed to participate in a month long study. Half were randomly assigned to a special no dessert diet and the other half ate dessert as usual. Half of the people in each group were randomly assigned to an exercise program, while the others did not exercise. Those who ate no desserts and engaged in exercise showed the most improvement.(a) What subjects were studied?

People suffering from insomnia

(b) What are the factors in this experiment and how many levels are in each factor?

2 factors: Dessert and Exercise (2 levels each)

(c) What is the number of treatments?

4 treatments

(d) What is the response variable that is measured?

improvement in ability to sleep

Completely Randomized Design: All experimental units have an equal chance of receiving any treatment.

Randomized Block Design: Randomization only occurs within blocks.

Matched Pairs Design: Used when there are 2 “treatments”. The pairs are created by some common variable, one person receives one treatment the pair received treatment 2.

Types of Experiments

Placebos and Blinding A “fake” treatment that looks just like the treatment

being tested is called a placebo.

In order to avoid the bias that might result from knowing the treatment assigned, we use blinding.

Blinding is when the subjects do not know whether they are receiving a treatment or a placebo.

In a double-blind experiment neither the subjects nor the experiments know who is receiving the treatment or the placebo.

The placebo effect occurs when a subject reacts favorably to a placebo when they have been given no medical treatment.