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1-1 Overview 1- 2 Types of Data 1- 3 Random Sampling 1- 4 Design of ExperimentsPowerPoint Presentation

1-1 Overview 1- 2 Types of Data 1- 3 Random Sampling 1- 4 Design of Experiments

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Experiment applies treatments to experimental units or subjects and attempts to isolate the effects of the treatments on a response variable

Event (Response) observe its effects on the subject(s) (Observe)

1- 2 Types of Data

1- 3 Random Sampling

1- 4 Design of Experiments

1- 5 Abuses of Statistics

Chapter 1

Introduction to Statistics

Statistics (Definition)

A collection of methods for planning experiments, obtaining data, and then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions based on the data

1-1 Overview

The complete collection of all data to be studied.

Census

The collection of data from every member of the population.

Sample

The collection of data from a subset of the population.

DefinitionsIdentify the population and sample in the study

A quality-control manager randomly selects 50 bottles of Coca-Cola to assess the calibration of the filing machine.

ExampleDescribes data usually through the use of graphs, charts and pictures. Simple calculations like mean, range, mode, etc., may also be used.

Inferencial Statistics

Uses sample data to make inferences (draw

conclusions) about an entire population

DefinitionsTest Question

Variables

Quantitative Data vs. Qualitative Data

Nominal Data vs. Ordinal Data

Discrete Data vs. Continuous Data

Univariate Data vs. Bivariate Data

1-2 Types of Data

a numerical measurement describing some characteristic of a population

Definitions

population

parameter

statistic

Definitions

- Statistic
- a numerical measurement describing some characteristic of a sample

- Parameter
- 51% of the entire population of the US is Female
- Statistic
- Based on a sample from the US population is was determined that 35% consider themselves overweight.

characteristics of the individuals (data) being measured or observed

represented as a symbol (x, Y, s, σ, µ, etc.).

Definitions

We further describe variables by distinguishing between Qualitative and Quantitative data (variables)

Definitions

Qualitative

Variables

Quantitative

- Quantitative data
- Numbers representing counts or measurements
- Qualitative (or categorical or attribute) data
- Can be separated into different categories that are distinguished by some nonnumeric characteristics

- Quantitative data
- x = The number of FLC students with blue eyes
- Qualitative (or categorical or attribute) data
- y = The eye color of FLC students

Quiz Question

- Of the adult U.S. population, 36% has an allergy. A sample of 1200 randomly selected adults resulted in 33.2% reporting an allergy.
- 1. Describe the variable and give its type
- 2. Describe the population
- 3. Describe the sample
- 4. What is the value of the parameter?
- 5. What is the value of the statistic?
- 6. Which statement is descriptive in nature?
- 7. Which statement is inferential in nature?

We further describe qualitative data by distinguishing between Nominal and Ordinal data

Definitions

Nominal

Qualitative Data

Ordinal

Nominal data are categorical data where the order of the categories is arbitrary

Example: race/ethnicity has values 1=White, 2=Hispanic, 3=American Indian, 4=Black, 5=Other. Note that the order of the categories is arbitrary.

Ordinal

Ordinal data are categorical data where there is a logical ordering to the categories

Example: scale that you see on many surveys: 1=Strongly disagree; 2=Disagree; 3=Neutral; 4=Agree; 5=Strongly agree.

Definitions

We further describe quantitative data by distinguishing between discrete and continuous data

Definitions

Discrete

Quantitative Data

Continuous

data result when the number of possible values is either a finite number or a ‘countable’ number of possible values

0, 1, 2, 3, . . .

Continuous

(numerical) data result from infinitely many possible values that correspond to some continuous scale or interval that covers a range of values without gaps, interruptions, or jumps

Definitions

2

3

The number of eggs that hens lay; for example, 3 eggs a day.

Continuous

The amounts of milk that cows produce; for example, 2.343115 gallons a day.

Examples

Involves the use of one variable (X)

Does not deal with causes and relationship

Bivariate Data

Involves the use of two variables (X and Y)

Deals with causes and relationships

Definitions

How many first year students attend FLC?

Bivariate Data

Is there a relationship (association) between then number of females in Computer Programming and their scores in Mathematics?

Example

1. Center: A representative or average value that indicates where the middle of the data set is located

2. Variation: A measure of the amount that the values vary among themselves or how data is dispersed

3. Distribution: The nature or shape of the distribution of data (such as bell-shaped, uniform, or skewed)

4. Outliers: Sample values that lie very far away from the vast majority of other sample values

5. Time: Changing characteristics of the data over time

Important Characteristics of Data

Almost all fields of study benefit from the application of statistical methods

Sociology, Genetics, Insurance, Biology, Polling, Retirement Planning, automobile fatality rates, and many more too numerous to mention.

Uses of Statistics1- 3 of statistical methodsDesign of Experiments

Identify your objective of statistical methods

Collect sample data

Use a random procedure that avoids bias

Analyze the data and form conclusions

Designing an ExperimentDefinition of statistical methods

- Observational Study
- measures the characteristics of a population by studying individuals in a sample, but does not attempt to manipulate or influence variables of interest

Examples of statistical methods

- Observational Study
- A poll is conducted in which 500 people are asked whom they plan to vote for in the upcoming election
- Experiment
- To determine the effect of type of fertilizers a farmer might divide 20 tomato plants into two groups. Group 1 received fertilizer 1 and Group 2 receives fertilizer 2. All other factors for the two groups are kept the same (sunlight, water, etc).

Experimental Design of statistical methods

- Define the treatment, experimental unit and response variable in the following experiment.
- To determine the effect of type of fertilizers a farmer might divide 20 tomato plants into two groups. Group 1 received fertilizer 1 and Group 2 receives fertilizer 2.
- All other factors for the two groups are kept the same (sunlight, water, etc). i.e., Confounding does not occur

Confounding of statistical methods

- Lurking variables:
- A variable that was not considered in a study but may affect study.

- Confounding:
- Occurs in a study when lurking variables affect the outcome.

Confounding of statistical methods

- Example:
- Flu shots are associated with a lower risk of being hospitalized or dying from influenza.

- Possible Lurking Variables:
- age
- health status
- mobility of the senior

Probability Experiment of statistical methods

- Experiment
- apply some treatment (Action)

- Example: Experiment: Toss a coin
- Event: Observe a tail

1- 4 of statistical methodsSampling

Random of statistical methods(type discussed in this class)

Systematic

Convenience

Stratified

Cluster

Methods of Sampling

TI-83 Calculator of statistical methods

Using a random number generator

- Press Math
- Cursor over to PRB
- Press “5” RandInt
- Enter (low value, high value, sample size)
Example:

RandInt(1,30,5) will select 5 random numbers between 1 and 30

Note: if you get duplicate numbers you should draw more numbers than you need and ignore the duplicates.

Definitions of statistical methods

- Simple Random Sample
- members of the population are selected in such a way that each has an equal chance of being selected (if not then sample is biased)

Random Sampling of statistical methods- selection so that each has an equalchance of being selected

Systematic Sampling of statistical methods

Select some starting point and then

select every K th element in the population

Convenience Sampling of statistical methods

use results that are easy to get

Stratified Sampling of statistical methods

subdivide the population into at

least two different subgroups that share the same characteristics, then draw a sample from each subgroup (or stratum)

Cluster Sampling of statistical methods- divide the population into sections (or clusters); randomly select some of those clusters; choose all members from selected clusters

Sampling Error of statistical methods

the difference between a sample result and the true population result; such an error results from chance sample fluctuations.

Nonsampling Error

sample data that are incorrectly collected, recorded, or analyzed (such as by selecting a biased sample, using a defective instrument, or copying the data incorrectly).

Errors in Sampling

Sampling Error (Example) of statistical methods

A recent poll showed potential voters favored the proposition 52% to 48%. The margin of error for the poll was 3%.

Nonsampling Error (Example)

During presidential election or 2000, early results from an Florida exit poll were skewed by a programming error.

Errors in Sampling

1-5 of statistical methodsAbuses of Statistics

- Bad Samples
- Small Samples
- Loaded Questions
- Misleading Graphs
- Pictographs
- Precise Numbers
- Distorted Percentages
- Partial Pictures
- Deliberate Distortions

Bad Samples of statistical methods

Inappropriate methods to collect data. BIAS (on test) Example: using phone books to sample data.

Small Samples (will have example on exam)

We will talk about same size later in the course. Even large samples can be bad samples.

Loaded Questions

Survey questions can be worked to elicit a desired response

Abuses of StatisticsAbuses of Statistics of statistical methods

- Bad Samples
- Small Samples
- Loaded Questions
- Misleading Graphs
- Pictographs
- Precise Numbers
- Distorted Percentages
- Partial Pictures
- Deliberate Distortions

Salaries of People with Bachelor’s Degrees and with High School Diplomas

$40,500

$40,500

$40,000

$40,000

30,000

35,000

$24,400

30,000

20,000

$24,400

25,000

10,000

20,000

0

Bachelor High School

Degree Diploma

Bachelor High School

Degree Diploma

(a)

(b)

(test question)

We should analyze the School Diplomasnumericalinformation given in the graph instead of being mislead by its general shape.

Abuses of Statistics School Diplomas

- Bad Samples
- Small Samples
- Loaded Questions
- Misleading Graphs
- Pictographs
- Precise Numbers
- Distorted Percentages
- Partial Pictures
- Deliberate Distortions

Double the length, width, and height of a cube, and the volume increases by a factor of eight

What is actually intended here? 2 times or 8 times?

Abuses of Statistics volume increases by a factor of eight

- Bad Samples
- Small Samples
- Loaded Questions
- Misleading Graphs
- Pictographs
- Precise Numbers
- Distorted Percentages
- Partial Pictures
- Deliberate Distortions

Abuses of Statistics volume increases by a factor of eight

- Precise Numbers
There are 103,215,027 households in the US. This is actually an estimate and it would be best to say there are about 103 million households.

- Distorted Percentages
100% improvement doesn’t mean perfect.

- Deliberate Distortions
Lies, Lies, all Lies

Abuses of Statistics volume increases by a factor of eight

- Bad Samples
- Small Samples
- Loaded Questions
- Misleading Graphs
- Pictographs
- Precise Numbers
- Distorted Percentages
- Partial Pictures
- Deliberate Distortions

Partial Pictures volume increases by a factor of eight

“Ninety percent of all our cars sold in this country in the last 10 years are still on the road.”

Problem: What if the 90% were sold in the last 3 years?

Abuses of StatisticsFactorial Notation volume increases by a factor of eight

8! = 8x7x6x5x4x3x2x1

Order of Operations

( )

POWERS

MULT. & DIV.

ADD & SUBT.

READ LIKE A BOOK

Keep number in calculator as long a possible

Using Formulas

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