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1-1 Overview 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)

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1-1 Overview

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


Definitions

Population

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.

Definitions


Example

Identify 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.

Example


Statistics

Broken into 2 areas

Descriptive Statistics

Inferencial Statistics

Definitions


Definitions1

Descriptive Statistics

Describes 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

Definitions

Test Question


Parameter vs. Statistic

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


Parameter

a numerical measurement describing some characteristic of a population

Definitions

population

parameter


sample

statistic

Definitions

  • Statistic

  • a numerical measurement describing some characteristic of a sample


Examples

  • 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.


Variable

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


Definitions

  • 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


Examples

  • Quantitative data

  • x = The number of FLC students with blue eyes

  • Qualitative (or categorical or attribute) data

  • y = The eye color of FLC students


Example

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

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


Discrete

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


Discrete

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


Univariate Data

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


Univariate Data

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


Uses of statistics

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 Statistics


1 3 design of experiments
1- 3  of statistical methodsDesign of Experiments


Designing an experiment

Identify your objective  of statistical methods

Collect sample data

Use a random procedure that avoids bias

Analyze the data and form conclusions

Designing an Experiment


Definition  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

  • Experiment

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


  • 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)

  • Event (Response)

  • observe its effects on the subject(s) (Observe)

    • Example: Experiment: Toss a coin

    • Event: Observe a tail


  • 1 4 sampling
    1- 4  of statistical methodsSampling


    Random  of statistical methods(type discussed in this class)

    Systematic

    Convenience

    Stratified

    Cluster

    Methods of Sampling


    Ti 83 calculator
    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 abuses of statistics
    1-5  of statistical methodsAbuses of Statistics

    • Bad Samples

    • Small Samples

    • Loaded Questions

    • Misleading Graphs

    • Pictographs

    • Precise Numbers

    • Distorted Percentages

    • Partial Pictures

    • Deliberate Distortions


    Abuses of statistics

    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 Statistics


    Abuses of statistics1
    Abuses 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 statistics2
    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 statistics3
    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 statistics4
    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 statistics5
    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 statistics6

    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 Statistics


    Factorial 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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