Transcript Chapter 1 Slides
Chapter 1 Introduction to Statistics 1-1 Overview 1- 2 Types of Data 1- 3 Abuses of Statistics 1- 4 Design of Experiments 1
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Overview 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 2
Definitions
Population
The complete collection of all data to be studied.
Sample
The subcollection data drawn from the population.
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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.
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Definitions
Statistics
Broken into 2 areas
Descriptive Statistics
Inferencial Statistics 5
Definitions
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 Test Question 6
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Types of Data
Parameter vs. Statistic
Quantitative Data vs. Qualitative Data
Discrete Data vs. Continuous Data 7
Definitions
Parameter
a numerical measurement describing some characteristic of a population population parameter 8
Definitions
Statistic
a numerical measurement describing some characteristic of a sample sample statistic 9
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.
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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 11
Examples
Quantitative data
The number of FLC students with blue eyes
Qualitative
(or categorical or attribute)
data
The eye color of FLC students 12
Definitions
We further describe quantitative data by distinguishing between
discrete
and
continuous
data Discrete Quantitative Data Continuous 13
Definitions
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 2 3 14
Examples
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.
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Definitions
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 16
Example
Univariate Data
How many first year students attend FLC?
Bivariate Data
Is there a relationship between then number of females in Computer Programming and their scores in Mathematics?
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Important Characteristics of Data 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 18
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.
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Abuses of Statistics
Bad Samples Small Samples Loaded Questions Misleading Graphs Pictographs Precise Numbers Distorted Percentages Partial Pictures Deliberate Distortions 20
Abuses of Statistics Bad Samples 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
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Abuses of Statistics
Bad Samples Small Samples Loaded Questions Misleading Graphs Pictographs Precise Numbers Distorted Percentages Partial Pictures Deliberate Distortions 22
Salaries of People with Bachelor’s Degrees and with High School Diplomas
$40,000
$40,500
$40,000
$40,500
35,000 30,000
$24,400
30,000 20,000
$24,400
25,000 10,000 20,000 Bachelor High School Degree Diploma (a)
(test question)
0 Bachelor High School Degree Diploma (b)
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We should analyze the
numerical
information given in the graph instead of being mislead by its general shape.
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Abuses of Statistics
Bad Samples Small Samples Loaded Questions Misleading Graphs Pictographs Precise Numbers Distorted Percentages Partial Pictures Deliberate Distortions 25
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?
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Abuses of Statistics
Bad Samples Small Samples Loaded Questions Misleading Graphs Pictographs Precise Numbers Distorted Percentages Partial Pictures Deliberate Distortions 27
Abuses of Statistics
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 28
Abuses of Statistics
Bad Samples Small Samples Loaded Questions Misleading Graphs Pictographs Precise Numbers Distorted Percentages Partial Pictures Deliberate Distortions 29
Abuses of Statistics Partial Pictures
“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?
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1-4
Design of Experiments
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Definition
Experiment
apply some treatment (Action)
Event
observe its effects on the subject(s) (Observe) Example: Experiment: Toss a coin Event: Observe a tail 32
Designing an Experiment Identify your objective Collect sample data Use a random procedure that avoids bias Analyze the data and form conclusions
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Methods of Sampling
Random (type discussed in this class) Systematic Convenience Stratified Cluster
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Definitions
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)
Simple Random Sample
(of size
n
) subjects selected in such a way that every possible sample of size
n
chance of being chosen has the same 35
Random Sampling
-
selection so that each has an
equal chance
of being selected 36
Systematic Sampling
Select some starting point and then select every K th element in the population 37
Convenience Sampling
use results that are easy to get 38
Stratified Sampling
subdivide the population into at least two different subgroups that share the same characteristics, then draw a sample from each subgroup (or stratum) 39
Cluster Sampling
-
divide the population into sections (or clusters); randomly select some of those clusters; choose all members from selected clusters 40
Definitions
Sampling Error 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).
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Using Formulas
Factorial Notation 8! = 8x7x6x5x4x3x2x1 Order of Operations 1. ( ) 2. POWERS 3. MULT. & DIV.
4. ADD & SUBT.
5. READ LIKE A BOOK Keep number in calculator as long a possible
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