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- 2 Types of Data
1- 3 Random Sampling
1- 4 Design of Experiments
1- 5 Abuses of Statistics
Introduction to Statistics
A collection of methods for planning experiments, obtaining data, and then organizing, summarizing, presenting, analyzing, interpreting, and drawing conclusions based on the data
The complete collection of all data to be studied.
The collection of data from every member of the population.
The collection of data from a subset of the population.Definitions
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
Broken into 2 areas
Describes data usually through the use of graphs, charts and pictures. Simple calculations like mean, range, mode, etc., may also be used.
Uses sample data to make inferences (draw
conclusions) about an entire populationDefinitions
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
characteristics of the individuals (data) being measured or observed
represented as a symbol (x, Y, s, σ, µ, etc.).
We further describe variables by distinguishing between Qualitative and Quantitative data (variables)
We further describe qualitative data by distinguishing between Nominal and Ordinal data
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 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.
We further describe quantitative data by distinguishing between discrete and continuous data
data result when the number of possible values is either a finite number or a ‘countable’ number of possible values
0, 1, 2, 3, . . .
(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
The number of eggs that hens lay; for example, 3 eggs a day.
The amounts of milk that cows produce; for example, 2.343115 gallons a day.
Involves the use of one variable (X)
Does not deal with causes and relationship
Involves the use of two variables (X and Y)
Deals with causes and relationships
How many first year students attend FLC?
Is there a relationship (association) between then number of females in Computer Programming and their scores in Mathematics?
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 Statistics
Identify your objective of statistical methods
Collect sample data
Use a random procedure that avoids bias
Analyze the data and form conclusionsDesigning an Experiment
Definition of statistical methods
Examples of statistical methods
Experimental Design of statistical methods
Confounding of statistical methods
Confounding of statistical methods
Probability Experiment of statistical methods
Random of statistical methods(type discussed in this class)
Methods of Sampling
Using a random number generator
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
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.
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
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.
Survey questions can be worked to elicit a desired responseAbuses of Statistics
Salaries of People with Bachelor’s Degrees and with High School Diplomas
Bachelor High School
Bachelor High School
We should analyze the School Diplomasnumericalinformation given in the graph instead of being mislead by its general shape.
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?
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.
100% improvement doesn’t mean perfect.
Lies, Lies, all Lies
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
MULT. & DIV.
ADD & SUBT.
READ LIKE A BOOK
Keep number in calculator as long a possible