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Chapter 1 - What is Statistics?

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Title: Chapter 1 - What is Statistics?


1
John Mainieri Mesa Community College
2
I LOVE STATISTICS!
3
Chapter 1 Data and Statistics
I need help!
  • Applications in Business and Economics
  • Data
  • Data Sources
  • Descriptive Statistics
  • Statistical Inference
  • Statistical Analysis
  • Using Microsoft Excel

4
Chapter 1 Objectives
  • To present a broad overview of the subject of
    statistics and its applications
  • To distinguish between descriptive and
    inferential statistics
  • To discuss sources of data
  • To introduce methods of sample selection
  • To study how to evaluate survey worthiness

5
Do Height of Students Exercise
  • Use Excel worksheet

6
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7
HISTOGRAM
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10
Grouped Data- Rounding RuleA sample of light
trucks using diesel fuel revealed these mileage's
per gallon of fuel used.
11
Data and Data Sets
  • Data are the facts and figures collected,
    summarized, analyzed, and interpreted.
  • The data collected in a particular study are
    referred
  • to as the data set.

12
Data Set
One Piece of Data
13
Elements, Variables, and Observations
  • The elements are the entities on which data are
  • collected.
  • A variable is a characteristic of interest for
    the elements.
  • The set of measurements collected for a
    particular
  • element is called an observation.

14
Variables
Element Names
Observation
15
Scales of Measurement
Scales of measurement include
Nominal
Interval
Ordinal
Ratio
The scale determines the amount of information
contained in the data.
The scale indicates the data summarization and
statistical analyses that are most appropriate.
16
Ordinal
Ratio
Nominal
17
Scales of Measurement
  • Nominal

Data are labels or names used to identify an
attribute of the element.
A nonnumeric label or numeric code may be used.
18
Scales of Measurement
  • Ordinal

The data have the properties of nominal data
and the order or rank of the data is meaningful.
A nonnumeric label or numeric code may be used.
19
Scales of Measurement
  • Ordinal

Example Students of a university are
classified by their class standing using a
nonnumeric label such as Freshman,
Sophomore, Junior, or Senior.
Alternatively, a numeric code could be used for
the class standing variable (e.g. 1 denotes
Freshman, 2 denotes Sophomore, and so on).
20
Scales of Measurement
  • Interval

The data have the properties of ordinal data,
and the interval between observations is
expressed in terms of a fixed unit of measure.
Interval data are always numeric.
21
Scales of Measurement
  • Interval

Example Melissa has an SAT score of 1205,
while Kevin has an SAT score of 1090.
Melissa scored 115 points more than Kevin.
22
Scales of Measurement
  • Ratio

The data have all the properties of interval
data and the ratio of two values is meaningful.
Variables such as distance, height, weight, and
time use the ratio scale.
This scale must contain a zero value that
indicates that nothing exists for the variable
at the zero point.
23
Scales of Measurement
  • Ratio

Example Melissas college record shows 36
credit hours earned, while Kevins record
shows 72 credit hours earned. Kevin has
twice as many credit hours earned as Melissa.
24
Qualitative and Quantitative Data
Data can be classified as being qualitative or
quantitative.
The statistical analysis that is appropriate
depends on whether the data for the variable are
qualitative or quantitative.
In general, there are more alternatives for
statistical analysis when the data are
quantitative.
25
Qualitative Data
Labels or names used to identify an attribute of
each element
Often referred to as categorical data
Can be either numeric or nonnumeric
Appropriate statistical analyses are rather
limited
26
Quantitative Data
Quantitative data indicate how many or how
much
discrete, if measuring how many
continuous, if measuring how much
Quantitative data are always numeric.
Ordinary arithmetic operations are meaningful
for quantitative data.
27
Scales of Measurement
Data
Qualitative
Quantitative
Numerical
Numerical
Non-numerical
Nominal
Ordinal
Nominal
Ordinal
Interval
Ratio
28
Quantitative
Qualitative or Categorical
29
Homework AssignmentData and Statistics Exercise
See hand-out.
30
Is this inferential or descriptive statistics?
31
Statistical Methods
  • Descriptive statistics
  • Collecting and describing data
  • Inferential statistics
  • Drawing conclusions and/or making decisions
    concerning a population based only on sample data

32
Descriptive Statistics
  • Collect data
  • e.g. Survey
  • Present data
  • e.g. Tables and graphs
  • Characterize data
  • e.g. Sample mean

33
Inferential Statistics
  • Estimation
  • e.g. Estimate the population mean weight using
    the sample mean weight
  • Hypothesis testing
  • e.g. Test the claim that the population mean
    weight is 120 pounds

Drawing conclusions and/or making decisions
concerning a population based on sample results.
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35
Sampling
  • What is the mean (average) grade for the two
    semesters?
  • You can add-up all of the grades and divide by
    the number of grades (students) or
  • You can take a sample!

36
Population Sample
37
and FUN too!!!
38
Would you take responsibility for quality if you
could sample only ONE meatball?
39
Reasons for Drawing a Sample
  • Less time consuming than a census
  • Less costly to administer than a census
  • Less cumbersome and more practical to administer
    than a census of the targeted population
  • The destructive nature of some tests (think
    meatballs)

40
Sampling
  • What kind of sample will you take?
  • Probability Sample or Non-probability Sample
  • Will you use a Simple Random Sample, a
    Systematic, Stratified , or Cluster Sample?

41
Types of Sampling Methods
Samples
Probability Samples
Non-Probability Samples
Simple Random
Stratified
Judgement
Chunk
Cluster
Systematic
Quota
Statistics for Managers, Levine,Berenson, Stephen
42
Probability Samples
Subjects of the sample are chosen based on known
probabilities.
Probability Samples
Simple Random
Systematic
Stratified
Cluster
Statistics for Managers, Levine,Berenson, Stephen
43
Simple Random Samples
  • Every individual or item from the frame has an
    equal chance of being selected
  • Selection may be with replacement or without
    replacement
  • Samples obtained from table of random numbers or
    computer random number generators

44
Systematic Samples
  • Decide on sample size n
  • Divide frame of N individuals into groups of k
    individuals kN/n
  • Randomly select one individual from the 1st group
  • Select every k-th individual thereafter

N 64 n 8 k 8
First Group
45
Stratified Samples
  • Population divided into two or more groups
    according to some common characteristic
  • Simple random sample selected from each group
  • The two or more samples are combined into one

46
Cluster Samples
  • Population divided into several clusters, each
    representative of the population
  • Simple random sample selected from each
  • The samples are combined into one

Population divided into 4 clusters.
47
N86
48
How to Sample
  • Assign a Code Number (sometimes called a
    reference number) to each grade.
  • Take a sample (n30) of the grades. Use the table
    of random numbers from Table E.1 on pages 702 or
    703 of your text.
  • Select a random starting point.
  • Which two digits will you use between 01 and 86?
    (Right two?)
  • Will you sample with replacement or without
    replacement? Why?

49
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50
Random Numbers Using Excel
  • Use the function
  • RANDBETWEEN
  • (Go to the Excel file via the activities page on
    the web. See the next two slides first.)

51
HOT TIPSAdd Analysis Tool Pack to Excel
  • After loading Excel- Go through the following
    sequence.
  • Click on Tools, Add-ins, Analysis Tool Pack, and
    Analysis Tool Pack-VBA, OK
  • (You may have to have an Excel file loaded to do
    this)

52
HOT TIPSManual Recalculation of Random Number
Table
  • After loading your random number table
  • click Tools, Options, Calculation,Manual, OK
  • when you want to recalculate the random numbers,
    press the F9 key.

53
Evaluating Survey Worthiness
  • What is the purpose of the survey?
  • Is the survey based on a probability sample?
  • Coverage error appropriate frame
  • Non response error follow up
  • Measurement error good questions elicit good
    responses
  • Sampling error always exists

54
Types of Survey Errors
  • Coverage error
  • Non response error
  • Sampling error
  • Measurement error

Excluded from frame.
Follow up on non responses.
Chance differences from sample to sample.
Bad Question!
55
Sampling Error
  • Compute the mean of your sample.
  • Compare it to the mean of the population on the
    following slide.
  • Why is it different?
  • The difference between the sample statistic and
    the population parameter is called sampling
    error.

56
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57
Inferential Statistics
  • When we take a sample to estimate a population
    parameter it is called ________.
  • The sample statistic is the sample mean.
  • The population parameter is the population mean.

58
Interval Estimates
  • If the sample mean is not equal to the population
    mean, of what use is it?
  • Would you be satisfied if you could be 95
    confident that the population mean was between
    two values? How about 99 confident?

59
Hypothesis Testing
  • In the semester grade example we asked the
    question, What was the mean grade?
  • We can also make statements about the population
    mean and then test to see if our statement
    (hypothesis) is correct.
  • Are you worried about rejecting the hypothesis
    when it is true? Can this happen if you use a
    sample?

60
Linear Regression and Correlation
  • What factors may be related to a students
    semester grade?

61
The Samplers by Rembrandt
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63
Louise
64
GBS 221, Chapter 1Introduction and Data
Collection
  • John Mainieri
  • Mesa Community College

65
Chapter 1and an Introduction to the course
  • Do you want this course to be graded on a
    curve?

66
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67
Is this a population or a sample? Why?
What is the Frame (data source)?
What is the random variable?
Is the random variable categorical or numerical?
Is it discrete or continuous?
What else would you like to know about the data?
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Semester Grades, Fall 98, Spring 99
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