STATISTICS FOR MANAGERS

A. Introduction to Statistics

1. Definitions

a. Descriptive statistics - describes the characteristics of a set of data

b. Inferential statistics - estimate characteristics of a population based on sample results

c. Population - totality of items under consideration

d. Sample - subset of population selected for analysis

e. Parameter - summary measure that describes a characteristic of a population

f. Statistic - summary measure that describes a characteristic of a sample from a population

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2. Data

a.  Variable types

(1) Time-series - hold unit constant, vary across time

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(2) Cross-section - hold time constant, vary across units

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(3) Categorical data - categories

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(4) Numerical data - numeric results

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(a) Discrete data - results from a counting process

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(a) Continuous data - results from a measuring process

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b.  Measurement scales

(1)  Nominal scale - no ranking of categories

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(2)  Ordinal scale - ranking of categories is implied

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(3)  Interval scale - no true zero point

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(4)  Ratio scale - involves a true zero point

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c.  Data sources

(1) Primary source - collect own data

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(2) Secondary source - data collected by someone else

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• Data distributed by individuals or organizations, experiments, surveys, observational studies, collected by business activities

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d. Data cleaning and recoding

(1)  Outliers - values vastly different from most of the other values

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(2)  Missing values - advanced software can deal with missing values

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(3)  Recoded variables - use original variables to create other variables

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3. Sampling

a. Concepts

(1) Frame - list of all items from which sample will be drawn

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(2) Replacement

• Sampling with replacement - observation returned to frame

• Sampling without replacement - observation not returned to frame

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(3) Types of samples

(a)  Probability sample - sample chosen on basis of known probabilities

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(b)  Nonprobability sample - probability of sample being chosen unknown

i)  Convenience sample - select items that are easy, inexpensive, and/or convenient

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ii)  Judgment sample - collect opinions of experts

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• World's Most Influential Person

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(4) Randomness

• 1970 Draft Lottery

• Random number table - Table E.1, p. 692 - 693

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• Spreadsheet

Excel function: =RANDBETWEEN(#1,#2)

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b. Sampling methods

• Used when dealing with probability samples

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(1) Simple random sample - each item equally likely to be chosen, use random numbers

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(2) Systematic sample - choose every kth item from a list

• Easier to do if data already in the form of a list

• Also easier if one item produced at a time

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(3) Stratified sample - divide into categories, random sample from each category

• Want sample to match characteristics of population

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(4) Cluster sample

• Divide population into clusters

• Choose clusters at random

• Random sample from each cluster

- Should be homogeneous across clusters, heterogeneous within clusters

- Less costly if observations scattered geographically

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c. Sources of error

(1)  Coverage error - exclude part of population

• Selection bias

Ex. - Literary Digest

• Video (@ 2:57)

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(2)  Nonresponse error - some people don’t respond

Ex. - Call screening

• Upper and lower classes less likely to respond

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(3)  Sampling error - wrong individuals chosen by chance

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(4)  Measurement error

(a) Question wording - ambiguous or leading

Ex. - Unemployment rate

Microsoft Rigged the Survey?

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(b) Interviewer’s effect on respondent - try to please interviewer

• "Halo" effect

Ex. - Race

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(c) Effort made by respondent - exaggeration, lack of effort

Ex. - TV ratings, consumer surveys

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• Key ethical issue is intent - okay if errors made unintentionally, unethical if deliberately done

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4. Descriptive Statistics

a. Measures of central tendency

(1) Mean (arithmetic mean)

(a) Population:

(b) Sample:

Ex. - Yen / $

AVERAGE function in Excel: =AVERAGE(data range)

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(2) Median

• Value where half of observations are above, half below

Ex. - Yen / $

MEDIAN function in Excel: =MEDIAN(data range)

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b. Measures of variation

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• Variance and standard deviation

(1) Population

Ex. - Yen / $

Population variance in Excel: =VARP(data range)

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(2) Sample

Ex. - Yen / $

Sample variance in Excel: =VAR(data range)

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(3) Standard deviation

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Ex. - Yen / $

Population standard deviation in Excel: =STDEVP(data range)

Sample standard deviation in Excel: =STDEV(data range)

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• StockCharts.com

• All measures given in the Descriptive Statistics function of Excel: Data | Data Analysis | Descriptive Statistics