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HRIR 8011

• “Statistics is a collection of procedures and principles for gaining and processing information in order to make decisions when faced with uncertainty.” (Utts, p. 3)

• Objective of HRIR 8011: learning to use information to make good (not lousy) decisions, which requires• Collecting information (data)• Analyzing data• Interpreting the results of the analyses

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Consider…

• Employees who are dissatisfied with their job are more likely to vote for a union than employees who are satisfied (HRIR 8071)

• Structured interviews are better than open-ended interviews when selecting new employees (HRIR 8031)

• An HR manager asks what is the market rate of pay?• An HR manager asks what can I do to reduce

absenteeism?• If low paid workers are absent more, do you raise

wages?

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The Focus of HRIR 8011

• Our focus…the procedures and principles of using information correctly

• When Professor Tubre says that you should use a cognitive ability test, question it! How do we know we should use it?

• What information is this conclusion based on?

• How were the data collected? Does that seem applicable to my situation?

• How were the data analyzed? Was that appropriate? What did they miss?

• Are the conclusions justified based on the data and the results?

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Index Numbers

• Index value = 100 X

• Price Index Example: if current cost is $3,300 and base period costs is $2,400 then

• Price Index = 100 X (3,300/2,400) = 137.5

• Interpretation: the current period is 37.5% percent higher than the base period

current value

base period value

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Time Series

5.0

5.5

6.0

6.5

7.0

7.5

8.0

8.5

Year 1 Year 2 Year 3

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Measurement

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Measurement

• Validity

• Reliability

• Bias

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Seven Measurement

Pitfalls• Deliberate bias• Unintentional bias• Desire to please• Asking the uninformed• Unnecessary complexity• Ordering of questions• Confidentiality and anonymity

• Source: Jessica M. Utts, Seeing Through Statistics, 2nd ed. (Pacific Grove, CA: Duxbury, 1999), p. 32.

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Cumulative Frequency

• Recall Eggs R Us

Race | Freq. Percent Cumul.‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑+‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑ African American | 87 15.10 15.10 Asian American | 6 1.04 16.15 Hispanic | 25 4.34 20.49 white | 458 79.51 100.00‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑+‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑‑ Total | 576 100.00

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Percentiles

• The pth percentile of a sample is the value for which at most p% of the measurements are less than that value and at most (100-p)% of the measurements are greater than that value

• Median

• Quartiles

• Deciles

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Box Plot

SmallestLargest

LowerQuartile

UpperQuartile

Median

{Middle halfof the data

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Box Plot

0 10 20 30 40

Age

0 2 4 6 8 10

Tenure

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A Box Plot in Labor

Source: Alan B. Krueger and Alexandre Mas, “Strikes, Scabs, and Tread Separations: Labor Strife and the Production of Defective Bridgestone/Firestone Tires,” Journal of Political Economy 112 (April 2004), pp. 252-289 at 274.

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A Simple cdf Example

xRelative

FrequencyCumulative Frequency

1 0.125 0.125

3 0.125 0. 250

4 0. 250 0.500

5 0.125 0.625

6 0.125 0.750

9 0.125 0.875

10 0.125 1.000

Consider the simple data set:

1, 4, 6, 4, 10, 9, 3, 5

This yields the following relative and cumulative frequencies

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A Simple cdf Example

0.000

0.125

0.250

0.375

0.500

0.625

0.750

0.875

1.000

0 1 2 3 4 5 6 7 8 9 10

xRelative

FrequencyCumulative Frequency

1 0.125 0.125

3 0.125 0. 250

4 0. 250 0.500

5 0.125 0.625

6 0.125 0.750

9 0.125 0.875

10 0.125 1.000

1. To make the cdf, start at zero and move to the right along the x-axis until you come to the first value of x (that is, x=1)

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A Simple cdf Example

0.000

0.125

0.250

0.375

0.500

0.625

0.750

0.875

1.000

0 1 2 3 4 5 6 7 8 9 10

xRelative

FrequencyCumulative Frequency

1 0.125 0.125

3 0.125 0. 250

4 0. 250 0.500

5 0.125 0.625

6 0.125 0.750

9 0.125 0.875

10 0.125 1.000

2. The value x=1 accounts for 0.125 of the cumulative frequency so the cdf jumps up to 0.125

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A Simple cdf Example

0.000

0.125

0.250

0.375

0.500

0.625

0.750

0.875

1.000

0 1 2 3 4 5 6 7 8 9 10

xRelative

FrequencyCumulative Frequency

1 0.125 0.125

3 0.125 0. 250

4 0. 250 0.500

5 0.125 0.625

6 0.125 0.750

9 0.125 0.875

10 0.125 1.000

3. Now continue to the right until you get to the next value (x=3) at which point the cdf jumps up another 0.125 to 0.250.

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A Simple cdf Example

0.000

0.125

0.250

0.375

0.500

0.625

0.750

0.875

1.000

0 1 2 3 4 5 6 7 8 9 10

xRelative

FrequencyCumulative Frequency

1 0.125 0.125

3 0.125 0. 250

4 0. 250 0.500

5 0.125 0.625

6 0.125 0.750

9 0.125 0.875

10 0.125 1.000

4. At x=4, note that the relative frequency is 0.25 (recall that there were two occurrences of 4 in the data set) so the cdf jumps 0.25 to 0.50.

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A Simple cdf Example

0.000

0.125

0.250

0.375

0.500

0.625

0.750

0.875

1.000

0 1 2 3 4 5 6 7 8 9 10

xRelative

FrequencyCumulative Frequency

1 0.125 0.125

3 0.125 0. 250

4 0. 250 0.500

5 0.125 0.625

6 0.125 0.750

9 0.125 0.875

10 0.125 1.000

5. Continuing for the remaining x values yields the completed cdf.

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Birth of a Distribution

< 5 5 to 9 > 9

3 Bins

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Birth of a Distribution

<2 2-4 4-6 6-8 8-1010-12 >12

7 Bins

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Birth of a Distribution

15 Bins

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Birth of a Distribution

33 Bins

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Birth of a Distribution

1000 Bins

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Different Distributions

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Even More Distributions

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Symmetrical Distributions

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Symmetrical Distribution

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Positively Skewed

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Negatively Skewed

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Symmetrical Distribution

Bell-shaped, symmetrical distribution

Will be very important for

statistical inference

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Additional Variance Example

0

0.5

1

1.5

2

2.5

3

11 12 13 14 15 16 170

1

2

3

4

5

6

7

8

9

11 12 13 14 15 16 17

Cyberland (1st 10 obs) Contrived Sample

=13.9X =13.9X

=1.97 =0.30