Measurement of Safety Performance

Week Five:

Math and Stats Fundamentals

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Why sound math skills for safety performance measurement?

  • Measurements / metrics should be reliable and accurate
  • Collected data must be analyzed
  • Useful comparisons between results and goals
  • Determine trends / changes
  • Validate controls
  • Validate analysis methods
  • Reliable forecasting

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Data Formats

  • Categorical Data
  • Categories (i.e., male / female; departments, etc.)
  • Ordinal Data
  • Survey Data
  • Likert Scales
  • Interval Data
  • Ratio Data

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Categorical Data

  • Categories (i.e., male / female; departments, etc.)
  • Only differentiate membership in a group
  • Least useful from statistical analysis standpoint

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Ordinal Data

  • “order” / “ordering”
  • Survey Data (i.e. Likert Scales)
  • No value comparisons
  • More useful statistically than categorical, but low

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Interval Data

  • Continuous / continuous scale
  • Equality between points on the scale
  • Zero is simply a “place holder”
  • Fair degree of flexibility
  • Example: Fahrenheit / Celsius thermometer
  • More statistically useful than categorical and ordinal

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Ratio Data

  • Continuous data
  • Zero is not simply a placeholder (represents the absence of a characteristic)
  • Magnitude between values exist
  • Counting number of instances
  • Highest degree of statistical usefulness

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Descriptive Statistics

  • Population Data
  • Measures of Central Tendency
  • Mean
  • Median
  • Mode
  • Measures of Variability
  • Range
  • Variance
  • Standard Deviation
  • Correlation Coefficient

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Inferential Statistics

  • Sample Data
  • Statistics that Allow for an Inference
  • Sampling Distribution
  • Differences between Means
  • Chi Square

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Mean

Mean =

Σ X

n

Σ X = sum of the individual items / observations / values

n = total number of individual items / observations / values

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Median

  • Point where 50% of the values lie above and 50% lie below
  • First arrange values / items from lowest to highest
  • If odd # of values / items, then median is the “middle” value / item
  • If even # of values / items, then average the two “middle” values / items

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Mode

  • Most Frequently Occurring #
  • There may be more than one mode in a set of data

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Range

  • Difference between the lowest value and the highest value in the distribution
  • Arrange from lowest to highest; subtract lowest from highest

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Variance for Samples

σ² =

Σ (x-mean)² + (y-mean)²

N-1

N= total number of observation

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Variance for Total Population

σ² =

Σ (x-mean)² + (y-mean)²

N

N= total number of observation

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Standard Deviation

√σ²

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Standard Deviation =

Σ (v1 – mean)² + (v2-mean)²….

n

Calculate Std. Deviation

* If entire population sampled.

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Standard Deviation =

Σ (v1 – mean)² + (v2-mean)²….

(n -1)

Calculate Std. Deviation

* If sample of population.

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Normal Distribution

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UCL

LCL

MEAN

Chart1

18
23
14
17
21
33
20
25
22
12
12
10
Month
# of Accidents
Monthly Accident Control Chart

Sheet1

J F M A M J J A S O N D
18 23 14 17 21 33 20 25 22 12 12 10

Sheet1

Month
# of Accidents
Monthly Accident Control Chart

Sheet2

Sheet3

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Creating A Control Chart: Steps

  • Plot Data on A Graph
  • Calculate and Place Mean on the Chart
  • Calculate and Place Control Limits

UCL / LCL Calculations for #s of Events / Samples

  • 95% Statistical Significance = 2 std. deviations from mean = 1.96 = normal distribution
  • UCL = X + (Z x S)
  • LCL = X – (Z x S)
  • X = mean
  • Z = normal distribution (in safety use 1.96)
  • S= Std. Deviation of Population

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  • 95% Statistical Significance = 2 std. deviations from mean = 1.96 = normal distribution
  • UCL = p + 1.96 √ (p(1-p)/n)
  • LCL = p – 1.96 √ (p(1-p)/n)
  • p= mean proportion / %

UCL / LCL Calculations for Proportions / %

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Correlations

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Correlations

Chart1

5 14
7 12
9 10
11 8
13 3
15 0
Safe Behavior
Incidents

Sheet1

Safe Behavior Incidents
Qtr 1 5 14
Qtr 2 7 12
Qtr 3 9 10
Qtr 4 11 8
Qtr 5 13 3
Qtr 6 15 0
Qtr7 18 2
Qtr 8 21 1

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Correlations

Chart1

5 9
7 10
5 8
8 7
4 9
6 7
3 8
4 4
Safe Behavior
Incidents

Sheet1

Safe Behavior Incidents
Qtr 1 5 9
Qtr 2 7 10
Qtr 3 5 8
Qtr 4 8 7
Qtr 5 4 9
Qtr 6 6 7
Qtr7 3 8
Qtr 8 4 4

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Correlation: Purpose?

Chart1

10 19
18 22
28 24
36 25
40 22
# of Obs.
Safe Behavior

Sheet1

Column1 # of Obs. Safe Behavior
Qtr 1 10 19
Qtr 2 18 22
Qtr 3 28 24
Qtr 4 36 25
Qtr 5 40 22
To update the chart, enter data into this table. The data is automatically saved in the chart.

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Pearson Correlation Coefficient

Tip: Use a Calculator with stats functions.

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Correlations – The Numbers

Strong Negative

Strong Positive

No Correlation

-1

0

+1

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N =

4 (1-p)

S² p

N= Total Number of Observations / Samples

p= % safe / % unsafe observed

S= Desired Level of Accuracy

95% Confidence Level – Two Std. Deviations from Mean

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Example:
Calculating Observation Reliability

  • Behavioral Observations: Safe Forklift Operation While Traveling in Warehouse
  • Observed: 75% Safe
  • Desire 10% Accuracy Level
  • 4 (1 -.75) / (0.01 X .75)
  • # of Observations Necessary = 133 (That’s a lot if you only have a few forklift drivers!)

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Monthly Accident Control Chart

0

10

20

30

40

Month

# of Accidents

Series1

182314172133202522121210

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