# 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

## 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

JFMAMJJASOND