OSH 200 - Important Assignment. Need Detailed Answers - 4-5 Hours Max
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MathLectureOSH200.pptOSH 200
Measurement of
Safety Performance
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 -1)
Calculate Std. Deviation
* If entire population sample
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Normal Distribution
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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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UCL
LCL
MEAN
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Chart1
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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
Sheet2
Sheet3
UCL / LCL Calculations for #s of Events / Samples
- 95% Statistical Significance = 2 std. deviations from mean = 1.96 = normal distribution
- UCL = X + Z*S
- LCL = x – Z*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]ˆ0.5
- LCL = p - 1.96[p(1-p)/n]ˆ0.5
- p= mean proportion / %
UCL / LCL Calculations for Proportions / %
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Standard Deviation =
√
Σ (v1 – mean)² + (v2-mean)²….
(n -1)
Calculate Std. Deviation
* If entire population sample
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Monthly Accident Control Chart
0
10
20
30
40
Month
# of Accidents
Series1
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