Statistics Formulas and Calculations

Statistics and Calculations

• n represents the number of variables, x is the mean, Sx is the standard deviation, and r is the correlation coefficient.
• Variance is calculated by squaring the standard deviation.
• Regression equation is a formula for a line that models a linear relationship between two quantitative variables, represented by Y = ax + b.
• a is the slope of the line, b is the y-intercept, and r is the correlation coefficient.

Correlation and Inference

• Correlation coefficient is an index of the extent to which two variables are associated, ranging from -1 to +1.
• Inferential statistics predict the probabilities of certain events occurring in a population.
• F-statistic is associated with problems involving ANOVA and inferences about standard deviations.

Descriptive Statistics and Sampling

• Descriptive statistics summarize population data.
• Accident statistics are used to measure performance, detect trouble spots, and fulfill OSHA record-keeping requirements.
• Safety Sampling is a technique using statistics to measure the effectiveness of line manager safety activities.

Errors and Hypotheses

• Type I error (alpha) is a false positive result, where the null hypothesis is rejected when it's true.
• Type II error (beta) is a false negative result, where the null hypothesis is accepted when it's false.

Human Body and Physiology

• Anthropometry is the scientific study of the measurements and proportions of the human body.
• Kinesiology is the study of human movement.
• Physiology is the study of body function.
• Bronchioles are airways in the lungs that lead from the bronchi to the alveoli.
• Alveoli are air sacs in the lungs, allowing oxygen to pass freely through the membrane (pleura).

Data Analysis and Visualization

• Histogram is a graph representing the frequency distribution of a set of data.
• Pictograms are pictorial symbols or signs representing an object or concept.
• Confidence interval is a statistical range, with a given probability, that takes random error into account.

Quality and Probability

• Pareto Analysis identifies the vital few contributors that account for most quality problems in a system (80/20).
• Probability is the ratio of ways an event can occur in a specified manner to the total number of ways the event can occur.
• P_s + P_f = 1, where P_s is the probability of success and P_f is the probability of failure.

Occupational Health and Safety

• Inhalation is the route of entry of contaminants of greatest concern in the majority of work environments.
• Factors determining the relative health hazard of an occupational contaminant include concentration of exposure, probability of absorption, ingestion, or inhalation, and duration of exposure.
• Viruses are sub-microscopic infectious agents that are unable to grow or reproduce outside a host cell.
• Bacteria are single-celled microorganisms that can exist either as independent organisms or as parasites.

Anatomy and Health

• Epidermis is the outer layer of skin.
• Dermis is the middle layer of skin.
• Subcutaneous is the layer under the skin (inner fatty).
• Cochlea is a coiled, bony, fluid-filled tube in the inner ear that triggers nerve impulses.
• Cochlear nerve is a nerve that carries signals from the cochlea to the brain.
• Organ of Corti contains four rows of hair cells tuned to certain sound frequencies.
• Tympanic membrane is the eardrum, separating the external from the middle ear.
• Eustachian tube serves to equalize pressure in the middle ear with the external atmospheric pressure.
• Sensorineural hearing loss occurs from repetitive noise occupational exposure and takes place in the inner ear.
• Presbycusis is a hearing loss that gradually occurs in most individuals as they grow older.

Standard Deviations and Probability

• Standard deviation is a measure of the average distance of all observations from the mean in a normal distribution.
• Approximately 99% of observations fall within 2.58 standard deviations of the mean, 95% within 1.96 standard deviations, and 90% within 1.64 standard deviations.
• Standard deviation is a measure of variation, calculated as the square root of the variance.
• Approximately 95.4% of observations fall between the mean +/- two standard deviations, and approximately 68.3% fall between the mean +/- one standard deviation.

Statistical Tests and Concepts

• Chi-square test is used to test for the equality of two frequencies or proportions, with a probability of error of 1% for a result with a chi-square statistic of 0.01.
• Least Square Method is a procedure for using sample data to find the estimated regression equation, minimizing the sum of the squares of the distances between the line and the points not on the line.
• Conditional Probability is the probability of an event (A), given that another event (B) has already occurred.
• Nonparametric statistics involve testing not based on population parameters, including tests of significance based on ordinal or nominal data, with the advantage of not requiring assumptions about normality of the distribution.
• ANOVA (Analysis of Variance) is an inferential statistical test for comparing the means of three or more groups.

Probability Rules and Concepts

• Mutually exclusive events are those where the result of the first event does not affect the second.
• Independent events are those where the outcome of one event does not affect the outcome of the second event.
• Dependent events are those where the outcome of one event depends on the outcome of a previous event.
• Additional Rule of Probability states that the probability that one of several mutually exclusive events will occur is the sum of the separate probabilities.
• Multiplication Rule of Probability states that the probability that two or more independent events will occur is the product of their separate probabilities.

Other Concepts

• In statistical analysis, the focus is on sets of numerical data, with the entire set of data from which the sample came being called the population.
• A random sample is one where each item from the population has an equal probability of being selected.
• Sound not reaching the inner ear due to problems with the mechanical transmission of sound could be caused by problems with the three bones of the middle ear, accumulations of cerumen, or infections or irritation resulting in blockage of the eustachian tube.

Lifting and Sound

• Recommended Weight Limit (RWL) is calculated as RWL = LC x HM x VM x DM x AM x FM x CM, where LC is the load constant, HM is the horizontal multiplier, VM is the vertical multiplier, DM is the distance multiplier, AM is the asymmetry multiplier, FM is the frequency multiplier, and CM is the coupling multiplier.
• Lifting Index (LI) is calculated as LI = L/RWL, where L is the load in kg and RWL is the Recommended Weight Limit.
• Ohm's Law states that V=IR, where V is voltage, I is current, and R is resistance.
• Total resistance in series is calculated as Rt = R1+R2+R3.
• The origin of the "A" weighting network on a sound level meter is to simulate the response of the human ear to sound pressure levels less than 55 dB, with "C" weighting at 1,000 Hz.
• The rule of thumb for predicting combined decibel readings from two separate measured noise sources, where the two sources differ by 3 dB, is to add 2 to the higher dB level.

Sampling Methods

• Cluster sampling: groups items from a population by similar characteristics, and the sample group is selected randomly.
• Stratified sampling: groups items from a population by similar characteristics, and the sample is obtained by randomly selecting within groups.
• Systematic sampling: items from a population are selected based on factors such as time or location/position.

Stress and Materials

• Tensile stress: pull or stretch a material apart.
• Shear stress: slide against itself in opposite directions.
• Compression stress: squeeze or compress a material.
• Torque stress: twisted in one direction and the other end is held motionless or twisted in the opposite direction.

Physics and Chemistry

• Vapor pressure: the pressure exerted by a volatile liquid at equilibrium conditions.
• Boiling point: the point where vapor pressure equals atmospheric pressure.
• Fick's Law: describes the relationships between molecular weight, diffusion coefficient, and the rate of diffusion.
• Henry's Law: covers solubilities of gases in water.
• Beer's Law: covers the absorption of EM radiation and its relation to concentration.
• Boyle's Law: addresses the relationship of pressure and volume at a constant temperature.

Safety Factor and Load

• Safety factor equation: SF = ultimate/allowable.
• Given a safety factor of 10, for a 2 cm rope with a tensile strength of 10,000 newtons, the maximum safe working load in kg is 102 kg.

Time Weighted Average (TWA)

• TWA equation: TWA = (T1C1 + T2C2 ... TnCn)/Tt.
• Example: a worker was exposed to the following levels of stuff during the 8-hr shift, the 8-hr TWA is 194 ppm.

Airborne Contaminants

• Mist: a term loosely applied to the dispersion of liquid particles, many of which are large enough to be individually visible without visual aid.
• Vapor: the gaseous form of a substance that is normally in a solid or liquid state at normal temperature and pressure.
• Gas: a substance above its critical temperature.
• Smoke: small gas-borne particles resulting from incomplete combustion and consisting predominantly of carbon and other combustible materials.
• Fog: a term loosely applied to visible aerosols in which the dispersed phase is liquid.
• Smog: a term derived from "smoke" and "fog" and applied to extensive atmospheric contamination by aerosols arising from a combination of natural and man-made sources.
• Dust: a term loosely applied to solid particles predominantly larger than colloidal and capable of temporary suspension in air or other gases.

Health and Occupational Hazards

• Inhalation: the route of entry of contaminants that is of greatest concern in the majority of work environments.
• Factors to determine the relative health hazard of an occupational contaminant: concentration of exposure, probability of absorption, ingestion, or inhalation, and duration of exposure.
• Virus: a sub-microscopic infectious agent that is unable to grow or reproduce outside a host cell.
• Bacteria: single-celled microorganisms that can exist either as independent organisms or as parasites.
• Antibody: a type of protein made by certain white blood cells in response to a foreign substance.

Anthropology and Skin

• Anthropology: the science that deals with the origins, physical and cultural development, biological characteristics, and social customs and beliefs of humankind.
• Epidermis: the outer layer of skin.
• Dermis: the middle layer of skin.

Electrical and Thermal

• Total resistance in parallel: 1/Rt = 1/R1 + 1/R2.
• Power: P = (force x distance) / time, or P = ExI, or P = I^2 x R.
• WBGT equation: WBGT = 0.7 WB + 0.3 GT.
• WBGT equation with solar load: WBGT = 0.7 WB + 0.2 GT + 0.1 DB.

Other Concepts

• Adiabatic Lapse Rate (ALR): the decrease in air temperature relative to an increase in altitude such that there is no exchange of energy.
• Maximum exposure to impulsive or impact noise: 140 dB peak.
• Doubling the sound intensity results in a 3 dB increase.
• A 73 dB sound pressure level was measured at 600 ft.

Anatomy of the Ear

• Subcutaneous refers to the area under the skin (inner fatty layer)
• The cochlea is a coiled, bony, fluid-filled tube in the inner ear that converts sound waves into nerve impulses
• The cochlea changes the energy from mechanical (fluid waves) to electrical (nerve impulses)

Components of the Ear

• The cochlear nerve is a nerve in the head that carries signals from the cochlea to the brain
• The organ of Corti contains four rows of hair cells tuned to specific sound frequencies
• The tympanic membrane (eardrum) separates the external ear from the middle ear and transmits sound from the air to the ossicles
• The Eustachian tube equalizes pressure in the middle ear with external atmospheric pressure and opens during swallowing and yawning

Types of Hearing Loss

• Sensorineural hearing loss occurs from repetitive noise exposure and takes place in the inner ear
• Presbycusis is a type of hearing loss that gradually occurs in most individuals as they grow older

Sound Measurement

• The SPL (sound pressure level) at 150 ft is 85 dB
• The "A" weighting network on a sound level meter simulates the response of the human ear to low levels of sound, below 55 dB
• The rule of thumb for combining decibels is to add 2 to the higher dB level when the two sources differ by 2-5 dB

Noise Measurement Equipment

• A sound level meter is a direct reading instrument used to measure sound pressure variation in air, with a frequency range of 20-20,000 Hz
• An octave-band analyzer is used to determine where the noise energy lies in the frequency spectrum
• A noise dosimeter is worn by workers to accumulate a record of noise energy exposure during the work shift

Physics and Math

• Total resistance in parallel is calculated as 1/Rt = 1/R1 + 1/R2
• Power (P) is calculated as P = (force x distance) / time, or P = ExI, or P = I^2 x R
• The WBGT (wet bulb globe temperature) equation is WBGT = 0.7 WB + 0.3 GT
• The WBGT equation with solar load is WBGT = 0.7 WB + 0.2 GT + 0.1 DB
• The adiabatic lapse rate (ALR) is the decrease in air temperature relative to an increase in altitude, with no exchange of energy
• The maximum exposure to 140 dB peak impulsive or impact noise should not exceed a certain duration

Sound and Distance

• Doubling the sound intensity results in a 3 dB increase
• When the distance is halved, the sound pressure level (SPL) increases by 6 dB

Anatomy of the Ear

• Subcutaneous refers to the area under the skin (inner fatty layer)
• The cochlea is a coiled, bony, fluid-filled tube in the inner ear that converts sound waves into nerve impulses
• The cochlea changes the energy from mechanical (fluid waves) to electrical (nerve impulses)

Components of the Ear

• The cochlear nerve is a nerve in the head that carries signals from the cochlea to the brain
• The organ of Corti contains four rows of hair cells tuned to specific sound frequencies
• The tympanic membrane (eardrum) separates the external ear from the middle ear and transmits sound from the air to the ossicles
• The Eustachian tube equalizes pressure in the middle ear with external atmospheric pressure and opens during swallowing and yawning

Types of Hearing Loss

• Sensorineural hearing loss occurs from repetitive noise exposure and takes place in the inner ear
• Presbycusis is a type of hearing loss that gradually occurs in most individuals as they grow older

Sound Measurement

• The SPL (sound pressure level) at 150 ft is 85 dB
• The "A" weighting network on a sound level meter simulates the response of the human ear to low levels of sound, below 55 dB
• The rule of thumb for combining decibels is to add 2 to the higher dB level when the two sources differ by 2-5 dB

Noise Measurement Equipment

• A sound level meter is a direct reading instrument used to measure sound pressure variation in air, with a frequency range of 20-20,000 Hz
• An octave-band analyzer is used to determine where the noise energy lies in the frequency spectrum
• A noise dosimeter is worn by workers to accumulate a record of noise energy exposure during the work shift

Physics and Math

• Total resistance in parallel is calculated as 1/Rt = 1/R1 + 1/R2
• Power (P) is calculated as P = (force x distance) / time, or P = ExI, or P = I^2 x R
• The WBGT (wet bulb globe temperature) equation is WBGT = 0.7 WB + 0.3 GT
• The WBGT equation with solar load is WBGT = 0.7 WB + 0.2 GT + 0.1 DB
• The adiabatic lapse rate (ALR) is the decrease in air temperature relative to an increase in altitude, with no exchange of energy
• The maximum exposure to 140 dB peak impulsive or impact noise should not exceed a certain duration

Sound and Distance

• Doubling the sound intensity results in a 3 dB increase
• When the distance is halved, the sound pressure level (SPL) increases by 6 dB

Anatomy of the Ear

• Subcutaneous refers to the area under the skin (inner fatty layer)
• The cochlea is a coiled, bony, fluid-filled tube in the inner ear that converts sound waves into nerve impulses
• The cochlea changes the energy from mechanical (fluid waves) to electrical (nerve impulses)

Components of the Ear

• The cochlear nerve is a nerve in the head that carries signals from the cochlea to the brain
• The organ of Corti contains four rows of hair cells tuned to specific sound frequencies
• The tympanic membrane (eardrum) separates the external ear from the middle ear and transmits sound from the air to the ossicles
• The Eustachian tube equalizes pressure in the middle ear with external atmospheric pressure and opens during swallowing and yawning

Types of Hearing Loss

• Sensorineural hearing loss occurs from repetitive noise exposure and takes place in the inner ear
• Presbycusis is a type of hearing loss that gradually occurs in most individuals as they grow older

Sound Measurement

• The SPL (sound pressure level) at 150 ft is 85 dB
• The "A" weighting network on a sound level meter simulates the response of the human ear to low levels of sound, below 55 dB
• The rule of thumb for combining decibels is to add 2 to the higher dB level when the two sources differ by 2-5 dB

Noise Measurement Equipment

• A sound level meter is a direct reading instrument used to measure sound pressure variation in air, with a frequency range of 20-20,000 Hz
• An octave-band analyzer is used to determine where the noise energy lies in the frequency spectrum
• A noise dosimeter is worn by workers to accumulate a record of noise energy exposure during the work shift

Physics and Math

• Total resistance in parallel is calculated as 1/Rt = 1/R1 + 1/R2
• Power (P) is calculated as P = (force x distance) / time, or P = ExI, or P = I^2 x R
• The WBGT (wet bulb globe temperature) equation is WBGT = 0.7 WB + 0.3 GT
• The WBGT equation with solar load is WBGT = 0.7 WB + 0.2 GT + 0.1 DB
• The adiabatic lapse rate (ALR) is the decrease in air temperature relative to an increase in altitude, with no exchange of energy
• The maximum exposure to 140 dB peak impulsive or impact noise should not exceed a certain duration

Sound and Distance

• Doubling the sound intensity results in a 3 dB increase
• When the distance is halved, the sound pressure level (SPL) increases by 6 dB

Standard Deviations

• A standard deviation is a measure of the average distance of all observations from the mean.
• In a normal distribution, approximately 99% of the observations will fall within 2.58 standard deviations of the mean, 95% within 1.96 standard deviations, and 90% within 1.64 standard deviations.
• Approximately 99.9% of the observations will fall within 3.49 standard deviations.
• Approximately 95.4% of the observations will fall between the mean +/- two standard deviations.
• Approximately 68.3% of the observations will fall between the mean +/- one standard deviation.

Chemical Reactions

• An exothermic reaction is a chemical reaction that releases heat and gives net energy to its surroundings.
• A chelating agent is a chemical compound capable of forming multiple chemical bonds to a metal ion.
• A buffer is a substance that reduces the change in hydrogen ion concentration (pH) otherwise produced by adding acids or bases to a solution.

Chemical Properties

• A mole of nitrogen gas can be described by all of the following: weighs 28 grams, has 6.024x10^23 N_2 molecules, and occupies 24.45 liters at 25°C and 1 atm.
• The pH scale represents the logarithm of the reciprocal of hydrogen-ion concentration in gram atoms per liter and provides a measure on a scale from 0 to 14 of the acidity or alkalinity of a solution.

Particle Properties

• Fibers are particles with a 3:1 length-to-width ratio.
• Fumes are solid particles that are condensed from metal oxides (metal fume fever) with a particle size of 0.01-0.2 microns.
• Aerosols are liquid droplets or solid particles dispersed in air that are fine enough particles to remain dispersed in air for prolonged periods.
• Mists are dispersions of liquid particles/droplets generated by condensation from the gaseous to liquid state (vapor) with a particle size of 40-400 microns.
• Vapor is the gaseous form of a substance that is normally in a solid or liquid state at normal temperature and pressure (NTP).
• Gas is a substance above its critical temperature.
• Smoke is small gas-borne particles resulting from incomplete combustion and consisting predominantly of carbon and other combustible materials.
• Fog is a term loosely applied to visible aerosols in which the dispersed phase is liquid.
• Smog is a term derived from "smoke" and "fog" and applied to extensive atmospheric contamination by aerosols arising from a combination of natural and man-made sources.

Sound Levels

• The origin of the "A" weighting network on a sound level meter is to simulate the response of the human ear to all of the following: relatively low levels of sound, at 40 phons, and at sound pressure levels less than 55 dB.
• The rule of thumb for predicting combined decibel readings from two separate noise sources is to add 2 when the two sources differ by 2-5 dB, and to add 3 when the two sources differ by 3 dB.
• In a manufacturing plant, noise measuring equipment most commonly used includes Sound Level Meter, Octave-Band Analyzer, and Noise Dosimeter.

Kinesiology and Physiology

• Kinesiology is the study of human movement.
• Physiology is the study of body function.

Data Analysis

• A histogram is a graph representing the frequency distribution of a set of data.
• A pictogram is a pictorial symbol or sign representing an object or concept.
• Confidence interval is a statistical range with a given probability, taking random error into account.

Anatomy and Respiratory System

• Bronchioles are airways in the lungs that lead from the bronchi to the alveoli.
• The pleura is a membrane surrounding the lungs.
• Alveoli are air sacs in the lungs, allowing oxygen to pass freely through the pleura.
• Dust is a term loosely applied to solid particles predominantly larger than colloidal and capable of temporary suspension in air or other gases.

Occupational Health

• Inhalation is the route of entry of contaminants that is of greatest concern in the majority of work environments.
• Factors determining the relative health hazard of an occupational contaminant include concentration of exposure, probability of absorption, ingestion, or inhalation, and duration of exposure.

Microbiology

• A virus is a sub-microscopic infectious agent that is unable to grow or reproduce outside a host cell.
• Bacteria are single-celled microorganisms that can exist either as independent organisms or as parasites.
• An antibody is a type of protein made by certain white blood cells in response to a foreign substance.

Anthropology and Skin

• Anthropology is the science that deals with the origins, physical and cultural development, biological characteristics, and social customs and beliefs of humankind.
• The epidermis is the outer layer of skin.
• The dermis is the middle layer of skin.
• The subcutaneous layer is the layer under the skin (inner fatty).

Hearing and Sound

• The cochlea is a coiled, bony, fluid-filled tube in the inner ear through which sound waves trigger nerve impulses.
• The cochlear nerve is a nerve in the head that carries signals from the cochlea of the inner ear to the brain.
• The organ of Corti contains four rows of hair cells tuned to certain sound frequencies.
• The tympanic membrane is the eardrum, a thin membrane that separates the external from the middle ear and transmits sound from the air to the ossicles inside the middle ear.
• The Eustachian tube serves to equalize pressure in the middle ear with the external atmospheric pressure.
• Sensorineural hearing loss is hearing loss from repetitive noise occupational exposure and takes place in the inner ear.
• Presbycusis is hearing loss that gradually occurs in most individuals as they grow older.

Lifting and Ergonomics

• The Recommended Weight Limit (RWL) is a formula used to calculate a recommended weight for lifting tasks.
• The Lifting Index (LI) is calculated by dividing the load (L) by the Recommended Weight Limit (RWL).
• Ohm's Law is V=IR, where V is voltage, I is current, and R is resistance.
• The total resistance in series is Rt = R1+R2+R3.

Sound and Noise

• The origin of the "A" weighting network on a sound level meter is to simulate the response of the human ear to sound levels.
• The rule of thumb for predicting combined decibel readings from two separate noise sources is to add 2 to the higher dB level when the two sources differ by 2-5 dB.
• In a manufacturing plant, noise measuring equipment commonly used includes sound level meters, octave-band analyzers, and noise dosimeters.

Standard Deviations

• A measure of the average distance of all observations from the mean.
• In a normal distribution, approximately 99% of observations fall within 2.58 standard deviations of the mean.
• Approximately 95.4% of observations fall between the mean +/- two standard deviations.
• Approximately 68.3% of observations fall between the mean +/- one standard deviation.
• The standard deviation is a measure of variation.
• The standard deviation of a set of data is the square root of the variance.

Statistical Concepts

• Chi-square statistic: a test for the equality of two frequencies or proportions.
• Least Square Method: a procedure for using sample data to find the estimated regression equation.
• Conditional Probability: the probability of an event (A), given that another (B) has already occurred.
• Nonparametric statistics: testing not based on population parameters; includes tests of significance based on ordinal or nominal data.
• ANOVA (analysis of variance): an inferential statistical test for comparing the means of three or more groups.

Human Physiology and Anatomy

• Kinesiology: the study of human movement.
• Physiology: the study of body function.
• Bronchioles: airways in the lungs that lead from the bronchi to the alveoli.
• Pleura: membrane surrounding the lungs.
• Alveoli: air sacs in the lungs, allowing oxygen to pass freely through the membrane.

Data Analysis

• Histogram: a graph representing the frequency distribution of a set of data.
• Pictograms: a pictorial symbol or sign representing an object or concept.
• Confidence interval: a statistical range, with a given probability, that takes random error into account.

Probability

• Probability: a ratio of ways an event can occur in a specified manner to the total number of ways the event can occur.
• P_s + P_f = 1, where P_s is the probability of success and P_f is the probability of failure.
• Mutually exclusive events: events where the result of the first event does not affect the second event.
• Independent events: events where the outcome of one event does not affect the outcome of the second event.
• Dependent events: events where the outcome of one event depends on the outcome of a previous event.
• Additional Rule of Probability: the probability that one of several mutually exclusive events will occur is the sum of the separate probabilities.
• Multiplication Rule of Probability: the probability that two or more independent events will occur is the product of their separate probabilities.

Other Concepts

• Anthrology: the science that deals with the origins, physical and cultural development, biological characteristics, and social customs and beliefs of humankind.
• Epidermis: the outer layer of skin.
• Dermis: the middle layer of skin.
• Pareto Analysis: identifying the vital few contributors that account for most quality problems in a system (80/20).
• Dust: a term loosely applied to solid particles predominantly larger than colloidal and capable of temporary suspension in air or other gases.
• Inhalation: the route of entry of contaminants that is of greatest concern in the majority of work environments.
• Virus: a sub-microscopic infectious agent that is unable to grow or reproduce outside a host cell.
• Bacteria: single-celled microorganisms that can exist either as independent organisms or as parasites.
• Antibody: a type of protein made by certain white blood cells in response to a foreign substance.

This quiz focuses on basic statistics formulas, including mean, standard deviation, and correlation coefficient, as well as calculating variance and regression equations.