6. Quantitative Methods and Tools Flashcards
Type of data - example (1, 2, 3, 4)
Discrete Data (Attributes)
Type of data - example (1.25, 5.49, 3.12)
Continuous Data (Variables)
Nominal
Can only count items
Indicates characteristic by name, category, number, presence/absence
Ordinal
Order is important
Grouping into categories having an attribute
Fixed or defined scale but no true zero
Potential zero point
Interval
There is a true zero
Can add, subtract, multiply and divide values
Ratio
Range, standard deviation, and variation describe..
Dispersion
Distribution of sample averages will tend toward a normal distribution as the sample size (n) increases. Thus, the sampling distribution of the mean will follow a normal distribution with a certain mean and standard deviation.
Central Limit Theorem
- Shows the pattern of variability around the center.
- Organizes information for ease in calculating the statistics, such as the sample mean and the sample standard deviation.
- The number of classes should be at about the square root of the sample size
Frequency Distributions
A type of histogram, 1st digit, 2nd digit…
Stem-and-Leaf Plots
Use five key data points to graphically compare data produced from different sources (different machines, operators, etc)
Box-and-Whisker Plots
Probability Plots are used to…
Used to determine the type of distribution from which a set of data may have come
The _______ of any single observation, xi, is the mean of the population, μ , from which the observation has come. The notation is given as E(xi) = μ
Expected Value
- Making a hypothesis of what we expect to find
- Collecting data
- Analyzing the data
- Drawing a conclusion about the validity of the hypothesis
Analytical Studies
Type of distribution where:
Most of the data points are concentrated around the average (bell shaped curve)
Normal Distribution
Type of distribution where:
Equal probability of outcomes
Uniform Distribution
Type of distribution where:
Variables are distributed jointly
Bivariate Normal Distribution
Which type of distribution:
Analyzes reliability. Similar to Poisson, is used to determine the average time between failures or average time between a number of occurrences
Examples - time between events, time to
Exponential Distribution
Which type of distribution:
Skewed-right with most data in the left tail, and consisting of the distribution of the random variable whose natural logarithm follows the normal distribution
Examples - response time, time-to-failure data, and time-to-repair data
Lognormal Distribution
Which type of distribution:
• β is the shape parameter – defines the probability distribution function
• θ is the scale parameter – describes the magnitude of the x-axis
• Both are greater than zero
Weibull Distribution – analyzed reliability.
Similar to lognormal
Examples - time to fail, time to repair, and material strength
Which type of distribution:
Used when testing a population variance against a known or assumed value of the population variance. It is skewed to the right (i.e., it has a long tail toward the large values of the distribution)
• Formed by summing the squares of the standard normal random values
Chi Square Distribution
Which type of distribution:
Used to determine the confidence interval of the population mean and confidence statistics when comparing the means of sample populations. The shape and area of the distribution approaches that of the normal distribution as the sample size increases.
Student’s T Distribution
Which type of distribution:
When parameter being measured takes on only certain values
Examples- integers
Discrete Distribution
Which type of distribution:
Used to estimate the number of instances a condition of interest occurs in a process or population. When the condition may occur multiple times in one sample unit and you are interested in knowing the number of individual characteristics found
Poisson Distribution
