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
Which type of distribution:
When items are drawn from a population without replacement. Similar in nature to the binomial distribution, except the sample size is large compared to the population. Appropriate whenever the sample size is greater than 10% of the population
Hypergeometric Distribution
Status if the difference between the sample and the population caused by the sampling method
Bias
Status if the average of all possible values is equal to the parameter being estimated
Unbiased
The standard deviation of a sample statistic or estimator indicating the amount of error that will occur when a sample mean is used to estimate the mean of a population
Standard Error
The stated coverage for a fixed proportion of the population with a declared confidence
Tolerance Interval
Change, or improvement, and one that could have occurred by chance magnitude of difference or change required to distinguish between a true difference, change, or improvement, and one that could have occurred by chance
Statistical Significance
The amount of difference, change, or improvement that will add practical, economic, or technical value to an organization. Often this is a constraint on the process flow.
Practical Significance
Comparing data sets by determining if the means are equal
Paired-Comparison Tests
Comparing an observed (O) frequency distribution to an expected (E) frequency distribution
Goodness-of-fit Tests
Determine if there are statistically significant differences among group means by analyzing group variances. Evaluates the importance of several factors of a set of data by subdividing the variation into component parts
Analysis of Variance (ANOVA)
Used to analyze data via a two-way classification involving two factors with data that are usually attribute in nature such as frequency or counts. This tool is used to test whether two sources of variation are statistically independent. The test statistic used is the Chi-square statistic (χ2).
Contingency Tables
(Shewhart) philosophy focusing on optimizing continuous improvement by using statistical tools for analyzing data, making inferences about process behavior, and then making a decision
Statistical Process Control (SPC)
In Regression Analysis, vertical distance between observed y and calculated y is used to calculate _____
Standard error of the estimate
If two variables have a linear correlation coefficient of -.97 , as one variable _____, the other ______
increases, decreases
______ helps reduce the effect of uncontrolled variables in an experiment
Randomization
______ can most cost-effectively detect and eliminate many software errors in a quality information system
Design Review and Code Inspections
______ is useful when data is in subgroups and time-ordered
X and R Chart
Type 2 error risk
Not rejecting the null hypothesis when it is false
A test for significance in an analysis of a variance table
F-Test
Removing larger number to view just decimal values
Data Coding
Chart:
Plotting data over time
Run Chart
Distribution most similar to normal distribution
Students T Distribution
Chart:
Variability from one individual value to another
Moving Range Chart
Benefit of using fraction factorial design instead of full factorial design
Reduces costs
Distribution of rolling dice
Uniform Distribution
Takes centering of the process into account
Ppk
If Cp = 1, the process variation is…
Equal to the specification width
The square of the correlation coefficient
Coefficient of Determination
