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Wilson Mar

Statistics vs. SPC (Statistical Process Control)

Statistical Process Control is the science of analyzing and variables over a period of time by identifying variables and taking action to improve them.

The science of using statistics using classifications. Statisticians use surveys to measure the characteristics, attitudes, and opinions of a population.

Consumer demographic characteristics describe what individual people are . These characteristics include:
• Ethnicity (White, Black, Hispanic, Asian, etc.)
• Age (Children, Teen, Adult, Elderly, etc.)
• Gender (Male or Female)
• Geographic Location (Country, State, County, City, Zip Code, etc.)
• Employment Status (Fully employed, Unemployed, etc.)
• Level of Education
• Job Title
• Years of Work Experience
• Income
• Savings
• Family Size
• Ownership (of cars, TV's, VCR's, stereos, computers, etc.)
• etc.

These characteristics are often combined for analysis. For example, TV advertisers prefer to use demographic groups such as "Adults aged 18 to 49, women aged 18 to 49, and men and women aged 25 to 54."

Psychographic characteristics describe how people think and behave.

Organizational demographic characteristics include:

• Dollars of assets used by the department
• Square feet of floor space used by the department
• Number of full time equivalent workers (FTE's)
• Department headcount (average number of people in the department)
• Geographic Location (Country, State, County, City, Zip Code, etc.)
• Level in the organization from the CEO
• Worker turnover rate

A varible which could affect the outcome.

A list of horizontal lines ( rows ) with vertical piles of columns .

The whole group about whose characteristics or opinions are being surveyed, even though only a sample sub-set of respondents are invited to respond to the survey.

Any group of respondents defined in terms of their responses to questions about their characteristics or opinions in the survey instrument.

The responses to a survey may be summarized and reported as a whole , but it is usually helpful to separate the results from a portion of the whole. For example, a sub-set may include only people from specific areas, job types, length of service, or other method of classification.

A sub-set can also be defined in terms of responses to items in the survey. For example, if there was a question about the frequency of meetings with a five point scale for responses from “never" through to “very frequent", we could create a subset comprising people who said they had meetings never or only occasionally.

A format for illustrating the portions of a total.

Pie chart of ethnicities in LA County

The number of people selected for participation in a survey.

The lower case letter "n" is typically used as a shorthand for this statistic. So "n=15" means a sample size of 15.

A person who answers responses to a survey instrument (or otherwise providing information about their characteristics, attitudes and opinions) in a survey.

A survey is the process of measuring the characteristics, attitudes, and opinions of respondents from a desired population. A count of surveys refers to the number of different survey projects for getting answers.

An instrument is the physical questionnaire form used to record data from respondents participating in a survey. A count of instruments refers to the number of different designs for getting answers.

God's TQM Questionaire

Each separate response on a survey instrument.

It is called an item because it might not actually be a question . An example of a survey item is when respondents are asked to respond to a statement such as "I like my job" by choosing one from a series of options by marking the box corresponding to the statement which the respondent agrees with most.

The count (number) of items multiplied by the number of respondents who completed and returned the survey.

For example, if 50 respondents answered all 10 items on their survey instrument, there would be 500 responses.

Some responses may need to be ignored (thrown out) if they are found invalid .

A group of similar items put together for summary reporting purposes. Used to calculate topic averages.

An option is one of a list of responses which could be selected by a respondent when answering a survey item.

A scale is the full range of the options. Examples of options of a scale include:

• A binary of 0 or 1 is "Yes" or "No"

• How strongly the respondent agrees or disagrees with a statement (on a “Likert" scale of 1 to 5):
  1. Strongly disagree
  2. Generally Disagree
  3. Neither agree or disagree
  4. Generally Agree
  5. Strongly Agree

• A 7 point frequency scale:
  1. Never
  2. Almost Never
  3. Occasionally
  4. Frequently
  5. Very Frequently
  6. Almost Always
  7. Always

• A 7 point preference scale:
  1. Like Not At All
  2. Not Like Very Much
  3. Not Like A Little
  4. Neither Like Nor Dislike
  5. Like A Little
  6. Like Very Much
  7. Like a Lot

Note that it is good practice for items to be consistent with each other by having them all increase in value as there is more agreement, frequency, etc.

Percentiles provide a way of comparing results from items using different scales.

An answer of 3 can mean different things depending on which scale was used for that answer.

For example, one item uses a 1-5 scale and another item uses a 1-7 scale. Both questions had the answer 3. On the first scale, this is exactly the midpoint, but on the second scale it is closer to the lowest possible score (1) than to the highest (7).

By working out how far along its possible scale each actual result lies, and expressing it as a percentage of the way along, we convert all results to percentages, and make them results comparable one with the other.

With a scale from 1 to 5, a score of 3 is at the 50th percentile. On a scale from 1 to 7, a score of 3 would be a percentile of 33.33.

If the scale runs from 1 to 5, a score of 2.3 gives a percentile of 32.5. On a scale from 1 to 7 a score of 2.3 gives a percentile of 21.67; and a score of 4 is the 50th percentile. If the scale is from 0 to 1 a score of 0.45 is the 45th percentile. On a scale of 1 to 5, a score of 1 gives a percentile of 0.

The level which the results of a survey is valid and can be relied upon for decision making.

A common reason for invalidating a survey is when there is not enough samples to be representative of the population. This happens if the response rate to a survey is too low.

The number of responses received, usually expressed as a percentage of the total number of respondents invited to respond to a survey.

A low response rate may be due to many factors.

What may make statistics from a survey unreliable as a bais for making valid conclusions .

A example of what may bias a survey.

The phenomenon where people get fed up with filling in survey questionnaires. This could happen when surveys are repeated too often, or when they appear to be irrelevant . Surveys which ask informants what they want changed, but after which no change occurs, will likely result in a lower response rate the next time the survey is given.

The result of adding several numbers together. For example, the total of 10, 20, and 30 is 60 .

The measure of the portion of a total. Percentages are expressed in a number from zero to 100, where zero is none of the total and 100 is all of the total. Percentages are calculated by dividing the part by the total amount. For example, 10 is 10% of 100, and 20 is 10% of 200.

Percentages are shown in histograms.

The measure of a relationship between two numbers -- a numerator divided by a denominator.

Another example is the Cash Ratio for a company -- one of several widely used financial measures of an organization's economic health. This ratio is calculated by dividing the organization's Current Assets by its Current Liabilities.

• A Current Ratio value of 2.0 means that the company has double the amount of Assets than it has in Liabilities.
  (Generally good)

• A Current Ratio value of 1.0 means that the company has the same amount of Assets as Liabilities.
  
• A Current Ratio value of 0.5 means that the company has half the Assets to cover its Liabilities.
  (Generally not good)

Financial Measures

These are typically collections of dollars rather than units of product or amount of processing time .

This technique is used because it allows different types of measures (such as dollars and counts) to be compared on a common basis.

For example, the US Bureau of Labor Statistics defines Productivity as the ratio of Output to the the number of hours used to create that output.

The measure against values at a fixed point in the past (such as July 1st, 1969). Well known indexes include the CPI (Consumer Price Index) which measures how much it costs to buy a hypothetical "basket" of goods at various points in time. The current value of the CPI reflects prices relative to prices on July 1st, 1969. An index value of 200 means that prices have doubled since the initial period.
Changes between two periods is the difference between the index values.

For more information about the CPI, visit the US Bureau of Labor Statistics CPI web page.

A measure of the central tendency in a group of numbers. For example, the average of 10, 20, and 30 is 20 . This is calculated by adding all three numbers together (10 + 20 + 30 = 60) and dividing this sum by the number of items added together (in this example, three).

The average of the results of items within a topic.

• Vertical Bar Charts use bars which extend up vertically to illustrate the value of each bar. The higher a bar is, the larger the value of that bar.
  

  

• Horizontal Bar Charts use bars which extend from left to right horizontally to illustrate the value of each bar.

  These charts are typically used to compare the values from different segments relative to each other.
  

  

• Segmented Bar Charts use bars to illustrate the value of segments within each bar. Each portion of a bar represents a different sub-set of the total.

  This format is typically used to compare the range of results from an opinion survey.

  each bar in a Segmented Bar Chart represents one item or topic from the survey. The total length of each bar represents 100 percent of all responses to that survey item.
  

  

• Stacked Bar Charts illustrate the value of both the total of each bar and the value of segments within each bar. Each segment of a bar represents a different portion or sub-set of the total.
  

  

• Comparative Bar Charts show several bar charts together so that different populations could be compared against each other.

  For example, Comparative Bar Charts are used to compare values of a population against a benchmark population.

  Comparative Bar Charts are also used to compare values of different sub-sets of a population.
  

Benchmark

A measured value used as a basis for comparison. A benchmark could be external or internal. External benchmarks are used to compare data from different (competing) organizations. Internal benchmarks are used to compare data created within the same organization.

A bar chart which illustrates the variability in a set of measurements as (in the form of) a frequency distribution. summary of variation in a set of data.

The pictorial nature of the HISTOGRAM lets people see patterns that are difficult to imagine in a simple table of numbers. The shape of the historgram can sometimes provide infomation of the process.

The HISTOGRAM is considered one of the "Seven Tools of Quality".

Variation is a measure of the amount of differences (or "diversity") within a population or a sub-set of a population.

There are several sources of variability:

• Man
• Machine (Equipment)
• Materials (Parts)
• Methods (the sequence of steps)
• Mother Nature (temperature, humidity, wind, etc.)

Standard deviations

A statistical measure of the extent of variation in a set of data. The standard deviation tells you the extent of the spread of the individual items around the average.

Pareto Charts

The name of a vertical bar chart which has bars arranged by frequency of occurance

(how many of each item).

This chart is used to show which items are the "vital few" opportunities and which are the "trivial many".

Like a stack of coins, the height of a bar represents how many of each item on the chart. The taller a bar is, the more of it was found in the sample. The tallest bar is the single most frequently occuring item. The shortest bar is the least frequently occuring item.

In a Pareto Chart, the bars are arranged so that the tallest bar -- the most frequent item -- is put on the left of the chart. This is done based on the "Pareto Principle", which states that a large portion of results are typically caused by a small portion of the effect. For example, we typically wear only 20% of the clothes 80% of the time. Studies of businesses typically find that the top 20% of customers typically provide 80% of the total sales revenues.

Thus, reducing the tallest bar (issue) is usually easier than reducing an already small bar to zero.

Radar Charts

spokes.

Statistical Significance

A calculation of whether differences in the results from two groups could be the result of real differences or of pure chance and random sampling error.

This is calculated by comparing the amount of difference between the two groups against the sampling error we could reasonably expect.

Weighting

A technique to adjust the importance of specific items. We can calculate weighted topic average results for a topic, and we can calculate weighted subset results.

Raw Scores

The response before any adjustments.

Atrributes

Values

The specific (1).


Trend Charts

Uses a line to show the effect of time on a measured variable.

A widely used example of this is the Trend Chart of growth in the US Civilian Labor Force.

Trend Charts provide the basic format for Control Charts.




Seasonality

A type of chart which illustrates the effect of regular cycles of time. This could be quarters of a year or over the 12 months of a year.




Area Charts

Uses solid areas of color to show the effect of time on a measured variable.


Baseline

An initial value used as the base for future comparison. Used in Trend Charts.

Control Charts

An advanced type of Trend Chart which illustrates the extent of variation by adding Upper and Lower control limits.

Control Limits

These are calculated based on the sample size. These are shown in control charts.

Chi Square

Measures the extent of variation of rows and columns of a table against the total amount of variation.

Process Capability

The extent of variation in a process. This is measured by the "Cp" and "CpK" indexes . "Cp" is "one tailed" and "CpK" is "two tailed".

Design of Experiments

A method to identify causes of variation by a consistent number of factors.

Failure Mode and Effects Analysis

A method to classify causes of problems

Calibration

The process of making sure that tools used to perform measurements are accurate by comparing them against a standard which is known to be comparable to national standards.

R&R (Repeatability and Reproducibility)

A method to simultaneously define two major sources of variation.
• Repeatability - How consistently tools can repeat the same readings.
• Reproducibility - How consistently operators can reproduce the same reading.

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