Sample Size

What is another name for general sampling?

Survey sampling

When does a Type II error occur?

The error occurs when you accept the null hypothesis when it is, in fact, not true.

When does a Type I error occur?

The error occurs when you reject the null hypothesis during a hypothesis test when, in fact, the null hypothesis is true.

What concept is key in selecting sample sizes for various hypothesis testing?

hypothesis testing errors

What is the Confidence Interval also known as?

margin of error

What assists in setting appropriate Alpha and Beta values?

real-world understanding

Guidelines for Calculating Sample Size When Testing Variance for Continuous Data

- set alpha at 0.05 - set beta at 0.10 or 0.20, 0.10 is less likely to produce a Type II error but requires larger sample size - set delta logically according to business needs or as a function of standard deviation

Questions to ask when Selecting Delta Value in Real World Application

1. How small does the difference have to be before it becomes practically insignificant to the customer? 2. What is the smallest delta that provides the best chance at exposing all benefits or information but is not so small as to be unfeasible? 3. What margin of error is tolerable in results?

Proportion Test

1. Proportion tests are run using attribute data. Attribute data almost always requires a larger sample size for accurate results than continuous data does. 2. Don't need to provide any information about population parameters such as sigma levels or standard deviation. 3. To calculate sample size required for accurate 1-Sample Proportion hypothesis testing, simply set alpha and beta and enter the proportions for both null and alternative hypothesis.

Information Required for Choosing Sample Size

1. Set the alpha level, normally it is 0.05. 2. Set beta level, can be set by the experimenter and a sample size will be calculated from the beta number. 3. Delta, the practical difference the experimenter wants to detect using the test 4. Standard deviation 5. Type of data, discrete or continuous 6. Type of hypothesis test

Delta Value

1. This is the value for the practical difference the experimenter wants to detect using the hypothesis test. Also known as "Critical Difference" 2. Working at smaller delta values means larger sample sizes or smaller measurement requirements, which take time to gather. 3. Delta should always be based on business needs or as a function of standard deviation. Delta is express as sigma, σ.

Questions to ask when Selecting Beta Value in Real World Application

1. What are the cost associated if the team made a Type II error, and not reject a null hypothesis. 2. What is the potential damage and cost if defective materials are passed to the customer? 3. What are the cost associated with lost time or resources in correcting a problem that comes from a Type II error.

Questions to ask when Selecting Alpha Value in Real World Application

1. What are the cost associated with an unnecessary change if the team made a Type I error. 2. What are the costs with rejecting materials that actually fits specifications 3. What are the costs associated with accepting the hypothesis that change did occur? Are there dangers or costs associated with concluding that a statistical change occurred? What are they?

Jumping off Point in Sample Size Test

A sample size that provides you some relevant information that is as accurate as you define and that you can use as a basis for future sampling

2-Sample T Test Sample Size Calculation

A type of calculation to perform when determining sample size for various hypothesis tests: - means testing - comparing means from 2 sets of data

1-Sample Z Test Sample Size Calculation

A type of calculation to perform when determining sample size for various hypothesis tests: - means testing - comparing to a target - you do not have sample statistics about the population (standard deviation is not known)

1-Sample T Test Sample Size Calculation

A type of calculation to perform when determining sample size for various hypothesis tests: - means testing - comparing to a target value - you already have sample statistics about the population

Design of Experiment (DOE) Sample Size Calculation

A type of calculation to perform when determining sample size for various hypothesis tests: - means testing - more than 2 sets of data - more than one factor for x

Analysis of Variance (ANOVA) Sample Size Calculation

A type of calculation to perform when determining sample size for various hypothesis tests: - means testing - more than 2 sets of data - only one factor for x

2-Sample Proportion Test Sample Size Calculation

A type of calculation to perform when determining sample size for various hypothesis tests: - proportion testing (rate, x per y) - comparing rate from two sets of data

1-Sample Proportion Test Sample Size Calculation

A type of calculation to perform when determining sample size for various hypothesis tests: - proportion testing (rate, x per y) - comparing rate of one data set to a target

2-Sample Variance Test Sample Size Calculation

A type of calculation to perform when determining sample size for various hypothesis tests: - variance testing - comparing variance from two sets of data

1-Sample Variance Test Sample Size Calculation

A type of calculation to perform when determining sample size for various hypothesis tests: - variance testing - comparing variance of one data set to a target

Confidence Level

Also known as the "margin of error:. Defined as the uncertainty associated with sampling.

Producer Risk

Another name for Type I error. It is called producer risk because if the null hypothesis is true but rejected, then the material that is within specifications will also be rejected leading to waste, extra cost, and lower employee morale.

Consumer Risk

Another name for Type II error. It is called consumer risk because if the null hypothesis is proven false but was accepted, then the product made did not meet specifications but thought to have met specifications and sold to the customers, leading to product returns, unsatisfied customers, and poor brand reputation.

Beta Level

Calculate beta risk from the sample size. Also known as the power value in Minitab. 0.1 beta = 0.9 power value or 0.2 beta = 0.8 power value.

What is an aspect of the sample variance test sample size calculation?

Comparing variance from two sets of data

Guidelines for Calculating Sample Size When Testing Proportions for Discrete/Binomial Data

If you have some information about the population, including standard deviation: - set alpha at 0.05 - set beta at 0.10 or 0.20, 0.10 is less likely to produce a Type II error but requires larger sample size - set delta logically according to business needs or as a function of standard deviation

Guidelines for Calculating Sample Size When Testing Means for Continuous Data

If you have some information about the population, including standard deviation: - set alpha at 0.05 - set beta at 0.10 or 0.20, 0.10 is less likely to produce a Type II error but requires larger sample size - set delta with absolute values as required by business needs or as a function of standard deviation

What is the advanced statistical analysis software most commonly used by Six Sigma experts?

Minitab

Minitab does what with the information about the test?

Minitab displays any deviations.

What is an aspect of the design of experiment (DOE) sample size calculation?

More than one factor for x

What does the data table returned by Minitab display?

Options for sample sizes for each difference and target power.

What makes proportion tests different from other tests?

Proportion tests deal with attributes - and rates - there is no need to provide any information about population parameters such as sigma levels or standard deviation.

Methods for Sample Size Calculation

Review the list below to determine what type of calculation to perform when determining sample size for various hypothesis tests: 1. 1-Sample T Test Sample Size Calculation 2. 1-Sample Z Test Sample Size Calculation 3. 2-Sample T Test Sample Size Calculation 4. 2-Sample Variance Test Sample Size Calculation 5. 1-Sample Variance Test Sample Size Calculation 6. 1-Sample Proportion Test Sample Size Calculation 7. 2-Sample Proportion Test Sample Size Calculation 8. Analysis of Variance (ANOVA) Sample Size Calculation 9. Design of Experiment (DOE) Sample Size Calculation

What is one of the baselines used when testing variance for continuous data?

Set delta greater than 1 and according to business needs, or, more often in Minitab, as a function of standard deviation.

What will always happen when conclusions are drawn about a population from sample data?

Some level of uncertainty

Even if you perform a calculation to determine an appropriate sample size - and you choose to ere on the side of caution by sampling at the largest count size returned by Minitab - you can draw the wrong inferences. Why?

The sample was not random

Type II Hypothesis Testing Error

This error occurs when you accept the null hypothesis when in fact it is not true. Type II error risks are denoted by beta. Also known as Consumer Risk.

Type I Hypothesis Testing Error

This error occurs when you reject the null hypothesis when the null hypothesis is actually true. Type I error risks are denoted by alpha. Also known as Producer Risk.

Survey Sampling

This is general sampling on an unknown population and requires alpha at 0.05, beta at 0.5, and delta to a proportion in keeping with a standard deviation of 1.

Sample Size

Use to determine information about a population. There is always some level of uncertainty involved and the larger the sample size the smaller the uncertainties becomes.

What does accuracy in inferential statistics require?

You have the right sample size