ASQ CSSBB Certified Six Sigma Black Belt – Analyze

1. Pattern of Variation

In this video we will discuss about analyze phase. Analyze Phase Overview and Objectives By the end of this phase, you’ll be able to explain the different patterns of variation. Describe inferential statistics illustrate hypothesis testing perform the different hypothesis tests for normal data perform the different hypothesis tests for nonnormal data pattern of Variation pattern of Variation Session Overview and Objectives By the end of this session, you’ll be able to explain multivariate analysis discuss different classes of distribution. Multivariate Analysis Multivariate Analysis In statistical process control, one tracks variables like pressure, temperature or PH by taking measurements at certain intervals. The underlying assumption is that the variables will have approximately one representative value when measured frequently. This is not the case.

Temperature in the cross section of a furnace will vary, and the thickness of a part may also vary depending on where each measurement is taken. Often the variation is within piece and the source of this variation is different from piece to piece and time to time variation the multivarry chart is a very useful tool for analyzing all three types of variation. Multivarry charts are used to investigate the stability or consistency of a process. The chart consists of a series of vertical lines or other appropriate schematics along a timescale. The length of each line or schematic shape represents the range of values found in each sample set. Multivarry sampling plan design procedure. Select the process and the characteristic to be investigated. Select the sample size and time frequency. Set up a tabulation sheet to record the time and values from each sample set.

Plot the multivariate chart on graph paper with time along the horizontal scale and the measured values on the vertical scale. Join the observed values with appropriate lines. Analyze the chart for variation both within the sample set from sample to sample and over time. It may be necessary to conduct additional studies to concentrate on the area or areas of apparent maximum variation. After process improvements, it will be necessary to repeat the multivariate study to confirm the results. Multivariate Analysis Tools Multivariate analysis is concerned with two or more dependent variables y one, y two being simultaneously considered for multiple independent variables x one, x two, etc.

Recent advances in computer software and hardware have made it possible to solve more problems using multivariate analysis. Some of the software programs available to solve multivariate problems include SPSS, S Plus, SAS and Minitab. Multivariate analysis has found wide usage in the social sciences, psychology or educational fields. Applications for multivariate analysis can also be found in the engineering, technology and scientific disciplines. We will learn the highlights of the following multivariate concepts or techniques discriminate Function Analysis Multivariate Analysis Discriminate Function Analysis Discriminate Function Analysis If one has a sample with known groups, discriminate analysis can be used to classify the observations or attributes into two or more groups. Discriminate analysis can be used as either a predictive or a descriptive tool.

The decisions could involve medical care, college success attributes, car, loan, credit worthiness, or the previous economic development issues. Discriminate analysis can be used as a follow up to the use of Menova. Again, linear combinations of predictors or groups are provided by the researcher. The possible number of linear combinations discriminate functions for a study would be the smaller of the number of groups, negative one or the number of variables. Some assumptions in discriminate analysis are the variables are multivariately normally distributed. The population variances and covariances among the dependent variables are the same, and the samples within the variables are randomly obtained and exhibit independence of scores from the other samples. Classes of Distributions Classes of distributions commonly used distributions include normal binomial, Poisson, chi square, students, T, and F distribution. Normal distribution has numerous applications useful when it is equally likely that readings will fall above or below the average.

When a sample of several random measurements is averaged, distribution of such repeated sample averages tends to be normally distributed regardless of the distribution of the measurements being averaged. Binomial distribution Used to model discrete data applies when population is large N greater than 50 and when sample size is small compared to population. Best applied when sample size is less than 10% of N, N is less than 110 n sampling is with replacement approximation to hyper. Geometric distribution Used to model situations having two possible outcomes. Fossil distribution Used to model discrete data. Used to model rates such as rabbits per acre, defects per unit, or arrivals per hour. Can be an approximation to binomial distribution when P is equal to or less than one 10th and sample size is fairly large. Used as a distribution for defect counts closely related to exponential distribution.

Chi square distribution not used to model physical phenomena like time to fail, etc. Used to make decisions and construct confidence intervals. This distribution is a special case of gamma distribution with a failure rate of two and degrees of freedom equal to two divided by the number of degrees of freedom for the corresponding cheese squared distribution, this is considered a sampling distribution. F distribution not used to model physical phenomena like time to fail, et cetera. Used to make decisions and construct confidence intervals.

Used extensively to test for equality of variances from two normal populations, this is considered a sampling distribution. Student’s distribution formed by combining standard normal random variables and a t square random variable equivalent to F distribution with one and v degrees of freedom. Commonly used for hypothesis testing and constructing confidence intervals for means used in place of normal distribution. When standard deviation is unknown. If the sample size is large, N is greater than 100, the error in the estimated standard deviation is small and t distribution is approximately normal. Summary Pattern of Variation In this session, you learned about multivariate analysis, different classes of distribution.

2. Inferential Statistics

In this video, let us discuss about Inferential Statistics inferential Statistics session overview and Objectives By the end of this session, you’ll be able to interpret inferences, identify sampling techniques and their uses. Discuss central limit Theorem understanding Inferences inferential Statistics Understanding inferences inferential statistics is a set of methods used to draw conclusions or inferences about characteristics of populations based on data from a sample. Mu the mean calculated for a population sigma the standard deviation calculated for a population. As you would see in the figure, inferences are not taken out of the population N, but a sample which is a subset of the data representing the population N.

Inferential Statistics understanding Inferences The objective of statistical inference is to draw conclusions about population characteristics based on the information contained in a sample. The steps involved in statistical inference are define the problem objective precisely decide if the problem will be evaluated by a onetale or two tail test formulate, a null hypothesis, and an alternate hypothesis. Select a test distribution and the critical value of the test statistic, reflecting the degree of uncertainty that can be tolerated. The alpha moo risk calculate a test statistic value from the sample information make an inference about the population by comparing the calculated value to the critical value. This step determines if the null hypothesis is to be rejected. If the null is rejected, the alternate must be accepted. Communicate the Findings to Interested Parties every day in our personal and professional lives, individuals are faced with decisions between choice A or choice B.

In most situations, relevant information is available, but it may be presented in a form that’s difficult to digest. Quite often, the data seems inconsistent or contradictory. In these situations, an intuitive decision may be a little more than an outright guess. While most people feel their intuitive powers are quite good, the fact is that decisions made on gut feeling are often wrong. Sampling Techniques and Uses Inferential Statistics Sampling Techniques and Uses Sampling is the process of selecting a small number of elements from a larger defined target group of elements population is the total group of elements we want to study. Sample is the subgroup of the population we actually study. Sample would mean a group of N employees chosen randomly from organization of population N.

Sampling is done in situations when the process involves destructive testing, for example, taste tests, car crashes, et cetera. When there are constraints of time and costs, when the populations cannot be easily captured. Sampling is not done in situations when the events and products are unique and cannot be replicable. Inferential statistics, sampling techniques and Uses sampling techniques can be classified into probability sampling. Probability sampling is when there is a probability of an event to occur. No probability sampling no probability sampling does not depend on the chance cause for an event to occur. Probability sampling includes simple random sampling, stratified random sampling, systematic sampling, cluster sampling. No. Probability sampling includes convenience sampling, judgment sampling, quota Sampling snowball Sampling inferential Statistics sampling Techniques and Uses probability Sampling simple random sampling is a method of sampling in which every unit has equal chance of being selected.

As you can see in the diagram, four samples are chosen and each has an equal chance of being selected. Stratified random sampling is a method of sampling in which stratum or groups are created and then units are picked randomly. As you can see in the diagram, two samples from each of the four groups or stratum are chosen. Systematic sampling is a method of sampling in which every Nth unit is selected from the population. As you can see in the diagram, every third unit is taken as a sample. Cluster sampling is a method of sampling in which clusters are sampled every teeth time. As you can see in the diagram, two samples at each hour are considered inferential statistics sampling techniques and uses nonprobability sampling. Convenience Sampling relies upon convenience and access. Judgment sampling relies upon belief that participants fit characteristics. Quota sampling emphasizes representation of specific characteristics.

Snowball sampling relies upon respondent referrals of others with like characteristics inferential statistics. Central Limit Theorem If a random variable x has mean mu and finite variance, sigma square as n increases, x approaches a normal distribution with mean mu and variance sigma times square, where sigma times square equals sigma square by N, and n is the number of observations on which the mean is based. The Central limit Theorem states the sample means xi will be more normally distributed around mu than individual readings xi. The distribution of sample means approaches normal regardless of the shape of the parent population. This is why XR control charts work. The spread in sample means xi is less than XJ, with the standard deviation of xi equal to the standard deviation of the population. Individuals divided by s, the square root of the sample size. As you can see in the diagram, the distribution of individuals is short in height and has a larger spread, whereas the distribution of sample means is narrower and has a smaller spread. Summary Inferential Statistics in this session you learned about understanding inferences, sampling technique and their uses. Central limit theorem.

3. Hypothesis Testing

In this video, let us discuss about hypothesis testing. Hypothesis Testing Session overview and Objectives By the end of this session, you’ll be able to define general concepts and goals of hypothesis testing. Explain significance level practical versus statistical Pvalue discuss alpha and beta risks identify different types of hypothesis tests, general concepts and goals of hypothesis Testing hypothesis Testing General Concepts as you can see in the first diagram, there could be multiple problems in a process. There could be a problem with centering where the process is not centered. It may be precise but not accurate. Similarly, as you can see in the second diagram, there could also be a problem with the spread processes may be accurate but not precise. Hypothesis. Testing general concepts, null hypothesis. This is the hypothesis to be tested. The null hypothesis directly stems from the problem statement and is denoted as h not. Examples if one is investigating whether a modified seed will result in a different yield acre, the null hypothesis would assume the yields to be the same.

H not is ya equal YB. If a strong claim is made that the average of process A is greater than the average of process B, the null hypothesis one tail would state that process A is less than process B. This is written as h not is A less than B. The procedure employed in testing a hypothesis is strikingly similar to a court trial. The hypothesis is that the defendant is presumed not guilty until proven guilty. However, the term innocent does not apply to a null hypothesis. A null hypothesis can only be rejected or failed to be rejected. It cannot be accepted because of lack of evidence to reject it. If the means of two populations are different, the null hypothesis of equality can be rejected if enough data is collected. When rejecting the null hypothesis, the alternate hypothesis must be accepted.

Hypothesis Testing Goals hypothesis testing has a goal to identify the difference between several measurement types as follows for continuous data, the difference in average can be identified and also the difference in variation. For discrete data, the difference in proportion defective can be identified. Significance practical versus Statistical Hypothesis Testing significance practical versus Statistical Pvalue is also known as probability value. It is obtained by use of statistical softwares and can be used to make statistical inferences. The general use of Pvalue is to infer the significance of the statistical test. Here are a few characteristics of Pvalue statistical measure which indicates the probability of making an alpha error the range values between zero and one we normally work with 5% alpha risk alpha should be specified before the hypothesis test is conducted. If the Pvalue is greater than five hundredths, then h not is true and there is no difference in the groups except h zero.

If the Pvalue is less than five hundredths, then h not is false and there is a statistically significant difference in the groups reject h zero. Hypothesis testing Significance practical versus statistical the purpose of hypothesis testing is not to question the calculated values but to make a judgment about the difference in the values of the two data sets. The first step is to write the hypothesis null and alternate. Next step after writing the hypotheses is to decide on the acceptance or rejection criteria of the null hypothesis. Alpha is called the significant level for a hypothesis testing. One alpha is called the confidence level for a hypothesis testing. We need a certain minimum confidence to reject the null hypothesis. In major scenarios, the value of alpha is 5% or five hundredths. However, in some of the industries such as pharmaceutical, airlines and automobiles to name a few, the alpha value can be as low as 110 thousandth or 100th percent.

The value of alpha is determined by the industry. Hypothesis Testing Significance practical versus statistical essentially, when we’re comparing two data sets, we want to see whether these two data sets have the same characteristics. If we are comparing two samples evidence null hypothesis is that they belong to the same population reality. For example, there is no difference between the two sample characteristics. If we are comparing a sample evidence with a given population reality, null hypothesis is that this sample belongs to the population.

If we do happen to prove a difference, we’re saying that there is more than one alpha percent confidence that this difference is genuine and not due to chance. The general rule is that null hypothesis advocates equality whereas the alternate hypothesis is the opposite of null hypothesis. Hypothesis Testing significance practical versus statistical acceptance rejection criteria for hypothesis a null hypothesis can be accepted slash rejected by using three methods. In critical value method we reject null hypothesis when the calculated value is greater than the tabular critical value for the corresponding distribution. We do not reject null hypothesis when the calculated value is not greater than the tabular critical value for the corresponding distribution. In probability method, the null hypothesis is rejected when the Pvalue is less than alpha. We fail to reject null hypothesis when Pvalue is not lesser than alpha. In confidence interval method we reject the null hypothesis when the hypothesized parameter value is not in the calculated confidence interval, whereas we do not reject the hypothesis when the hypothesized parameter value is within the calculated confidence interval.

Risk alpha and beta hypothesis testing risk alpha and beta types of Errors When formulating a conclusion regarding a population based on observations from a small sample, two types of errors are possible alpha error or type one error. This occurs when the null hypothesis is rejected when it is in fact true. The probability of making a type one error is called or degree of risk alpha and is commonly referred to as the producer’s risk in sampling examples are incoming products are good but called bad. A process change is thought to be different when in fact there is no difference. Beta error or type two error. This error occurs when the null hypothesis is not rejected, when it should be rejected. This error is called the consumer’s risk in sampling and is denoted by the symbol b beta. Examples are incoming products are bad but called good.

An adverse process change has occurred, but it is thought to be no different. The degree of risk or is normally chosen by the concerned parties. Alpha is normally taken as 5% in arriving at the critical value of the test statistic. The assumption is that a small value for degree of risk is desirable. Unfortunately, a small or risk increases the risk for a fixed sample size. Alpha and beta are inversely related. Increasing the sample size can reduce both the alpha and beta risks. Hypothesis Testing Risk alpha and beta type one error p reject h zero when h zero is true equals alpha type two error p accept h zero when h zero is false equals beta pvalue statistical measure which indicates the probability of making an alpha error. The values range between zero and one. We normally work with 5% alpha risk. A Pvalue lower than five hundredths means that we reject the null hypothesis and accept alternate hypothesis types of Hypothesis Test hypothesis Testing types of Hypothesis Test The different types of hypothesis tests depend upon the data types of output dependent variable y and the input independent variable x. If both y and x variables are continuous, we perform a simple linear regression and or a correlation analysis. If the y variable is discrete and x variable is continuous, we perform a logistic regression. If the y value is continuous and x variable is discrete. For normal data, we perform one sample t test, two sample t test paired ttest one way inova fattest homogeneity of variants among others. Likewise, for nonnormal data, we perform Man Whitney test, Criscal Wallace test, moods median test, Friedman test, one sample sign test, one sample Wilcoxon test among others.

If y variable is discrete and x variable is also discrete, we then perform cheese square test. We will discuss about all these types of hypothesis tests in upcoming sessions. Hypothesis Testing sample Size in the Statistical Inference Discussion Thus far it has been assumed that the sample size N for hypothesis testing has been given and that the critical value of the test statistic will be determined based on the degree of risk error that can be tolerated. The ideal procedure, however, is to determine the U and B error desired and then to calculate the sample size necessary to obtain the desired decision confidence. The sample size N needed for hypothesis testing depends on the desired type one alpha and type two beta risk. The minimum value to be detected between the population means mu mu, not the variation in the characteristic being measured. Sigma.

Hypothesis testing point and interval estimates, continuous data. Large samples use the normal distribution to calculate the confidence for the mean. X plus slash minus z alpha by two, multiply by standard deviation divided by square root of N where X equals sample average sigma equals the population standard deviation. N equals sample size. Z alpha by two equals the normal distribution value for a desired confidence level. Continuous data. Small samples use the normal distribution to calculate the confidence for the mean.

X plus slash minus t alpha by two, multiply by s divided by the square root of n, where X equals a sample average, s equals the population’s standard deviation, n equals sample size, t alpha by two equals the t distribution value for a desired confidence level and N one degrees of freedom. Point and interval estimates are discussed in the explanation of minitab usage later. Summary Hypothesis Testing In this session, you learned about general concepts and goals of hypothesis testing. Significance level practical versus statistical Pvalue. Alpha and beta risks different types of hypothesis tests.

4. Hypothesis Testing with Normal Data

In this video, let us discuss about hypothesis testing with normal data. Hypothesis Testing with Normal Data session Overview and Objectives By the end of this session, you’ll be able to perform t tests, illustrate variance tests, perform oneway ANOVA normality testing and Sample Size Calculation hypothesis Testing with Normal Data data Sample Size Calculation How many samples do I need? The answer to this question is determined by the following factors type of data discrete or continuous SD or PD value what will be the standard deviation or proportion? Defectives confidence level how confident you want to be. Sample Size Formula for Continuous Data Sample size for continuous data can be calculated by n is equal to 196 multiplied by standard deviation divided by delta, the whole square. Here, the standard deviation is the estimated standard deviation of our population, and delta is the precision or the level of uncertainty in your estimate that you’re willing to accept. Hypothesis Testing with normal data sample Size Data Calculation discrete Data Previously, we had seen the sample size formula for continuous data. Now let us see the sample size formula for discrete data.

Sample size for discrete data can be calculated by n is equal to 1. 96 divided by delta, the whole square p multiple multiply by one minus p, where p is the proportioned effective that we’re estimating, and delta is the precision or the level of uncertainty in your estimate that you’re willing to accept. Summary hypothesis testing with normal data. In this lesson, you learned about t tests. Variance tests one way ANOVA.

5. One-way Anova

One way ANOVA if you want to compare mean performance of more than two factors, you can use one way ANOVA you want to compare the mean average handle time of six teams in your process. The null hypothesis is the mean average handle time of team A is equal to the mean average handle time of team B is equal to the mean average handle time of team C is equal to the mean average handle time of Team D is equal to the mean average handle time of Team E, which is equal to the mean average handle time of Team F. The alternate hypothesis is at least one of them. At least one of the mean average handle time is different from others. Copy and paste the data in minitab.

Choose stat anoa one way. In response, enter HD in factor, enter Team Lead and then click OK. In the session window output you will find the Pvalue as less than zero zero five, indicating that we reject the null hypothesis. Thus, mean average handle time of at least one team is different from others. Thank you.

• Category: Uncategorized