Before starting any type of analysis classify the data set as either continuous or attribute, and in many cases it is a combination of both types. Continuous data is seen as a variables that can be measured on a continuous scale like time, temperature, strength, or monetary value. A test is to divide the benefit in half and see if it still is practical.

Attribute, or discrete, data can be connected with a defined grouping and after that counted. Examples are classifications of good and bad, location, vendors’ materials, product or process types, and scales of satisfaction including poor, fair, good, and ideal. Once an item is classified it can be counted as well as the frequency of occurrence can be determined.

Another determination to help make is whether or not the info is **统计代写**. Output variables are frequently known as the CTQs (essential to quality characteristics) or performance measures. Input variables are what drive the resultant outcomes. We generally characterize a product or service, process, or service delivery outcome (the Y) by some purpose of the input variables X1,X2,X3,… Xn. The Y’s are driven by the X’s.

The Y outcomes can be either continuous or discrete data. Samples of continuous Y’s are cycle time, cost, and productivity. Samples of discrete Y’s are delivery performance (late or punctually), invoice accuracy (accurate, not accurate), and application errors (wrong address, misspelled name, missing age, etc.).

The X inputs can additionally be either continuous or discrete. Examples of continuous X’s are temperature, pressure, speed, and volume. Types of discrete X’s are process (intake, examination, treatment, and discharge), product type (A, B, C, and D), and vendor material (A, B, C, and D).

Another set of X inputs to always consider are the stratification factors. These are generally variables that may influence the product, process, or service delivery performance and really should not be overlooked. If we capture these details during data collection we can study it to figure out if this makes a difference or otherwise not. Examples are period of day, day of each week, month of the year, season, location, region, or shift.

Given that the inputs can be sorted through the outputs and also the data can be classified as either continuous or discrete selecting the statistical tool to utilize boils down to answering the question, “The facts that we want to know?” This is a listing of common questions and we’ll address every one separately.

Exactly what is the baseline performance? Did the adjustments made to the procedure, product, or service delivery make a difference? Are there any relationships in between the multiple input X’s as well as the output Y’s? If there are relationships will they produce a significant difference? That’s enough questions to be statistically dangerous so let’s start with tackling them one at a time.

Precisely what is baseline performance? Continuous Data – Plot the information in a time based sequence using an X-MR (individuals and moving range control charts) or subgroup the info using an Xbar-R (averages and range control charts). The centerline of the chart gives an estimate in the average in the data overtime, thus establishing the baseline. The MR or R charts provide estimates in the variation with time and establish top of the and lower 3 standard deviation control limits for that X or Xbar charts. Create a Histogram in the data to see a graphic representation in the distribution from the data, test it for normality (p-value needs to be much in excess of .05), and compare it to specifications to gauge capability.

Minitab Statistical Software Tools are Variables Control Charts, Histograms, Graphical Summary, Normality Test, and Capability Study between and within.

Discrete Data. Plot the data in a time based sequence using a P Chart (percent defective chart), C Chart (count of defects chart), nP Chart (Sample n times percent defective chart), or perhaps a U Chart (defectives per unit chart). The centerline supplies the baseline average performance. The upper and lower control limits estimate 3 standard deviations of performance above and below the average, which accounts for 99.73% of expected activity as time passes. You will get an estimate from the worst and greatest case scenarios before any improvements are administered. Develop a Pareto Chart to see a distribution from the categories along with their frequencies of occurrence. When the control charts exhibit only normal natural patterns of variation with time (only common cause variation, no special causes) the centerline, or average value, establishes the capacity.

Minitab Statistical Software Tools are Attributes Control Charts and Pareto Analysis. Did the adjustments created to the process, product, or service delivery change lives?

Discrete X – Continuous Y – To test if two group averages (5W-30 vs. Synthetic Oil) impact gas mileage, use a T-Test. If you can find potential environmental concerns that may influence the exam results use a Paired T-Test. Plot the final results on the Boxplot and assess the T statistics with all the p-values to produce a decision (p-values less than or equal to .05 signify which a difference exists with at the very least a 95% confidence that it is true). When there is a difference select the group with the best overall average to fulfill the aim.

To check if 2 or more group averages (5W-30, 5W-40, 10W-30, 10W-40, or Synthetic) impact gas mileage use ANOVA (analysis of variance). Randomize the order of the testing to minimize any time dependent environmental influences on the test results. Plot the results on a Boxplot or Histogram and measure the F statistics with the p-values to create a decision (p-values less than or equal to .05 signify that a difference exists with a minimum of a 95% confidence that it must be true). If you have a change pick the group with the best overall average to meet the objective.

In either of the above cases to evaluate to find out if you will find a difference in the variation caused by the inputs since they impact the output utilize a Test for Equal Variances (homogeneity of variance). Make use of the p-values to create a decision (p-values less than or similar to .05 signify which a difference exists with a minimum of a 95% confidence that it must be true). When there is a change pick the group with the lowest standard deviation.

Minitab Statistical Software Tools are 2 Sample T-Test, Paired T-Test, ANOVA, and Test for Equal Variances, Boxplot, Histogram, and Graphical Summary. Continuous X – Continuous Y – Plot the input X versus the output Y using a Scatter Plot or maybe you will find multiple input X variables make use of a Matrix Plot. The plot provides a graphical representation from the relationship in between the variables. If it appears that a relationship may exist, between one or more from the X input variables and the output Y variable, conduct a Linear Regression of a single input X versus one output Y. Repeat as essential for each X – Y relationship.

The Linear Regression Model gives an R2 statistic, an F statistic, and the p-value. To become significant to get a single X-Y relationship the R2 should be more than .36 (36% of the variation inside the output Y is explained through the observed changes in the input X), the F ought to be much greater than 1, and also the p-value should be .05 or less.

Minitab Statistical Software Tools are Scatter Plot, Matrix Plot, and Fitted Line Plot.

Discrete X – Discrete Y – In this sort of analysis categories, or groups, are in comparison to other categories, or groups. For instance, “Which cruise line had the highest client satisfaction?” The discrete X variables are (RCI, Carnival, and Princess Cruise Companies). The discrete Y variables would be the frequency of responses from passengers on their own satisfaction surveys by category (poor, fair, good, very good, and excellent) that connect with their vacation experience.

Conduct a cross tab table analysis, or Chi Square analysis, to judge if there have been differences in degrees of satisfaction by passengers based upon the cruise line they vacationed on. Percentages can be used for the evaluation and the Chi Square analysis provides a p-value to further quantify whether or not the differences are significant. The entire p-value linked to the Chi Square analysis ought to be .05 or less. The variables that have the largest contribution towards the Chi Square statistic drive the observed differences.

Minitab Statistical Software Tools are Table Analysis, Matrix Analysis, and Chi Square Analysis.

Continuous X – Discrete Y – Does the price per gallon of fuel influence consumer satisfaction? The continuous X is definitely the cost per gallon of fuel. The discrete Y is definitely the consumer satisfaction rating (unhappy, indifferent, or happy). Plot the info using Dot Plots stratified on Y. The statistical method is a Logistic Regression. Once again the p-values are used to validate that a significant difference either exists, or it doesn’t. P-values which are .05 or less mean that we have a minimum of a 95% confidence that a significant difference exists. Use the most regularly occurring ratings to make your determination.

Minitab Statistical Software Tools are Dot Plots stratified on Y and Logistic Regression Analysis. Are there relationships involving the multiple input X’s and the output Y’s? If you will find relationships will they change lives?

Continuous X – Continuous Y – The graphical analysis is really a Matrix Scatter Plot where multiple input X’s can be evaluated from the output Y characteristic. The statistical analysis strategy is multiple regression. Measure the scatter plots to look for relationships involving the X input variables and the output Y. Also, search for multicolinearity where one input X variable is correlated with another input X variable. This really is analogous to double dipping therefore we identify those conflicting inputs and systematically take them out through the model.

Multiple regression is actually a powerful tool, but requires proceeding with caution. Run the model with variables included then review the T statistics and F statistics to identify the first set of insignificant variables to remove from the model. During the second iteration from the regression model turn on the variance inflation factors, or VIFs, which are used to quantify potential multicolinearity issues five to ten are issues). Assess the Matrix Plot to recognize X’s linked to other X’s. Eliminate the variables using the high VIFs and the largest p-values, but ihtujy remove one of the related X variables in a questionable pair. Assess the remaining p-values and take off variables with large p-values from your model. Don’t be blown away if this type of process requires a few more iterations.

If the multiple regression model is finalized all VIFs will be less than 5 and all of p-values will likely be under .05. The R2 value should be 90% or greater. It is a significant model as well as the regression equation can now be employed for making predictions as long while we keep the input variables in the min and max range values that were utilized to produce the model.

Minitab Statistical Software Tools are Regression Analysis, Step Wise Regression Analysis, Scatter Plots, Matrix Plots, Fitted Line Plots, Graphical Summary, and Histograms.

Discrete X and Continuous X – Continuous Y

This situation requires the use of designed experiments. Discrete and continuous X’s can be utilized as the input variables, nevertheless the settings on their behalf are predetermined in the appearance of the experiment. The analysis strategy is ANOVA which was mentioned before.

Is an illustration. The aim would be to reduce the quantity of unpopped kernels of popping corn in a bag of popped pop corn (the output Y). Discrete X’s could possibly be the make of popping corn, form of oil, and model of the popping vessel. Continuous X’s might be quantity of oil, amount of popping corn, cooking time, and cooking temperature. Specific settings for each of the input X’s are selected and included in the statistical experiment.

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