Before starting any type of analysis classify the data set as either continuous or attribute, and even it is a combination of both types. Continuous details are characterized by variables that can be measured on a continuous scale including time, temperature, strength, or monetary value. A test is to divide the benefit by 50 percent and find out if it still makes sense.

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

The next determination to create is whether or not the information is **统计作业代写**. Output variables are often called the CTQs (important 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 through the X’s.

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

The X inputs can also be either continuous or discrete. Examples of continuous X’s are temperature, pressure, speed, and volume. Examples 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 would be the stratification factors. These are variables that may influence the item, process, or service delivery performance and should not be overlooked. Whenever we capture this information during data collection we can study it to determine if it makes a difference or not. Examples are time of day, day of every week, month of the season, season, location, region, or shift.

Since the inputs can be sorted from your 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, “What exactly is it that we wish to know?” This is a list of common questions and we’ll address every one separately.

What exactly is the baseline performance? Did the adjustments designed to the process, product, or service delivery make a difference? Are there relationships 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 begin by tackling them one-by-one.

Precisely what is baseline performance? Continuous Data – Plot the data in a time based sequence using an X-MR (individuals and moving range control charts) or subgroup the info utilizing an Xbar-R (averages and range control charts). The centerline from the chart offers an estimate in the average in the data overtime, thus establishing the baseline. The MR or R charts provide estimates from the variation over time and establish top of the and lower 3 standard deviation control limits for the X or Xbar charts. Produce a Histogram from the data to view a graphic representation from the distribution of the data, test it for normality (p-value should be much in excess of .05), and compare it to specifications to assess 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 utilizing 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. Top of the and lower control limits estimate 3 standard deviations of performance above and underneath the average, which makes up about 99.73% of all expected activity over time. You will get a bid from the worst and greatest case scenarios before any improvements are administered. Develop a Pareto Chart to look at a distribution of the categories as well as their frequencies of occurrence. When the control charts exhibit only normal natural patterns of variation as time passes (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 procedure, product, or service delivery make a difference?

Discrete X – Continuous Y – To test if two group averages (5W-30 vs. Synthetic Oil) impact gasoline consumption, use a T-Test. If you will find potential environmental concerns that may influence the test results make use of a Paired T-Test. Plot the results on the Boxplot and measure the T statistics with all the p-values to make a decision (p-values under or similar to .05 signify which a difference exists with at the very least a 95% confidence that it is true). If there is a positive change pick the group using the best overall average to meet the objective.

To test if two or more group averages (5W-30, 5W-40, 10W-30, 10W-40, or Synthetic) impact fuel useage use ANOVA (analysis of variance). Randomize the order in the testing to lower any time dependent environmental influences on the test results. Plot the outcomes on a Boxplot or Histogram and assess the F statistics with all the p-values to make a decision (p-values under or equal to .05 signify that the difference exists with at least a 95% confidence that it must be true). When there is a change select the group with all the best overall average to meet the goal.

In either of the aforementioned cases to test to see if you will find a difference within the variation caused by the inputs because they impact the output make use of a Test for Equal Variances (homogeneity of variance). Use the p-values to produce a decision (p-values lower than or comparable to .05 signify which a difference exists with a minimum of a 95% confidence that it must be true). If you have a change choose 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 there are multiple input X variables make use of a Matrix Plot. The plot supplies a graphical representation in the relationship between the variables. If it seems that a relationship may exist, between several from the X input variables as well as the output Y variable, conduct a Linear Regression of merely one 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, as well as the p-value. To be significant to get a single X-Y relationship the R2 needs to be in excess of .36 (36% of the variation inside the output Y is explained from the observed modifications in the input X), the F ought to be much in excess of 1, as well as the p-value needs to 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 when compared with other categories, or groups. As an example, “Which cruise line had the best customer satisfaction?” The discrete X variables are (RCI, Carnival, and Princess Cruise Lines). The discrete Y variables would be the frequency of responses from passengers on the satisfaction surveys by category (poor, fair, good, very good, and ideal) that relate to their vacation experience.

Conduct a cross tab table analysis, or Chi Square analysis, to evaluate if there have been variations in amounts of satisfaction by passengers based upon the cruise line they vacationed on. Percentages are used for the evaluation as well as the Chi Square analysis supplies a p-value to further quantify whether the differences are significant. The general p-value related to the Chi Square analysis needs to be .05 or less. The variables which have the biggest 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 fee per gallon of fuel influence consumer satisfaction? The continuous X is definitely the cost per gallon of fuel. The discrete Y will be 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 employed to validate that a significant difference either exists, or it doesn’t. P-values that are .05 or less mean that people have a minimum of a 95% confidence which a significant difference exists. Utilize the most frequently occurring ratings to make your determination.

Minitab Statistical Software Tools are Dot Plots stratified on Y and Logistic Regression Analysis. Are there any relationships involving the multiple input X’s and also the output Y’s? If there are relationships do they really make a difference?

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 technique is multiple regression. Evaluate the scatter plots to search for relationships involving the X input variables and also the output Y. Also, look for multicolinearity where one input X variable is correlated with another input X variable. This can be analogous to double dipping so we identify those conflicting inputs and systematically remove them from the model.

Multiple regression is 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 your model. Throughout the second iteration of the regression model turn on the variance inflation factors, or VIFs, which are utilized to quantify potential multicolinearity issues five to ten are issues). Review the Matrix Plot to recognize X’s linked to other X’s. Remove the variables using the high VIFs as well as the largest p-values, but ihtujy remove one of the related X variables inside a questionable pair. Evaluate the remaining p-values and remove variables with large p-values from the model. Don’t be surprised if this type of process requires some more iterations.

If the multiple regression model is finalized all VIFs will be less than 5 and all p-values will be under .05. The R2 value should be 90% or greater. This is a significant model as well as the regression equation can now be utilized for making predictions as long since we maintain the input variables in the min and max range values that were used to make 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 using designed experiments. Discrete and continuous X’s can be utilized as the input variables, however the settings on their behalf are predetermined in the appearance of the experiment. The analysis strategy is ANOVA which had been earlier mentioned.

Is an example. The aim is always to reduce the amount of unpopped kernels of popping corn in a bag of popped pop corn (the output Y). Discrete X’s could be the type of popping corn, form of oil, and shape of the popping vessel. Continuous X’s may be quantity of oil, quantity of popping corn, cooking time, and cooking temperature. Specific settings for each of the input X’s are selected and incorporated into the statistical experiment.