Before starting any kind of analysis classify the data set as either continuous or attribute, and in some cases it is a combination of both types. Continuous information is seen as a variables that can be measured on a continuous scale such as time, temperature, strength, or value. A test is to divide the worth by 50 percent and discover if it still is sensible.

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

The following determination to help make is whether the data is **统计作业代写**. Output variables are often referred to as CTQs (critical 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 function of the input variables X1,X2,X3,… Xn. The Y’s are driven from 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 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. Samples 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 continually consider are the stratification factors. These are variables that may influence the item, process, or service delivery performance and must not be overlooked. Whenever we capture this information during data collection we can study it to figure out if this makes a difference or otherwise not. Examples are duration of day, day of the week, month of the year, season, location, region, or shift.

Since the inputs can be sorted through the outputs and also the data can be considered either continuous or discrete selecting the statistical tool to apply boils down to answering the question, “What exactly is it that we wish to know?” The following is a summary of common questions and we’ll address every one separately.

What exactly is the baseline performance? Did the adjustments created to this process, product, or service delivery change lives? Are there any relationships involving 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 by tackling them one at a time.

What exactly is baseline performance? Continuous Data – Plot the data in a time based sequence employing an X-MR (individuals and moving range control charts) or subgroup the data using an Xbar-R (averages and range control charts). The centerline in the chart offers an estimate in the average from the data overtime, thus establishing the baseline. The MR or R charts provide estimates from the variation with time and establish the top and lower 3 standard deviation control limits for your X or Xbar charts. Create a Histogram from the data to see a graphic representation of the distribution in the data, test it for normality (p-value should 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 employing a P Chart (percent defective chart), C Chart (count of defects chart), nP Chart (Sample n times percent defective chart), or 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 expected activity with time. You will possess a bid in the worst and finest case scenarios before any improvements are administered. Create a Pareto Chart to view a distribution from the categories as well as their frequencies of occurrence. In the event the control charts exhibit only normal natural patterns of variation over 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 designed to this process, product, or service delivery really make a difference?

Discrete X – Continuous Y – To check if two group averages (5W-30 vs. Synthetic Oil) impact fuel useage, utilize a T-Test. If you will find potential environmental concerns that may influence the test results use a Paired T-Test. Plot the outcomes on a Boxplot and evaluate the T statistics using the p-values to create a decision (p-values lower than or equal to .05 signify that the difference exists with a minimum of a 95% confidence that it must be true). When there is a positive change select the group with all the best overall average to meet the objective.

To evaluate if several group averages (5W-30, 5W-40, 10W-30, 10W-40, or Synthetic) impact gas mileage use ANOVA (analysis of variance). Randomize the order in the testing to minimize any time dependent environmental influences on the test results. Plot the results on a Boxplot or Histogram and assess the F statistics using the p-values to create a decision (p-values less than or equal to .05 signify which a difference exists with at least a 95% confidence that it must be true). When there is a positive change choose the group with the best overall average to satisfy the goal.

In either of the aforementioned cases to evaluate to determine if there exists a difference within the variation brought on by the inputs because they impact the output utilize a Test for Equal Variances (homogeneity of variance). Use the p-values to make a decision (p-values lower than or comparable to .05 signify which a difference exists with at the very least a 95% confidence that it must be true). If there is a change choose the group using 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 if perhaps you can find multiple input X variables use a Matrix Plot. The plot supplies a graphical representation from the relationship in between the variables. If it appears that a partnership may exist, between one or more in the X input variables and the output Y variable, conduct a Linear Regression of merely one input X versus one output Y. Repeat as required for each X – Y relationship.

The Linear Regression Model provides an R2 statistic, an F statistic, and the p-value. To be significant for any single X-Y relationship the R2 ought to be greater than .36 (36% in the variation inside the output Y is explained through the observed changes in the input X), the F needs to be much more than 1, and also 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 kind of analysis categories, or groups, are in comparison to other categories, or groups. For instance, “Which cruise line had the best client satisfaction?” The discrete X variables are (RCI, Carnival, and Princess Cruise Lines). The discrete Y variables are definitely the frequency of responses from passengers on their satisfaction surveys by category (poor, fair, good, great, and ideal) that relate with their vacation experience.

Conduct a cross tab table analysis, or Chi Square analysis, to examine if there was differences in amounts of satisfaction by passengers based on the cruise line they vacationed on. Percentages are used for the evaluation and also the Chi Square analysis supplies a p-value to further quantify whether or not the differences are significant. The entire p-value associated with the Chi Square analysis needs to be .05 or less. The variables that have the largest contribution to 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 cost per gallon of fuel influence consumer satisfaction? The continuous X will be 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. Yet 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 we have at the very least a 95% confidence which a significant difference exists. Make use of the most often occurring ratings to create 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 you can find relationships do they really change lives?

Continuous X – Continuous Y – The graphical analysis is actually a Matrix Scatter Plot where multiple input X’s can be evaluated from the output Y characteristic. The statistical analysis method is multiple regression. Measure the scatter plots to look for relationships involving the X input variables and also 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 so we identify those conflicting inputs and systematically eliminate them from the model.

Multiple regression is actually a powerful tool, but requires proceeding with caution. Run the model with all variables included then evaluate the T statistics and F statistics to identify the first set of insignificant variables to eliminate from your model. Throughout the second iteration of the regression model turn on the variance inflation factors, or VIFs, which are used to quantify potential multicolinearity issues 5 to 10 are issues). Review the Matrix Plot to recognize X’s linked to other X’s. Take away the variables with all the high VIFs as well as the largest p-values, but ihtujy remove one of the related X variables in a questionable pair. Review the remaining p-values and take off variables with large p-values from your model. Don’t be surprised if this type of process requires some more iterations.

When the multiple regression model is finalized all VIFs will be under 5 and all sorts of p-values is going to be under .05. The R2 value should be 90% or greater. It is a significant model as well as the regression equation can certainly be used for making predictions as long as we keep the input variables inside the min and max range values which were used 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 case requires using designed experiments. Discrete and continuous X’s can be utilized for the input variables, nevertheless the settings to them are predetermined in the design of the experiment. The analysis method is ANOVA that was 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 may be the type of popping corn, type of oil, and form of the popping vessel. Continuous X’s might be quantity of oil, level of popping corn, cooking time, and cooking temperature. Specific settings for each one of the input X’s are selected and included in the statistical experiment.