Prior to starting any sort of analysis classify the data set as either continuous or attribute, and in many cases it is a blend of both types. Continuous data is described as variables that can be measured on a continuous scale such as time, temperature, strength, or monetary value. A test is to divide the worth in half and see if it still makes sense.

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 including poor, fair, good, and ideal. Once an item is classified it may be counted and the frequency of occurrence may be determined.

Another determination to create is whether or not the **代写统计学** is an input variable or perhaps an output variable. Output variables tend to be referred to as CTQs (critical to quality characteristics) or performance measures. Input variables are what drive the resultant outcomes. We generally characterize an item, process, or service delivery outcome (the Y) by some function 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. Types of continuous Y’s are cycle time, cost, and productivity. Examples 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 be either continuous or discrete. Types 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. They are variables that could influence the product, process, or service delivery performance and should not be overlooked. If we capture this information during data collection we are able to study it to figure out if it makes a difference or otherwise. Examples are time, day of the week, month of the season, season, location, region, or shift.

Now that the inputs could be sorted from the outputs as well as the **SPSS代写** can be classified as either continuous or discrete the selection of the statistical tool to use depends upon answering the question, “What exactly is it that we want to know?” This is a list of common questions and we’ll address each one of these separately.

What exactly is the baseline performance? Did the adjustments created to the process, product, or service delivery make a difference? Are there any relationships involving the multiple input X’s as well as the output Y’s? If you will find relationships will they make a significant difference? That’s enough questions to be statistically dangerous so let’s start with tackling them one-by-one.

What exactly is baseline performance? Continuous Data – Plot the information in a time based sequence utilizing an X-MR (individuals and moving range control charts) or subgroup the data employing an Xbar-R (averages and range control charts). The centerline of the chart offers an estimate of the average from the data overtime, thus establishing the baseline. The MR or R charts provide estimates in the variation with time and establish the lower and upper 3 standard deviation control limits for that X or Xbar charts. Develop a Histogram of the data to view 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 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 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 underneath the average, which makes up about 99.73% of expected activity as time passes. You will get an estimate from the worst and best case scenarios before any improvements are administered. Produce a Pareto Chart to view a distribution of the categories along with their frequencies of occurrence. If 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 ability.

Minitab Statistical Software Tools are Attributes Control Charts and Pareto Analysis. Did the adjustments designed to this process, product, or service delivery make a difference?

Discrete X – Continuous Y – To check if two group averages (5W-30 vs. Synthetic Oil) impact gasoline consumption, make use of a T-Test. If you will find potential environmental concerns which could influence the exam results make use of a Paired T-Test. Plot the final results over a Boxplot and assess the T statistics with 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 is true). When there is a change select the group with all the best overall average to meet the objective.

To test if several group averages (5W-30, 5W-40, 10W-30, 10W-40, or Synthetic) impact gasoline consumption use ANOVA (analysis of variance). Randomize the transaction of the testing to reduce at any time dependent environmental influences on the test results. Plot the outcomes on a Boxplot or Histogram and assess the F statistics with the p-values to produce a decision (p-values less than or comparable to .05 signify that a difference exists with at least a 95% confidence that it must be true). When there is a difference choose the group using the best overall average to satisfy the aim.

In either of the aforementioned cases to check to determine if there is a difference in the variation due to the inputs since they impact the output make use of a Test for Equal Variances (homogeneity of variance). Make use of the p-values to produce a decision (p-values under or similar to .05 signify that the difference exists with at least a 95% confidence that it is true). When there is a positive change select 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 employing a Scatter Plot or if you can find multiple input X variables utilize a Matrix Plot. The plot offers a graphical representation from the relationship between the variables. If it would appear that a relationship may exist, between a number of 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 required for each X – Y relationship.

The Linear Regression Model provides an R2 statistic, an F statistic, as well as the p-value. To be significant to get a single X-Y relationship the R2 ought to be more than .36 (36% from the variation within the output Y is explained through the observed modifications in the input X), the F needs to be much greater 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 when compared with other categories, or groups. For example, “Which cruise line had the highest 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, excellent, and excellent) that connect with their vacation experience.

Conduct a cross tab table analysis, or Chi Square analysis, to examine if there have been differences in levels of satisfaction by passengers based upon the cruise line they vacationed on. Percentages are used for the evaluation and the Chi Square analysis offers a p-value to help quantify whether or not the differences are significant. The overall p-value associated with the Chi Square analysis needs to be .05 or less. The variables which 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 price per gallon of fuel influence consumer satisfaction? The continuous X is the cost per gallon of fuel. The discrete Y is the consumer satisfaction rating (unhappy, indifferent, or happy). Plot the **北美作业代写招聘** using Dot Plots stratified on Y. The statistical method is a Logistic Regression. Once more the p-values are utilized to validate that the significant difference either exists, or it doesn’t. P-values which can be .05 or less suggest that we now 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 as well as the output Y’s? If there are relationships will they change lives?

Continuous X – Continuous Y – The graphical analysis is really a Matrix Scatter Plot where multiple input X’s may be evaluated against the output Y characteristic. The statistical analysis technique is multiple regression. Evaluate the scatter plots to look for relationships between 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 therefore we identify those conflicting inputs and systematically eliminate them from your model.

Multiple regression is actually a powerful tool, but requires proceeding with caution. Run the model with all variables included then review the T statistics (T absolute value =1 is not significant) and F statistics (F =1 is not significant) to identify the first set of insignificant variables to remove from the model. During the second iteration of the regression model turn on the variance inflation factors, or VIFs, which are used to quantify potential multicolinearity issues (VIFs 5 are OK, VIFs> five to ten are issues). Assess the Matrix Plot to distinguish X’s associated with other X’s. Remove the variables with all the high VIFs and the largest p-values, but only remove one of many related X variables inside a questionable pair. Evaluate the remaining p-values and remove variables with large p-values >>0.05 from fidtkv model. Don’t be blown away if the process requires some more iterations.

If the multiple regression model is finalized all VIFs is going to be lower than 5 and all sorts of p-values will likely be less than .05. The R2 value needs to be 90% or greater. This is a significant model and also the regression equation can now be employed for making predictions so long as we maintain the input variables in the min and max range values which 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 case requires using designed experiments. Discrete and continuous X’s bring the input variables, however the settings to them are predetermined in the appearance of the experiment. The analysis technique is ANOVA that was earlier mentioned.

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