# NCSS Statistical Software. X-bar and s Charts

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Chapter 243 Introduction This procedure generates X-bar and s (standard deviation) control charts for variables. The format of the control charts is fully customizable. The data for the subgroups can be in a single column or in multiple columns. This procedure permits the defining of stages. For the X-bar chart, the center line can be entered directly or estimated from the data, or a sub-set of the data. Similarly sigma may be estimated from the data or a standard sigma value may be entered. A list of out-of-control points can be produced in the output, if desired, and means and standard deviation values may be stored to the spreadsheet. X-bar and s Control Charts X-bar and s charts are used to monitor the mean and variation of a process based on samples taken from the process at given times (hours, shifts, days, weeks, months, etc.). The measurements of the samples at a given time constitute a subgroup. Typically, an initial series of subgroups is used to estimate the mean and standard deviation of a process. The mean and standard deviation are then used to produce control limits for the mean and standard deviation of each subgroup. During this initial phase, the process should be in control. If points are out-of-control during the initial (estimation) phase, the assignable cause should be determined and the subgroup should be removed from estimation. Determining the process capability (see R & R Study and Capability Analysis procedures) may also be useful at this phase. Once the control limits have been established of the X-bar and s charts, these limits may be used to monitor the mean and variation of the process going forward. When a point is outside these established control limits it indicates that the mean (or variation) of the process is out-of-control. An assignable cause is suspected whenever the control chart indicates an out-of-control process

2 Other Control Charts for the Mean and Variation of a Process The X-bar and s charts are very similar to the popular X-bar and R charts, the difference being that the standard deviation is estimated from the mean standard deviation in the former, and from the mean range in the latter. The X-bar and s charts are generally recommended over the X-bar and R charts when the subgroup sample size is moderately large (n > 10), or when the sample size is variable from subgroup to subgroup (Montgomery, 2013). Two additional control charts available for monitoring the process mean are the cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) charts. The CUSUM and EWMA charts differ from the X-bar charts in that they take into account the information of previous means at each point rather than just the current mean. The CUSUM and EWMA charts are more sensitive to smaller shifts in the mean since they use the cumulative information of the sequence of means. However, CUSUM and EWMA methods also assume a reliable estimate or known value for the true standard deviation is available. When only a single response is available at each time point, then the individuals and moving range (I-MR) control charts can be used for early phase monitoring of the mean and variation. CUSUM and EWMA charts may also be used for single responses, and are useful when small changes in the mean need to be detected. Control Chart Formulas Suppose we have k subgroups, each of size n. Let x ij represent the measurement in the j th sample of the i th subgroup. Formulas for the Points on the Chart The i th subgroup mean is calculated using and the subgroup standard deviation is calculated with x n n x ij j= i = 1, s i = n ( x ij x i ) j = 1 n 1 2. Estimating the X-bar Chart Center Line (Grand Mean) In the procedure, the grand average may be input directly, or it may be estimated from a series of subgroups. If it is estimated from the subgroups the formula for the grand average is x k n i i= 1 j= 1 = k i= 1 n x i ij

3 243-3 If the subgroups are of equal size, the above equation for the grand mean reduces to k x x x k x x k k i i = = = Estimating Sigma Mean of Standard Deviations The true standard deviation (sigma) may be input directly, or it may be estimated from the standard deviations by 4 ˆ c s = σ where s s k i i k = = 1 ( ) σ µ σ s s E c = = 4 The calculation of E(s) requires the knowledge of the underlying distribution of the x ij s. Making the assumption that the x ij s follow the normal distribution with constant mean and variance, the values for c 4 are obtained from c n n n = Γ Γ Estimating Sigma Weighted Approach When the sample size is variable across subgroups, a weighted approach is recommended for estimating sigma (Montgomery, 2013): 2 1/ ) ( ˆ = = = = k i i k i i i k n s n s σ X-bar Chart Limits The lower and upper control limits for the X-bar chart are calculated using the formulas = n m x LCL σˆ + = n m x UCL σˆ

4 where m is a multiplier (usually set to 3) chosen to control the likelihood of false alarms (out-of-control signals when the process is in control). Estimating the s Chart Center Line If a standard sigma (standard deviation) value is entered by the user, the s Chart center line is computed using s = c 4 σ If the standard deviation is estimated from a series of subgroups, the s chart center line is given by s, whether computed by the mean of standard deviations approach, or by the weighted approach. s Chart Limits The lower and upper control limits for the s chart are calculated using the formula LCL = s m ˆ σ 1 c UCL = s + m ˆ σ 1 c where m is a multiplier (usually set to 3) chosen to control the likelihood of false alarms, and c 4 is defined above, and is based on the assumption of normality Runs Tests The strength of control charts comes from their ability to detect sudden changes in a process that result from the presence of assignable causes. Unfortunately, the X-bar chart is poor at detecting drifts (gradual trends) or small shifts in the process. For example, there might be a positive trend in the last ten subgroups, but until a mean goes above the upper control limit, the chart gives no indication that a change has taken place in the process. Runs tests can be used to check control charts for unnatural patterns that are most likely caused by assignable causes. Runs tests are sometimes called pattern tests, out-of-control tests, or zones rules. While runs tests may be helpful in identifying patterns or smaller shifts in the mean, they also increase the likelihood of false positive indications. The rate of false positives is typically measured using the average run length (the average length of a run before a false positive is indicated). When several runs tests are used the average run length of the control chart becomes very short. Two alternatives to consider before using runs tests are the CUSUM and EWMA control charts. Runs tests are generally advised against when there is only one observation per subgroup. In this case, the rate of false positives is quite high (average run length is short). In order to perform the runs tests, the control chart is divided into six equal zones (three on each side of the centerline). Since the control limit is three sigma limits (three standard deviations of the mean) in width, each zone is one sigma wide and is labeled A, B, or C, with the C zone being the closest to the centerline. There is a lower zone A and an upper zone A. The same is true for B and C. The runs tests look at the pattern in which points fall in these zones. The runs tests used in this procedure are described below. Test 1: Any Single Point Beyond Zone A This runs test simply indicates a single point is beyond one of the two three-sigma limits. Test 2: Two of Three Successive Points in Zone A or Beyond This usually indicates a shift in the process average. Note that the two points have to be in the same Zone A, upper or lower. They cannot be on both sides of the centerline. The third point can be anywhere

5 Test 3: Four of Five Successive Points in Zone B or Beyond This usually indicates a shift in the process average. Note that the odd point can be anywhere. Test 4: Eight Successive Points in Zone C or Beyond All eight points must be on one side of the centerline. This is another indication of a shift in the process average. Test 5: Fifteen Successive Points Fall in Zone C on Either Side of the Centerline Although this pattern might make you think that the variation in your process has suddenly decreased, this is usually not the case. It is usually an indication of stratification in the sample. This happens when the samples come from two distinct distributions having different means. Perhaps there are two machines that are set differently. Try to isolate the two processes and check each one separately. Test 6: Eight of Eight Successive Points Outside of Zone C This usually indicates a mixture of processes. This can happen when two supposedly identical production lines feed a single production or assembly process. You must separate the processes to find and correct the assignable cause. There are, of course, many other sets of runs tests that have been developed. You should watch your data for trends, zig-zags, and other nonrandom patterns. Any of these conditions could be an indication of an assignable cause and would warrant further investigation. Issues in Using Control Charts There are several additional considerations surrounding the use of control charts that will not be addressed here. Some important questions are presented below without discussion. For a full treatment of these issues you should consider a statistical quality control text such as Ryan (2011) or Montgomery (2013). Subgroup Size How many items should be sampled for each subgroup? Some common values are 5, 10, and 20. How does the subgroup size affect my use of control charts? What about unequal subgroup sizes? Dealing with Out-of-Control Points How do you deal with out-of-control points once they have been detected? Should they be included or excluded in the process average and standard deviation? Control Limit Multiplier Three-sigma limits are very common. When should one consider a value other than three? Startup Time How many subgroups should be used to establish control for my process? Normality Assumption How important is the assumption of normality? How do I check this? Should I consider a transformation? (See also the Box-Cox Transformation and Capability Analysis procedures in NCSS.) 243-5

6 Data Structure In this procedure, the data may be in either of two formats. The first data structure option is to have the data in several columns, with one subgroup per row. Example dataset S1 S2 S3 S4 S The second data structure option uses one column for the response data, and either a subgroup size or a second column defining the subgroups. Alternative example dataset Response Subgroup In the alternative example dataset, the Subgroup column is not needed if every subgroup is of size 5 and the user specifies 5 as the subgroup size. If there are missing values, the Subgroup column should be used, or the structure of the first example dataset

7 Procedure Options This section describes the options available in this procedure. To find out more about using a procedure, go to the Procedures chapter. Variables Tab This panel specifies the variables that will be used in the analysis. Input Type Specify whether the data is in a single response column or in multiple columns with one subgroup per row. Response Column and Subgroup Column or Subgroup Size Response Subgroup Multiple Columns with One Subgroup Per Row X1 X2 X Variables Response Column Response Variable Specify the column with the data values. The data values are separated into subgroups below using the Subgroup Specification options. Subgroup Specification Specify whether subgroups are defined by a Subgroup ID variable, or by a subgroup size. If the subgroup size is 3, then subgroups are formed by going down the response column in groups of 3. The first subgroup would be 5, 6, 4; the second would be 3, 7, 6; and so on

8 Subgroup ID Variable Specify the column containing the subgroup identifiers. Response ID Variable A new subgroup is created for each change in the Subgroup ID Variable, going down. Subgroup Size Specify the number of individuals in each subgroup. Response If the subgroup size is 3, then subgroups are formed by going down the response column in groups of 3. The first subgroup would be 5, 6, 4; the second would be 3, 7, 6; and so on. Variables Multiple Columns Data Variables Specify the columns containing the sample responses. Each row represents a subgroup. X1 X2 X

9 If only one variable is specified, NCSS automatically generates an individuals chart with a moving-range of size 2. Stages Number of Stages Specify whether the analyses and charts are to be produced based on a single set of subgroups, or a series of sets of subgroups. Typically a single stage is used unless you wish to have separate estimation for various segments of the subgroups. When using multiple stages, the software requires that there be at least one subgroup in every stage specified. Stage Specification Specify whether the various stages will be defined using a variable (column) with a unique value for each stage, or by entering a range of rows for each stage. Stage Variable X1 X2 X3 Stage Enter a range for each stage 1-50, , This would produce three stages. The first stage would be made up of rows 1 to 50, the second stage would be rows 51 to 100, and the third stage would be rows 101 to 150. Stage Variable Specify the variable (column) that contains the identifiers for each stage. X1 X2 X3 Stage Variable A new stage is created for each change in the Stage Variable, going down

10 Stage Ranges Enter a range for each stage using a dash. Separate each stage with a comma. Example: 1-50, , This would produce three stages. The first stage would be made up of rows 1 to 50, the second stage would be rows 51 to 100, and the third stage would be rows 101 to 150. Specify Rows in Calculations Specification Method Select which method will be used to specify the rows of the data to be used to form subgroups. All Rows All rows in the response column(s) will be used. Enter First Row and Last Row Specify the first row and the last row of the data for use in calculations. First N Rows (Enter N) The data beginning at Row 1 and ending at Row N will be used in calculations. Last N Rows (Enter N) Subgroups will be formed from the last N rows of the dataset. Keep Rows Variable Specify a variable and a value in that variable column that will be used to determine which rows are used to form the subgroups. Remove Rows Variable Specify a variable and a value in that variable column that will be used to determine which rows will not be used to form the subgroups. First Row Specify the beginning row to be used for the first subgroup. Last Row Specify the last row to be used for the last subgroup. N Enter the number of rows to be used in forming subgroups. Keep Rows Variable This variable (column) is used to specify which rows of the data will be used to form the subgroups for the calculations. Keep Rows Value This value determines which rows of the Keep Rows Variable will be used in the calculation portion of the analysis

11 Remove Rows Variable This variable (column) is used to specify which rows of the data will not be used to form the subgroups for the calculations. Remove Rows Value This value determines which rows of the Remove Rows Variable will not be used in the calculation portion of the analysis. Specify Rows in Charts Specification Method Select which method will be used to specify the rows of the data to be used to form subgroups for the charts. All Rows All rows in the response column(s) will be used. Enter First Row and Last Row Specify the first row and the last row of the data for use in the plots. First N Rows (Enter N) The data beginning at Row 1 and ending at Row N will be used in the plots. Last N Rows (Enter N) Subgroups will be formed from the last N rows of the dataset. Keep Rows Variable Specify a variable and a value in that variable column that will be used to determine which rows are used to form the subgroups. Remove Rows Variable Specify a variable and a value in that variable column that will be used to determine which rows will not be used to form the subgroups. First Row Specify the beginning row to be used for the first subgroup. Last Row Specify the last row to be used for the last subgroup. N Enter the number of rows to be used in forming subgroups. Keep Rows Variable This variable (column) is used to specify which rows of the data will be used to form the subgroups for the plots. Keep Rows Value This value determines which rows of the Keep Rows Variable will be used in the plots. Remove Rows Variable This variable (column) is used to specify which rows of the data will not be used to form the subgroups for the plots

12 Remove Rows Value This value determines which rows of the Remove Rows Variable will not be used in the plots. Labels (Optional) Subgroup Label Variable Specify a variable (column) that contains the desired x axis (subgroup) labels for plots. If left blank, the plot will use the subgroup number. The format of the labels is controlled on the x axis tab of the plot format window. Point Label Variable Specify a variable (column) that contains the desired individual point labels for plots. If left blank, no point labels are shown. The format of the labels is controlled on the main chart tab of the plot format window. Lines & Limits Tab The options on the Lines & Limits tab are used to specify the center line method, the limit multipliers, and the method by which sigma is estimated. X-bar Chart Options Center Line Options Center Line Specification Specify whether the X-bar chart center line will be estimated from the data, or whether it will be specified directly. From Data Estimate the center line from the subgroups specified for calculations. Enter Center Line Value(s) Specify directly the center line for the X-bar chart. If multiple stages are used, separate the center line values for each stage by spaces. Use a Variable with Center Line Value(s) Specify a column containing the center line value in row 1. If multiple stages are used, a center line value should be entered in a separate cell for each stage, beginning with row 1 for the first stage. Center Line Value(s) Enter the value to be used for the center line of the X-bar chart. If multiple stages are used, separate the center line values for each stage by spaces. Center Line Variable Specify a column containing the center line value in row 1. If multiple stages are used, a center line value should be entered in a separate cell for each stage, beginning with row 1 for the first stage. X-bar Chart Options Specification Limits Lower Limit Enter an optional lower specification limit for display on the X-bar chart. These limits are not the control limits. Upper Limit Enter an optional upper specification limit for display on the X-bar chart. These limits are not the control limits

13 Target Specification Enter an optional target value for display on the X-bar chart. Sigma Estimation Options Sigma Specification Specify the method by which Sigma will be estimated for use in the charts. From Data s-bar Estimate Estimate sigma based on the average of the standard deviations. Only the subgroups specified for use in calculations will be used. From Data Weighted Approach Estimate This method estimates s-bar using a special formula that is recommended when the subgroup size varies across subgroups. Only the subgroups specified for use in calculations will be used. Enter Standard Sigma Value(s) In this case the sigma value is entered directly. The corresponding s-bar value for plots is back-calculated from this value. If multiple stages are used, separate the sigma values for each stage by spaces. Use a Variable with Standard Sigma Value(s) Specify a column containing the standard sigma value in row 1. The corresponding s-bar value for plots is back-calculated from this value. If multiple stages are used, a sigma value should be entered in a separate cell for each stage, beginning with row 1 for the first stage. Sigma Value(s) Enter the value to be used for the standard sigma. If multiple stages are used, separate the sigma values for each stage by spaces. Sigma Variable Specify a column containing the standard sigma value in row 1. The corresponding s-bar value for plots is backcalculated from this value. If multiple stages are used, a sigma value should be entered in a separate cell for each stage, beginning with row 1 for the first stage. Limit Multipliers Primary Limit Multiplier This option specifies the multiplier of sigma for the primary control limits. For the well-known 3-sigma limits, the multiplier is set to 3. Secondary Limit Multiplier This option specifies the multiplier of sigma for the optional, secondary control limits. The secondary limits may be shown on the plot by checking the 'Secondary Limit' option on the plot format window

14 Reports Tab The following options control the format of the reports. Specify Reports Chart Summary (Control Limits and Estimation) Section This report gives the numeric values of the center lines and limits, as well as the sigma estimation section. Out-of-Control List Section This report shows the out-of-control points and the corresponding reason (runs test or outside control limit). Report Options Precision Specify the precision of numbers in the report. A single-precision number will show seven-place accuracy, while a double-precision number will show thirteen-place accuracy. Note that the reports are formatted for single precision. If you select double precision, some numbers may run into others. Also note that all calculations are performed in double precision regardless of which option you select here. This is for reporting purposes only. Variable Names This option lets you select whether to display variable names, variable labels, or both. Page Title This option specifies a title to appear at the top of each page. Plot Subtitle This option specifies a subtitle to appear at the top of each plot. Tab This panel sets the options used to define the appearance of the X-bar chart and the s chart. Select Plots X-bar Chart and s (Standard Deviation) Chart Each chart is controlled by three form objects: 1. A checkbox to indicate whether the chart is displayed. 2. A format button used to call up the plot format window (see Quality Control Chart Format Window Options below for more formatting details). 3. A second checkbox used to indicate whether the chart can be edited during the run. Storage Tab The options on this panel control the automatic storage of the means and standard deviations on the current dataset

15 Storage Columns Store Means in Column You can automatically store the means of each subgroup into the column specified here. Warning: Any data already in this column is replaced. Be careful not to specify columns that contain important data. Store Standard Deviations in Column You can automatically store the range of each row into the column specified here. Warning: Any data already in this column is replaced. Be careful not to specify columns that contain important data. Quality Control Chart Format Window Options This section describes a few of the specific options available on the first tab of the control chart format window, which is displayed when a quality control chart format button is pressed. Common options, such as axes, labels, legends, and titles are documented in the Graphics Components chapter

16 [Xbar] / [Range] Chart Tab Symbols Section You can modify the attributes of the symbols using the options in this section. A wide variety of sizes, shapes, and colors are available for the symbols. The symbols for in-control and out-ofcontrol points are specified independently. There are additional options to label out-of-control points. The label for points outside the primary control limits is the subgroup number. The label for points that are out-of-control based on the runs test is the number of the first runs test that is signaled by this point. The user may also specify a column of point labels on the procedure variables tab, to be used to label all or some of the points of the chart. The raw data may also be shown, based on customizable raw data symbols. Lines Section You can specify the format of the various lines using the options in this section. Note that when shading is desired, the fill will be to the bottom for single lines (such as the mean line), and between the lines for pairs of lines (such as primary limits). Lines for the zones, secondary limits, and specification limits are also specified here

17 Titles, Legend, Numeric Axis, Group Axis, Grid Lines, and Background Tabs Details on setting the options in these tabs are given in the Graphics Components chapter. The legend does not show by default, but can easily be included by going to the Legend tab and clicking the Show Legend checkbox. Example 1 Analysis (Phase I) This section presents an example of how to run an initial X-bar and s Chart analysis to establish control limits. The data represent 50 subgroups of size 5. The data used are in the QC dataset. We will analyze the variables D1 through D5 of this dataset. You may follow along here by making the appropriate entries or load the completed template Example 1 by clicking on Open Example Template from the File menu of the window. 1 Open the QC dataset. From the File menu of the NCSS Data window, select Open Example Data. Click on the file QC.NCSS. Click Open. 2 Open the window. Using the Analysis or Graphics menu or the Procedure Navigator, find and select the procedure. On the menus, select File, then New Template. This will fill the procedure with the default template. 3 Specify the variables. On the window, select the Variables tab. Double-click in the Data Variables text box. This will bring up the variable selection window. Select D1 through D5 from the list of variables and then click Ok. D1-D5 will appear in the Data Variables box. 4 Run the procedure. From the Run menu, select Run Procedure. Alternatively, just click the green Run button. Center Line Section Center Line Section for Subgroups 1 to 50 Number of Subgroups 50 Center Line Estimate Estimated Grand Average (X-bar-bar) s-bar This section displays the center line values that are to be used in the X-bar and s charts. Estimated Grand Average (X-bar-bar) This value is the average of all the observations. If all the subgroups are of the same size, it is also the average of all the X-bars. s-bar This is the average of the standard deviations

18 Primary Control Limit Section Primary Control Limit Section for Subgroups 1 to 50 These limits are based on a subgroup of size 5. Primary Control Limits Chart Type Lower Upper X-bar s This report gives the lower and upper limits for each of the charts, corresponding to a specific subgroup size. X-bar Lower and Upper Primary Control Limits These limits are the primary control limits of the X-bar chart, as defined in the sub-section X-bar Chart Limits of the Control Chart Formulas section toward the beginning of this chapter. s Lower and Upper Primary Control Limits These limits are the primary control limits of the s chart, as defined in the sub-section s Chart Limits of the Control Chart Formulas section toward the beginning of this chapter. Since the lower limit for the s chart is less than 0, it has been reset to 0. Sigma Estimation Section Sigma Estimation Section for Subgroups 1 to 50 Estimation Estimated Estimated Type Value Sigma Ranges (R-bar) Standard Deviations (s-bar)* Weighted Approach (s-bar) * Indicates the estimation type used in this report. This report gives the estimation of the population standard deviation (sigma) based on three estimation techniques. The estimation technique used for the plots in this procedure is based on the ranges. Estimation Type The two formulas for estimating sigma based on the standard deviation are shown earlier in this chapter in the Control Chart Formulas section. The formulas for the Ranges method are shown in the X-bar and R Charts chapter. Estimated Value This column gives the R-bar and s-bar estimates based on the corresponding formulas. Estimated Sigma This column gives estimates of the population standard deviation (sigma) based on the corresponding estimation type

19 The first plot shows the sample means, as well as the centerline and control limits for the process mean, based on the 50 subgroups. This process appears to be in control. The second plot shows the sample standard deviations for each subgroup, as well as the corresponding centerline and limits. The s chart seems to indicate the variation is also in control. Out-of-Control List Out-of-Control List for Subgroups 1 to 50 Subgroup Subgroup Mean s Label Reason s: 4 of 5 in zone B or beyond This report provides a list of the subgroups that failed one of the runs tests (including points outside the control limits). The report shows that subgroup 30 is the final point of 4 out of 5 points in Zone B. This run does not appear to indicate a clear shift in the process variation

20 Example 2 Analysis (Phase II) This section presents a continuation of the previous example. In this example the limits are based on the first 50 observations, but the means and ranges are monitored for an additional 100 subgroups. The data are given in the columns D1ext D5ext of the QC dataset. You may follow along here by making the appropriate entries or load the completed template Example 2 by clicking on Open Example Template from the File menu of the window. 1 Open the QC dataset. From the File menu of the NCSS Data window, select Open Example Data. Click on the file QC.NCSS. Click Open. 2 Open the window. Using the Analysis or Graphics menu or the Procedure Navigator, find and select the procedure. On the menus, select File, then New Template. This will fill the procedure with the default template. 3 Specify the variables. On the window, select the Variables tab. Double-click in the Data Variables text box. This will bring up the variable selection window. Select D1ext through D5ext from the list of variables and then click Ok. D1ext-D5ext will appear in the Data Variables box. 4 Specify the Rows in Calculations. Under Specify Rows in Calculations, set the Specification Method to First N rows (Enter N). Set N to Run the procedure. From the Run menu, select Run Procedure. Alternatively, just click the green Run button. Center Line, Control Limits, and Estimation Sections Center Line Section for Subgroups 1 to 50 Number of Subgroups 50 Center Line Estimate Estimated Grand Average (X-bar-bar) s-bar Primary Control Limit Section for Subgroups 1 to 50 These limits are based on a subgroup of size 5. Primary Control Limits Chart Type Lower Upper X-bar s Sigma Estimation Section for Subgroups 1 to 50 Estimation Estimated Estimated Type Value Sigma Ranges (R-bar)* Standard Deviations (s-bar) Weighted Approach (s-bar)

21 Since the first 50 subgroups are the same as those of Example 1, and since only the first 50 subgroups are used in the calculations for this run, the results for these sections are the same as those of Example 1. These plots have the same limits as those of Example 1. It appears there may have been a shift in process for the last 30 or 40 subgroups, as evidenced by the large majority of points above the center line and out-of-control signal from subgroup

22 Out-of-Control List Out-of-Control List for Subgroups 1 to 150 Subgroup Subgroup Mean s Label Reason s: 4 of 5 in zone B or beyond s: 8 in zone C or beyond X-bar: 2 of 3 in zone A X-bar: 4 of 5 in zone B or beyond X-bar: 4 of 5 in zone B or beyond X-bar: 4 of 5 in zone B or beyond X-bar: 4 of 5 in zone B or beyond X-bar: 8 in zone C or beyond X-bar: 8 in zone C or beyond X-bar: 8 in zone C or beyond X-bar: 8 in zone C or beyond X-bar: 8 in zone C or beyond X-bar: 8 in zone C or beyond s: 4 of 5 in zone B or beyond s: 8 in zone C or beyond s: 8 in zone C or beyond X-bar: beyond control limits X-bar: 4 of 5 in zone B or beyond X-bar: 4 of 5 in zone B or beyond X-bar: 4 of 5 in zone B or beyond X-bar: 4 of 5 in zone B or beyond X-bar: 4 of 5 in zone B or beyond This list indicates a large number of out-of-control signals (by Runs tests) for subgroups 121 and beyond

23 Example 3 X-bar Chart with Additional Formatting This example uses the same setup as Example 2, except that a variety of improvements are made in the plot format. These improvements are made by clicking the X-bar Chart format button on the X-bar & s charts tab. You can load the completed template Example 3 by clicking on Open Example Template from the File menu of the window. X-bar Chart As shown here, a variety of enhancements can be made to the formatting of the control charts to make the chart as easy to read as possible. The numbers above the points near the end represent the number of the first runs test that is signaled by that point

24 Example 4 with Stages This section presents X-bar and s charts for the scenario of multiple stages in a process. In the QC Stage dataset a significant change had been made in the process after subgroup 70. This change merits a new evaluation of the process mean and standard deviation, beginning at subgroup 71. In this example, the process mean and standard deviation for each stage are to be determined based on the first 30 subgroups. You may follow along here by making the appropriate entries or load the completed template Example 4 by clicking on Open Example Template from the File menu of the window. 1 Open the QC Stage dataset. From the File menu of the NCSS Data window, select Open Example Data. Click on the file QC Stage.NCSS. Click Open. 2 Open the window. Using the Analysis or Graphics menu or the Procedure Navigator, find and select the procedure. On the menus, select File, then New Template. This will fill the procedure with the default template. 3 Specify the variables. On the window, select the Variables tab. Double-click in the Data Variables text box. This will bring up the variable selection window. Select D1 through D5 from the list of variables and then click Ok. D1-D5 will appear in the Data Variables box. 4 Specify the stages. On the window, select the Variables tab. For Number of Stages select Multiple Stages. For Stage Variable select Stage. 5 Specify the Rows in Calculations. Under Specify Rows in Calculations, set the Specification Method to Keep Rows Variable. Enter Use all rows where variable CalcRows equals 1. 6 Run the procedure. From the Run menu, select Run Procedure. Alternatively, just click the green Run button

25 Center Line, Control Limits, and Estimation Sections Center Line Section for Subgroups 1 to 70 where CalcRows equals 1 Number of Subgroups 30 Center Line Estimate Estimated Grand Average (X-bar-bar) s-bar Primary Control Limit Section for Subgroups 1 to 70 where CalcRows equals 1 These limits are based on a subgroup of size 5. Primary Control Limits Chart Type Lower Upper X-bar s Sigma Estimation Section for Subgroups 1 to 70 where CalcRows equals 1 Estimation Estimated Estimated Type Value Sigma Ranges (R-bar) Standard Deviations (s-bar)* Weighted Approach (s-bar) * Indicates the estimation type used in this report. Center Line Section for Subgroups 71 to 120 where CalcRows equals 1 Number of Subgroups 30 Center Line Estimate Estimated Grand Average (X-bar-bar) s-bar Primary Control Limit Section for Subgroups 71 to 120 where CalcRows equals 1 These limits are based on a subgroup of size 5. Primary Control Limits Chart Type Lower Upper X-bar s Sigma Estimation Section for Subgroups 71 to 120 where CalcRows equals 1 Estimation Estimated Estimated Type Value Sigma Ranges (R-bar) Standard Deviations (s-bar)* Weighted Approach (s-bar) * Indicates the estimation type used in this report. This report shows the center line, limit, and sigma estimates for each of the two stages. The center line estimate changes from about 51 to about 46. There also appears to be a change in sigma of about 6.3 to about

26 The change in process mean and variation from the first stage to the second is reflected in the X-bar and s charts

### NCSS Statistical Software

Chapter 155 Introduction graphically display tables of means (or medians) and variability. Following are examples of the types of charts produced by this procedure. The error bars may represent the standard

### Scatter Plots with Error Bars

Chapter 165 Scatter Plots with Error Bars Introduction The procedure extends the capability of the basic scatter plot by allowing you to plot the variability in Y and X corresponding to each point. Each

### NCSS Statistical Software

Chapter 148 Introduction Bar charts are used to visually compare values to each other. This chapter gives a brief overview and examples of simple 3D bar charts and two-factor 3D bar charts. Below is an

### NCSS Statistical Software

Chapter 142 Introduction The pie chart is constructed by dividing a circle into two or more sections or slices. The chart is used to show the proportion that each part is of the whole. Hence, it should

### Regression Clustering

Chapter 449 Introduction This algorithm provides for clustering in the multiple regression setting in which you have a dependent variable Y and one or more independent variables, the X s. The algorithm

### HOW TO USE MINITAB: QUALITY CONTROL

HOW TO USE MINITAB: QUALITY CONTROL 1 Noelle M. Richard 08/27/14 INTRODUCTION * Click on the links to jump to that page in the presentation. * Two Major Components: 1. Control Charts Used to monitor a

### NCSS Statistical Software. K-Means Clustering

Chapter 446 Introduction The k-means algorithm was developed by J.A. Hartigan and M.A. Wong of Yale University as a partitioning technique. It is most useful for forming a small number of clusters from

### Extended control charts

Extended control charts The control chart types listed below are recommended as alternative and additional tools to the Shewhart control charts. When compared with classical charts, they have some advantages

### All Possible Regressions

Chapter 312 Introduction Often, theory and experience give only general direction as to which of a pool of candidate variables (including transformed variables) should be included in the regression model.

### Gamma Distribution Fitting

Chapter 552 Gamma Distribution Fitting Introduction This module fits the gamma probability distributions to a complete or censored set of individual or grouped data values. It outputs various statistics

### Canonical Correlation

Chapter 400 Introduction Canonical correlation analysis is the study of the linear relations between two sets of variables. It is the multivariate extension of correlation analysis. Although we will present

### Factor Analysis. Chapter 420. Introduction

Chapter 420 Introduction (FA) is an exploratory technique applied to a set of observed variables that seeks to find underlying factors (subsets of variables) from which the observed variables were generated.

### Comparables Sales Price

Chapter 486 Comparables Sales Price Introduction Appraisers often estimate the market value (current sales price) of a subject property from a group of comparable properties that have recently sold. Since

### 3D Scatter Plots. Chapter 170. Introduction

Chapter 170 Introduction The 3D scatter plot displays trivariate points plotted in an X-Y-Z grid. It is particularly useful for investigating the relationships among these variables. The influence of a

### Confidence Intervals for Cp

Chapter 296 Confidence Intervals for Cp Introduction This routine calculates the sample size needed to obtain a specified width of a Cp confidence interval at a stated confidence level. Cp is a process

### Journal of Statistical Software

JSS Journal of Statistical Software June 2009, Volume 30, Issue 13. http://www.jstatsoft.org/ An Excel Add-In for Statistical Process Control Charts Samuel E. Buttrey Naval Postgraduate School Abstract

### Confidence Intervals for Cpk

Chapter 297 Confidence Intervals for Cpk Introduction This routine calculates the sample size needed to obtain a specified width of a Cpk confidence interval at a stated confidence level. Cpk is a process

### Lin s Concordance Correlation Coefficient

NSS Statistical Software NSS.com hapter 30 Lin s oncordance orrelation oefficient Introduction This procedure calculates Lin s concordance correlation coefficient ( ) from a set of bivariate data. The

### Kenyon College ECON 375 Introduction to Econometrics Spring 2011, Keeler. Introduction to Excel January 27, 2011

Kenyon College ECON 375 Introduction to Econometrics Spring 2011, Keeler Introduction to Excel January 27, 2011 1. Open Excel From the START button, go to PROGRAMS and then MICROSOFT OFFICE, and then EXCEL.

### NCSS Statistical Software Principal Components Regression. In ordinary least squares, the regression coefficients are estimated using the formula ( )

Chapter 340 Principal Components Regression Introduction is a technique for analyzing multiple regression data that suffer from multicollinearity. When multicollinearity occurs, least squares estimates

### Instruction Manual for SPC for MS Excel V3.0

Frequency Business Process Improvement 281-304-9504 20314 Lakeland Falls www.spcforexcel.com Cypress, TX 77433 Instruction Manual for SPC for MS Excel V3.0 35 30 25 LSL=60 Nominal=70 Capability Analysis

### Basic Pivot Tables. To begin your pivot table, choose Data, Pivot Table and Pivot Chart Report. 1 of 18

Basic Pivot Tables Pivot tables summarize data in a quick and easy way. In your job, you could use pivot tables to summarize actual expenses by fund type by object or total amounts. Make sure you do not

### Confidence Intervals for the Area Under an ROC Curve

Chapter 261 Confidence Intervals for the Area Under an ROC Curve Introduction Receiver operating characteristic (ROC) curves are used to assess the accuracy of a diagnostic test. The technique is used

### SPC Response Variable

SPC Response Variable This procedure creates control charts for data in the form of continuous variables. Such charts are widely used to monitor manufacturing processes, where the data often represent

### Frequency Tables. Chapter 500. Introduction. Frequency Tables. Types of Categorical Variables. Data Structure. Missing Values

Chapter 500 Introduction This procedure produces tables of frequency counts and percentages for categorical and continuous variables. This procedure serves as a summary reporting tool and is often used

### Confidence Intervals for the Difference Between Two Means

Chapter 47 Confidence Intervals for the Difference Between Two Means Introduction This procedure calculates the sample size necessary to achieve a specified distance from the difference in sample means

### An Introduction to Graphing in Excel

An Introduction to Graphing in Excel This example uses Excel to graph Y vs X. This problem starts as follows: 1.Complete the following table and on graph paper, graph the line for the equation x 2y = Identify

### Confidence Intervals for One Standard Deviation Using Standard Deviation

Chapter 640 Confidence Intervals for One Standard Deviation Using Standard Deviation Introduction This routine calculates the sample size necessary to achieve a specified interval width or distance from

### Directions for Creating a Column Graph and Plotting the Standard Deviation of the Average in Excel 2007

Directions for Creating a Column Graph and Plotting the Standard Deviation of the Average in Excel 2007 We will create a column graph comparing 5 volumes and their average volume for 5 Zinc washers. Also

### NCSS Statistical Software

Chapter 06 Introduction This procedure provides several reports for the comparison of two distributions, including confidence intervals for the difference in means, two-sample t-tests, the z-test, the

### Charts in Excel 2007

Charts in Excel 2007 Contents Introduction Charts in Excel 2007...1 Part 1: Generating a Basic Chart...1 Part 2: Adding Another Data Series...4 Part 3: Other Handy Options...6 Introduction Charts in Excel

### Trial 9 No Pill Placebo Drug Trial 4. Trial 6.

An essential part of science is communication of research results. In addition to written descriptions and interpretations, the data are presented in a figure that shows, in a visual format, the effect

### Minitab Guide. This packet contains: A Friendly Guide to Minitab. Minitab Step-By-Step

Minitab Guide This packet contains: A Friendly Guide to Minitab An introduction to Minitab; including basic Minitab functions, how to create sets of data, and how to create and edit graphs of different

### MINITAB ASSISTANT WHITE PAPER

MINITAB ASSISTANT WHITE PAPER This paper explains the research conducted by Minitab statisticians to develop the methods and data checks used in the Assistant in Minitab 17 Statistical Software. Capability

### Business Objects Enterprise version 4.1. Report Viewing

Business Objects Enterprise version 4.1 Note about Java: With earlier versions, the Java run-time was not needed for report viewing; but was needed for report writing. The default behavior in version 4.1

### Stepwise Regression. Chapter 311. Introduction. Variable Selection Procedures. Forward (Step-Up) Selection

Chapter 311 Introduction Often, theory and experience give only general direction as to which of a pool of candidate variables (including transformed variables) should be included in the regression model.

### Correlation Matrix. Chapter 401. Introduction. Discussion

Chapter 401 Introduction This program calculates Pearsonian and Spearman-rank correlation matrices. It allows missing values to be deleted in a pair-wise or row-wise fashion. When someone speaks of a correlation

### ISyE 512 Chapter 6. Control Charts for Variables. Instructor: Prof. Kaibo Liu. Department of Industrial and Systems Engineering UW-Madison

ISyE 512 Chapter 6 Control Charts for Variables Instructor: Prof. Kaibo Liu Department of Industrial and Systems Engineering UW-Madison Email: kliu8@wisc.edu Office: oom 017 (Mechanical Engineering Building)

### Introduction to Microsoft Excel 2007/2010

to Microsoft Excel 2007/2010 Abstract: Microsoft Excel is one of the most powerful and widely used spreadsheet applications available today. Excel's functionality and popularity have made it an essential

### Variables Control Charts

MINITAB ASSISTANT WHITE PAPER This paper explains the research conducted by Minitab statisticians to develop the methods and data checks used in the Assistant in Minitab 17 Statistical Software. Variables

### Intermediate PowerPoint

Intermediate PowerPoint Charts and Templates By: Jim Waddell Last modified: January 2002 Topics to be covered: Creating Charts 2 Creating the chart. 2 Line Charts and Scatter Plots 4 Making a Line Chart.

### Working with Excel in Origin

Working with Excel in Origin Limitations When Working with Excel in Origin To plot your workbook data in Origin, you must have Excel version 7 (Microsoft Office 95) or later installed on your computer

### Statgraphics Getting started

Statgraphics Getting started The aim of this exercise is to introduce you to some of the basic features of the Statgraphics software. Starting Statgraphics 1. Log in to your PC, using the usual procedure

### Getting Started with Access 2007

Getting Started with Access 2007 1 A database is an organized collection of information about a subject. Examples of databases include an address book, the telephone book, or a filing cabinet full of documents

### One-Way ANOVA using SPSS 11.0. SPSS ANOVA procedures found in the Compare Means analyses. Specifically, we demonstrate

1 One-Way ANOVA using SPSS 11.0 This section covers steps for testing the difference between three or more group means using the SPSS ANOVA procedures found in the Compare Means analyses. Specifically,

### Petrel TIPS&TRICKS from SCM

Petrel TIPS&TRICKS from SCM Knowledge Worth Sharing Pie Charts or Bubble Maps This TIPS&TRICKS is intended to aid a person working in Petrel who needs to make a display showing the relative proportion

### HOW TO... Use Excel. Overview

Page 1 of 9 Overview Excel is a spreadsheet application in the Microsoft Office suite. Excel can be used to create and format workbooks in order to analyze data, write formulas, calculations, and charts

### Appendix 2.1 Tabular and Graphical Methods Using Excel

Appendix 2.1 Tabular and Graphical Methods Using Excel 1 Appendix 2.1 Tabular and Graphical Methods Using Excel The instructions in this section begin by describing the entry of data into an Excel spreadsheet.

### Data Matching Optimal and Greedy

Chapter 13 Data Matching Optimal and Greedy Introduction This procedure is used to create treatment-control matches based on propensity scores and/or observed covariate variables. Both optimal and greedy

### Microsoft Access Rollup Procedure for Microsoft Office 2007. 2. Click on Blank Database and name it something appropriate.

Microsoft Access Rollup Procedure for Microsoft Office 2007 Note: You will need tax form information in an existing Excel spreadsheet prior to beginning this tutorial. 1. Start Microsoft access 2007. 2.

### University of Southern California Marshall Information Services

University of Southern California Marshall Information Services Determine Breakeven Price Using Excel - Using Goal Seek, Data Tables, Vlookup & Charts This guide covers how to determine breakeven price

### Excel Lab. Figure 1.1: Adding two numbers together in Excel

Excel Lab This document serves as an introduction to Microsoft Excel. Example 1: Excel is very useful for performing arithmetic operations. Suppose we want to add 2 + 3. We begin by entering the number

### Pivot Tables/Charts (Microsoft Excel 2010)

Pivot Tables/Charts (Microsoft Excel 2010) You can use pivot tables whenever you want to summarize a large amount of data, such as customer lists, salesperson quarter/annual sales amounts, etc. Microsoft

### Shewhart control charts

Shewhart control charts Menu: QC.Expert Control charts Control charts are constructed to decide whether a process is under statistical control and to monitor any departures from this state. This means

### Figure 1: Excel s data grid and addressing

This is meant to be a short tutorial in how to effectively use Microsoft Excel, a software package that most people are generally familiar with, to plot and analyze scientific data. Basic Excel: First

### Market Pricing Override

Market Pricing Override MARKET PRICING OVERRIDE Market Pricing: Copy Override Market price overrides can be copied from one match year to another Market Price Override can be accessed from the Job Matches

### Formatting Data. Format as a Table. Filter Data. Conditional Formatting. Eliminate Duplicate Records. Summarize Data: Subtotals

Formatting Data Format as a Table Filter Data Conditional Formatting Eliminate Duplicate Records Summarize Data: Subtotals Formatting Data Use the following options to format your data: Automatically adjust

### Excel Using Pivot Tables

Overview A PivotTable report is an interactive table that allows you to quickly group and summarise information from a data source. You can rearrange (or pivot) the table to display different perspectives

Excel 2010: Create your first spreadsheet Goals: After completing this course you will be able to: Create a new spreadsheet. Add, subtract, multiply, and divide in a spreadsheet. Enter and format column

### Summary of important mathematical operations and formulas (from first tutorial):

EXCEL Intermediate Tutorial Summary of important mathematical operations and formulas (from first tutorial): Operation Key Addition + Subtraction - Multiplication * Division / Exponential ^ To enter a

### Data Analysis. Using Excel. Jeffrey L. Rummel. BBA Seminar. Data in Excel. Excel Calculations of Descriptive Statistics. Single Variable Graphs

Using Excel Jeffrey L. Rummel Emory University Goizueta Business School BBA Seminar Jeffrey L. Rummel BBA Seminar 1 / 54 Excel Calculations of Descriptive Statistics Single Variable Graphs Relationships

### Control Charts for Variables. Control Chart for X and R

Control Charts for Variables X-R, X-S charts, non-random patterns, process capability estimation. 1 Control Chart for X and R Often, there are two things that might go wrong in a process; its mean or its

### Excel 2007 - Using Pivot Tables

Overview A PivotTable report is an interactive table that allows you to quickly group and summarise information from a data source. You can rearrange (or pivot) the table to display different perspectives

### Point Biserial Correlation Tests

Chapter 807 Point Biserial Correlation Tests Introduction The point biserial correlation coefficient (ρ in this chapter) is the product-moment correlation calculated between a continuous random variable

### Excel Tutorial. Bio 150B Excel Tutorial 1

Bio 15B Excel Tutorial 1 Excel Tutorial As part of your laboratory write-ups and reports during this semester you will be required to collect and present data in an appropriate format. To organize and

### Pivot Table Reporting

QUICK DOC: [Pivot Table Reporting} Pivot Table Reporting For the purposes of this document we are using the Utility Consumption Tracking Module to create our report and charts, but almost any data exported

### Analysis Tools in Geochemistry for ArcGIS

Analysis Tools in Geochemistry for ArcGIS The database that is used to store all of the geographic information in Geochemistry for ArcGIS is Esri s file Geodatabase (fgdb). This is a collection of tables

### Scientific Graphing in Excel 2010

Scientific Graphing in Excel 2010 When you start Excel, you will see the screen below. Various parts of the display are labelled in red, with arrows, to define the terms used in the remainder of this overview.

### Excel 2007 Basic knowledge

Ribbon menu The Ribbon menu system with tabs for various Excel commands. This Ribbon system replaces the traditional menus used with Excel 2003. Above the Ribbon in the upper-left corner is the Microsoft

### Using Microsoft Excel

Using Microsoft Excel Key skill [Where it is introduced] To open MS Excel. To open an existing spreadsheet. How to do it! Start > All Programs > Microsost Office > Microsoft Office Excel 2003 File > Open

### Pearson's Correlation Tests

Chapter 800 Pearson's Correlation Tests Introduction The correlation coefficient, ρ (rho), is a popular statistic for describing the strength of the relationship between two variables. The correlation

### Factorial Analysis of Variance

Chapter 560 Factorial Analysis of Variance Introduction A common task in research is to compare the average response across levels of one or more factor variables. Examples of factor variables are income

### SECTION 2-1: OVERVIEW SECTION 2-2: FREQUENCY DISTRIBUTIONS

SECTION 2-1: OVERVIEW Chapter 2 Describing, Exploring and Comparing Data 19 In this chapter, we will use the capabilities of Excel to help us look more carefully at sets of data. We can do this by re-organizing

### NICK COLLIER - REPAST DEVELOPMENT TEAM

DATA COLLECTION FOR REPAST SIMPHONY JAVA AND RELOGO NICK COLLIER - REPAST DEVELOPMENT TEAM 0. Before We Get Started This document is an introduction to the data collection system introduced in Repast Simphony

### Using SPSS 20, Handout 3: Producing graphs:

Research Skills 1: Using SPSS 20: Handout 3, Producing graphs: Page 1: Using SPSS 20, Handout 3: Producing graphs: In this handout I'm going to show you how to use SPSS to produce various types of graph.

### There are six different windows that can be opened when using SPSS. The following will give a description of each of them.

SPSS Basics Tutorial 1: SPSS Windows There are six different windows that can be opened when using SPSS. The following will give a description of each of them. The Data Editor The Data Editor is a spreadsheet

### Leave blank unless Formatting as Table. Data labels

Type a data table from which to create a chart Type the data to be used for a chart like this: 1992 1993 Bird 3 2 Cat 21 29 Dog 24 12 Other 4 No Pet 25 24 Leave blank unless Formatting as Table Data labels

### One-Minute Spotlight. The Crystal Ball Scatter Chart

The Crystal Ball Scatter Chart Once you have run a simulation with Oracle s Crystal Ball, you can view several charts to help you visualize, understand, and communicate the simulation results. This Spotlight

### Charts and Pivot Tables. Training Manual

Charts and Pivot Tables Training Manual Excel 2007 Table of Contents Section 1: Working With Charts... 1 Lesson 1.1: Working With Charts, Part 1...2 Creating a Chart...2 Formatting a Chart...4 Modifying

### Point-Biserial and Biserial Correlations

Chapter 302 Point-Biserial and Biserial Correlations Introduction This procedure calculates estimates, confidence intervals, and hypothesis tests for both the point-biserial and the biserial correlations.

Advanced Microsoft Excel 2010 Table of Contents THE PASTE SPECIAL FUNCTION... 2 Paste Special Options... 2 Using the Paste Special Function... 3 ORGANIZING DATA... 4 Multiple-Level Sorting... 4 Subtotaling

### Excel 2007 Intermediate Documentation

Learning Outcomes Create complex formulas Utilize advanced (conditional) formatting Create and customize graphical displays Table of Contents Excel 2007 Intermediate Documentation The Center for Teaching,

### 10 CONTROL CHART CONTROL CHART

Module 10 CONTOL CHT CONTOL CHT 1 What is a Control Chart? control chart is a statistical tool used to distinguish between variation in a process resulting from common causes and variation resulting from

### A simple three dimensional Column bar chart can be produced from the following example spreadsheet. Note that cell A1 is left blank.

Department of Library Services Creating Charts in Excel 2007 www.library.dmu.ac.uk Using the Microsoft Excel 2007 chart creation system you can quickly produce professional looking charts. This help sheet

### Microsoft Excel 2010 Part 3: Advanced Excel

CALIFORNIA STATE UNIVERSITY, LOS ANGELES INFORMATION TECHNOLOGY SERVICES Microsoft Excel 2010 Part 3: Advanced Excel Winter 2015, Version 1.0 Table of Contents Introduction...2 Sorting Data...2 Sorting

### MAX CHART: COMBINING X-BAR CHART AND S CHART

Statistica Sinica 8(1998), 63-71 MAX CHART: COMBINING X-BAR CHART AND S CHART Gemai Chen and Smiley W. Cheng University of Regina and University of Manitoba Abstract: Control chart techniques have been

### Microsoft Excel 2010 Prepared by Computing Services at the Eastman School of Music July 2010

Microsoft Excel 2010 Prepared by Computing Services at the Eastman School of Music July 2010 Contents Microsoft Office Interface... 4 File Ribbon Tab... 5 Microsoft Office Quick Access Toolbar... 6 Appearance

### Gage Studies for Continuous Data

1 Gage Studies for Continuous Data Objectives Determine the adequacy of measurement systems. Calculate statistics to assess the linearity and bias of a measurement system. 1-1 Contents Contents Examples

### Guidelines for Completing the VDOT Form C 13CPM

Guidelines for Completing the VDOT Form C 13CPM CONSTRUCTION DIVISION 1. OVERVIEW The VDOT Form C 13CPM is required to prepare and submit the Contractor s Progress Earnings Schedule as specified in the

### Distribution (Weibull) Fitting

Chapter 550 Distribution (Weibull) Fitting Introduction This procedure estimates the parameters of the exponential, extreme value, logistic, log-logistic, lognormal, normal, and Weibull probability distributions

### To open a CMA file > Download and Save file Start CMA Open file from within CMA

Example name Effect size Analysis type Level Multiple outcomes reading and math Standardized mean difference Multiple outcomes from same subjects Advanced Synopsis This analysis uses fictional data. Each

### How to Use a Data Spreadsheet: Excel

How to Use a Data Spreadsheet: Excel One does not necessarily have special statistical software to perform statistical analyses. Microsoft Office Excel can be used to run statistical procedures. Although

### Probability Distributions

CHAPTER 5 Probability Distributions CHAPTER OUTLINE 5.1 Probability Distribution of a Discrete Random Variable 5.2 Mean and Standard Deviation of a Probability Distribution 5.3 The Binomial Distribution

### MARS STUDENT IMAGING PROJECT

MARS STUDENT IMAGING PROJECT Data Analysis Practice Guide Mars Education Program Arizona State University Data Analysis Practice Guide This set of activities is designed to help you organize data you collect

### Data analysis. Data analysis in Excel using Windows 7/Office 2010

Data analysis Data analysis in Excel using Windows 7/Office 2010 Open the Data tab in Excel If Data Analysis is not visible along the top toolbar then do the following: o Right click anywhere on the toolbar

### Create a Poster Using Publisher

Contents 1. Introduction 1. Starting Publisher 2. Create a Poster Template 5. Aligning your images and text 7. Apply a background 12. Add text to your poster 14. Add pictures to your poster 17. Add graphs

### Below is a very brief tutorial on the basic capabilities of Excel. Refer to the Excel help files for more information.

Excel Tutorial Below is a very brief tutorial on the basic capabilities of Excel. Refer to the Excel help files for more information. Working with Data Entering and Formatting Data Before entering data

### Discrete Random Variables and their Probability Distributions

CHAPTER 5 Discrete Random Variables and their Probability Distributions CHAPTER OUTLINE 5.1 Probability Distribution of a Discrete Random Variable 5.2 Mean and Standard Deviation of a Discrete Random Variable

### Appendix E: Graphing Data

You will often make scatter diagrams and line graphs to illustrate the data that you collect. Scatter diagrams are often used to show the relationship between two variables. For example, in an absorbance