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Instructions
Instructions for Example Repeatability and Reproducibility CalculationsCarl Houtman 11/22/2004
This spreadsheet provides an implementation of the calculations found in TAPPI standard T 1200, "Interlaboratory Evaluation of Test Methods to Determine TAPPI Repeatability and Reproducibility". These are also the same calculations specified in ASTM E 691. The data come from the examples given in these two standards.
Please note that these calculations assume a balanced design, that is, each laboratory provided the same number of measurements. In the case of both the 32 and 69 lb examples one data point is missing. While not formally a balanced design, these missing data points do not have a large impact on the results. The reason that these calculations are insensitive is that there are eight or nine other laboratories supplying the full information and there was only one data point missing. If you are facing a situation where the number of laboratories is less than 8 or more than 2 measurements are missing, more complex methods are required. You likely will have to seek the advice of a statistician.
To add a new data set (1) move to one of the example worksheets (2) by using the command "Move or Copy Sheet" under the "Edit" menu item, duplicate a worksheet. Remember to check "Create a Copy" box. (3) enter the new data starting in Cell B5. The current default limits are 10 measurements per laboratory and 25 laboratories, but these limits could be expanded by adjusting all of the sums. The data for a particular laboratory is entered into a single column. The calculations are automatically repeated each time a new entry is made. For missing data leave a blank. Do not enter a zero.
The h and k statistics are calculated and shown in the plots. These values provide tests of the consistency of the data and are discussed in section 10 of the TAPPI standard. If the data for a particular laboratory exceeds the critical value, you should investigate the potential causes for these deviations from the rest of the population.
Below the h and k plots is shown a histogram of the data. Data points that do not appear to be part of a central normal distribution should also be investigated.
35 lbThese data are taken from T1200 sp00 for 35 lb linerboard (unbalanced)Laboratory12345678910111213141516171819202122232425data187.887.691.386.895.390.591.289.186.5data286.686.491.388.786.992.889.088.789.8data381.487.389.286.194.491.391.387.082.1data486.083.488.787.287.486.088.892.0data5data6data7data8data9data10Mean85.586.290.187.291.090.290.588.487.60.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.0Std Dev2.801.921.371.104.472.931.300.954.310000000000000000Std Dev27.853.681.881.2119.948.561.690.9018.550000000000000000h statistic-1.51-1.150.80-0.651.230.810.98-0.05-0.450.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00h critical (+)2.232.232.232.232.232.232.232.232.230000000000000000h critical (-)-2.23-2.23-2.23-2.23-2.23-2.23-2.23-2.23-2.230.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00k statistic1.050.720.510.411.671.100.490.361.610.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00k critical1.921.921.921.921.921.922.091.921.920000000000000000Count44444434400000000000000000000000000000000000000000Grand MeanX88.5ERROR: this is not a balanced design the calculation is incorrectGrand Std DevSx2.0Countp9Repeat Std DevSr2.7Repeatabilityr7.4Repeatability %%r8.4%Reproduce Std DevSR3.1ReproducibilityR8.5Reproducibility %%R9.6%min81.473.30max95.376.40difference1.3979.6082.7285.9189.01992.21095.4398.50101.70104.803.2
35 lb
&APage &Pdata+critical value-critical valueh statistics test
42 lb
&APage &Pdatacritical valuek statistics test
69 lb
ValueNumber of Occurences
GlucoseThese data are taken from T1200 sp00 for 42 lb linerboard (the only complete set)Laboratory12345678910111213141516171819202122232425data1122.5118.7120.6123.0116.0132.9123.0120.0123.7data2121.7123.5121.2120.0117.6122.8124.1113.6125.7data3124.6122.8117.8121.9122.4123.2118.0113.8121.7data4116.3120.0117.5118.0116.4127.0121.0118.9127.6data5data6data7data8data9data10Mean121.3121.3119.3120.7118.1126.5121.5116.6124.70.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.0Std Dev3.532.281.902.202.954.682.683.352.540000000000000000Std Dev212.505.183.604.848.6821.937.1711.236.470000000000000000h statistic0.060.05-0.60-0.12-0.981.760.14-1.481.170.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00h critical (+)2.232.232.232.232.232.232.232.232.230000000000000000h critical (-)-2.23-2.23-2.23-2.23-2.23-2.23-2.23-2.23-2.230.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00k statistic1.170.760.630.730.981.560.891.110.840.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00k critical1.921.921.921.921.921.921.921.921.920000000000000000Count44444444400000000000000000000000000000000000000000Grand MeanX121.10Grand Std DevSx3.1Countp9Repeat Std DevSr3.0Repeatabilityr8.3Repeatability %%r6.9%Reproduce Std DevSR4.0ReproducibilityR11.1Reproducibility %%R9.2%min113.6102.20max132.9106.60difference1.93111.00115.42119.810124.219128.64133.01137.40141.80146.204.4
Glucose
&APage &Pdata+critical value-critical valueh statistics test
&APage &Pdatacritical valuek statistics test
ValueNumber of Occurences
These data are taken from T1200 sp00 for 69 lb linerboard (unbalanced)Laboratory12345678910111213141516171819202122232425data1147.7149.5134.5140.5147.0148.7141.0134.1data2133.0137.5139.9139.7141.7149.2144.8140.8data3136.3141.6141.3139.7143.8142.3139.6142.0data4139.8147.1143.9145.2154.3139.0130.6data5data6data7data8data9data10Mean139.2142.9140.7141.0144.4148.6141.1136.90.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.0Std Dev6.316.105.182.002.244.922.615.440.000000000000000000Std Dev239.8237.2026.804.015.0224.186.7929.580.000000000000000000h statistic-0.750.29-0.32-0.250.731.91-0.21-1.400.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00h critical (+)2.152.152.152.152.152.152.152.150.000000000000000000h critical (-)-2.15-2.15-2.15-2.15-2.15-2.15-2.15-2.150.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00k statistic1.361.311.110.430.481.060.561.170.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00k critical1.902.061.901.901.901.901.901.900.000000000000000000Count43444444000000000000000000000000000000000000000000Grand MeanX141.8ERROR: this is not a balanced design the calculation is incorrectGrand Std DevSx3.5Countp8Repeat Std DevSr4.7Repeatabilityr12.9Repeatability %%r9.1%Reproduce Std DevSR5.4ReproducibilityR14.9Reproducibility %%R10.5%min130.6117.50max154.3122.80difference2.37128.00133.22138.44143.614148.98154.12159.31164.50169.705.2
&APage &Pdata+critical value-critical valueh statistics test
&APage &Pdatacritical valuek statistics test
ValueNumber of Occurances
These data are taken from ASTM E691Laboratory12345678910111213141516171819202122232425data141.0341.1741.0139.3741.8843.2841.0843.36data241.4542.0040.6842.3741.1940.5041.2742.65data341.3741.1542.6642.6341.3242.2839.0241.72data4data5data6data7data8data9data10Mean41.341.441.541.541.542.040.542.60.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.0Std Dev0.220.491.061.810.371.411.250.820.000000000000000000Std Dev20.050.241.133.280.131.981.560.680.000000000000000000h statistic-0.39-0.13-0.11-0.10-0.090.83-1.751.750.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00h critical (+)2.152.152.152.152.152.152.152.150.000000000000000000h critical (-)-2.15-2.15-2.15-2.15-2.15-2.15-2.15-2.150.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00k statistic0.210.461.001.700.341.321.170.770.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00k critical2.062.062.062.062.062.062.062.060.000000000000000000Count33333333000000000000000000000000000000000000000000Grand MeanX41.50Grand Std DevSx0.6Countp8Repeat Std DevSr1.1Repeatabilityr2.9Repeatability %%r7.1%Reproduce Std DevSR1.1ReproducibilityR2.9Reproducibility %%R7.1%min39.035.10max43.436.40difference0.43437.6038.9040.1241.41142.7943.9245.2046.4047.701.3
&APage &Pdata+critical value-critical valueh statistics test
&APage &Pdatacritical valuek statistics test
ValueNumber of Occurences
