Descriptive Statistics Summary Tables

Chapter 201 Descriptive Statistics Summary Tables Itroductio This procedure is used to summarize cotiuous data. Large volumes of such data may be easily summarized i statistical tables of meas, couts, stadard deviatios, etc. Categorical group variables may be used to calculate summaries for idividual groups. The tables are similar i structure to those produced by cross tabulatio. This procedure produces tables of the followig summary statistics: Cout Missig Cout Sum Mea Stadard Deviatio (Std Dev) Stadard Error (Std Error) Lower 95% Cofidece Limit for the Mea (95% LCL) Upper 95% Cofidece Limit for the Mea (95% UCL) Media Miimum Maximum Rage Iterquartile Rage (IQR) 10th Percetile (10th Pctile) 25th Percetile (25th Pctile) 75th Percetile (75th Pctile) 90th Percetile (90th Pctile) Variace Mea Absolute Deviatio (MAD) Mea Absolute Deviatio from the Media (MADM) Coefficiet of Variatio (COV) Coefficiet of Dispersio (COD) Skewess Kurtosis Types of Categorical Variables Note that we will refer to two types of categorical variables: Group Variables ad Break Variables. The values of a Group Variable are used to defie the rows, sub rows, ad colums of the summary table. Up to two Group Variables may be used per table. Group Variables are ot required. Break Variables are used to split a database ito subgroups. A separate report is geerated for each uique set of values of the break variables. 201-1

Data Structure The data below are a subset of the Resale dataset provided with the software. This (computer simulated) data gives the sellig price, the umber of bedrooms, the total square footage (fiished ad ufiished), ad the size of the lots for 150 residetial properties sold durig the last four moths i two states. This data is represetative of the type of data that may be aalyzed with this procedure. Oly the first 8 of the 150 observatios are displayed. Resale dataset (subset) State Price Bedrooms TotalSqft LotSize Nev 260000 2 2042 10173 Nev 66900 3 1392 13069 Vir 127900 2 1792 7065 Nev 181900 3 2645 8484 Nev 262100 2 2613 8355 Nev 147500 2 1935 7056 Nev 167200 2 1278 6116 Nev 395700 2 1455 14422 Missig Values Observatios with missig values i either the group variables or the cotiuous data variables are igored. The procedure also allows you to specify up to 5 additioal values to be cosidered as missig i categorical group variables. Summary Statistics The followig sectios outlie the summary statistics that are available i this procedure. Cout The umber of o-missig data values,. If o frequecy variable was specified, this is the umber of rows with o-missig values. Missig Cout The umber of missig data values. If o frequecy variable was specified, this is the umber of rows with missig values. Sum The sum (or total) of the data values. Sum = x i i= 1 201-2

Mea The average of the data values. x = i=1 x i Variace The sample variace, s 2, is a popular measure of dispersio. It is a average of the squared deviatios from the mea. Stadard Deviatio (Std Dev) s 2 i = 1 = ( x x ) The sample stadard deviatio, s, is a popular measure of dispersio. It measures the average distace betwee a sigle observatio ad the mea. It is equal to the square root of the sample variace. i 1 2 s = i = 1 ( x x ) i 1 2 Stadard Error (Std Error) The stadard error of the mea, a measure of the variatio of the sample mea about the populatio mea, is computed by dividig the sample stadard deviatio by the square root of the sample size. 95% Cofidece Iterval for the Mea (95% LCL & 95% UCL) s x = This is the upper ad lower values of a 95% cofidece iterval estimate for the mea based o a t distributio with 1 degrees of freedom. This iterval estimate assumes that the populatio stadard deviatio is ot kow ad that the data for this variable are ormally distributed. s 95% CI = ± t a s x /2, 1 x Miimum The smallest data value. Maximum The largest data value. 201-3

Rage The differece betwee the largest ad smallest data values. Percetiles Rage = Maximum Miimum The 100p th percetile is the value below which 100p% of data values may be foud (ad above which 100p% of data values may be foud).the 100p th percetile is computed as Z 100p = (1-g)X [k1] + gx [k2] where k1 equals the iteger part of p(+1), k2=k1+1, g is the fractioal part of p(+1), ad X [k] is the k th observatio whe the data are sorted from lowest to highest. Media The media (or 50th percetile) is the middle umber of the sorted data values. Media = Z 50 Iterquartile Rage (IQR) The differece betwee the 75th ad 25th percetiles (the 3rd ad 1st quartiles). This represets the rage of the middle 50% of the data. It serves as a robust measure of the variatio i the data. IQR = Z 75 Z 25 Mea Absolute Deviatio (MAD) A measure of dispersio that is ot affected by outliers as much as the stadard deviatio ad variace. It measures the average absolute distace betwee a sigle observatio ad the mea. MAD = i = 1 x i x Mea Absolute Deviatio from the Media (MADM) A measure of dispersio that is eve more robust to outliers tha the mea absolute deviatio (MAD) sice the media is used as the ceter poit of the distributio. It measures the average absolute distace betwee a sigle observatio ad the media. MADM xi Media i= = 1 201-4

Coefficiet of Variatio (COV) A relative measure of dispersio used to compare the amout of variatio i two samples. It is calculated by dividig the stadard deviatio by the mea. Sometimes it is referred to as COV or CV. Coefficiet of Dispersio (COD) s COV = x A robust, relative measure of dispersio. It is calculated by dividig the robust mea absolute deviatio from the media (MADM) by the media. It is frequetly used i real estate or tax assessmet applicatios. Skewess COD = MADM Media = i= 1 xi Media Media Measures the directio ad degree of asymmetry i the data distributio. where m r = i = 1 ( x x ) i r m Skewess = 3 m 3/2 2 Kurtosis Measures the heaviess of the tails i the data distributio. where m r = i = 1 ( x x ) i r m Kurtosis = 4 m 2 2 201-5

Procedure Optios This sectio describes the optios available i this procedure. To fid out more about usig a procedure, tur to the Procedures chapter. Variables Tab This pael specifies the variables that will be used i the aalysis ad the summary table cotets ad layout. Summary Table Cotets ad Layout Data Variable(s) Specify oe or more variables whose descriptive statistics are to be calculated. These statistics, selected from those available, will be computed for each combiatio of the values i the categorical group variables (if ay) that you have selected. The data i these variables must be umeric. Text values will be skipped i the calculatios. Table Positio for Data Variable(s) Select the positio for Data Variable(s) i the summary table(s). See Layout Preview for Items i the Table. The optios are Auto The positio for the data variable(s) is automatically determied based o the locatio of other items i the table. Rows Each data variable is listed as a separate row i the table. Colums Each data variable is listed as a separate colum i the table. Sub Rows Each data variable is listed as a separate sub row i the table. Tables A separate table is created for each data variable. The positios for Data Variable(s) ad for Statistics ca both be set to Tables oly if there is at least oe group variable. I this case, a separate table is created for each Data Variable/Statistic combiatio. Plots Plots are created with a table s row item o the group axis ad the colum item as the leged variable. Whe there is oly oe colum, the sub row item is used as the leged variable. For combied plots from tables with rows, sub rows, ad colums, the rows ad sub rows are combied oto the group axis ad the colums are icluded i the leged. Statistics Select oe or more statistics to be icluded i the table(s) ad plot(s). The statistics are computed separately for each Data Variable. If oe or more Group Variables are etered, the statistics are computed for each combiatio of the group values. The order of the statistics o the table(s) ad plot(s) ca be chaged usig the up/dow arrow buttos to the right. 201-6

Table Positio for Statistics Select the positio for Statistics i the summary table(s). See Layout Preview for Items i the Table. The optios are Auto The positio for the statistics is automatically determied based o the locatio of other items i the table. Rows Each statistic is listed as a separate row i the table. Colums Each statistic is listed as a separate colum i the table. Sub Rows Each statistic is listed as a separate sub row i the table. Tables A separate table is created for each statistic. The positios for Data Variable(s) ad for Statistics ca both be set to Tables oly if there is at least oe group variable. I this case, a separate table is created for each Data Variable/Statistic combiatio. Plots Plots are created with a table s row item o the group axis ad the colum item as the leged variable. Whe there is oly oe colum, the sub row item is used as the leged variable. For combied plots from tables with rows, sub rows, ad colums, the rows ad sub rows are combied oto the group axis ad the colums are icluded i the leged. Iclude Group Variable 1, 2 Check to iclude a categorical group variable i the table. Whe oly Group Variable 1 is used, statistics are computed for each uique group value. Whe both Group Variable 1 ad Group Variable 2 are used, statistics are computed for each combiatio of group values. Group Variable 1, 2 Specify oe or more categorical group variables. The categories may be text (e.g. Low, Med, High ) or umeric (e.g. 1, 2, 3 ). Whe oly Group Variable 1 is used, statistics are computed for each uique group value. Whe both Group Variable 1 ad Group Variable 2 are used, statistics are computed for each combiatio of group values. If more tha oe variable is etered for Group Variable 1, a separate table will be created for each variable etered. The data values i each variable will be sorted alpha-umerically before beig listed i the table. If you wat the values to be displayed i a differet order, specify a custom value order for the data colums etered here usig the Colum Ifo Table o the Data Widow. 201-7

Table Positio for Group Variable 1, 2 Select the positio for the values of the Group Variable i the summary table(s). See Layout Preview for Items i the Table. The optios are Auto The positio for the group variable is automatically determied based o the locatio of other items i the table. Rows Each group variable is listed as a separate row i the table. Colums Each group variable is listed as a separate colum i the table. Sub Rows Each group variable is listed as a separate sub row i the table. Plots Plots are created with a table s row item o the group axis ad the colum item as the leged variable. Whe there is oly oe colum, the sub row item is used as the leged variable. For combied plots from tables with rows, sub rows, ad colums, the rows ad sub rows are combied oto the group axis ad the colums are icluded i the leged. Create Other Group Variables from Numeric Data Check this box to create group variables from umeric data. Whe checked, additioal optios will be displayed to specify how the umeric data will be classified ito categorical variables. If you choose to create group variables from umeric data, you do ot have to eter a categorical group variable i the iput box above (but you ca). If both umeric ad categorical group variables are etered, a separate table ad aalysis will be calculated for each variable. Numeric Variable(s) to Categorize Specify oe or more variables that have oly umeric values. Numeric values from these variables will be combied ito a set of categories usig the categorizatio optios that follow. If more tha oe variable is etered, a separate table will be created for each variable. For example, suppose you wat to tabulate a variable cotaiig idividual icome values ito four categories: Below 10000, 10000 to 40000, 40000 to 80000, ad Over 80000. You could select the icome variable here, set Group Numeric Data ito Categories Usig to List of Iterval Upper Limits ad set the List to 10000 40000 80000. 201-8

Group Numeric Data ito Categories Usig Choose the method by which umeric data will be combied ito categories. The choices are: Number of Itervals, Miimum, ad/or Width This optio allows you to specify the categories by eterig ay combiatio of the three parameters: Number of Itervals Miimum Width All three are optioal. Number of Itervals This is the umber of itervals ito which the values of the umeric variables are categorized. If ot eough itervals are specified to reach past the maximum data value, more will be added. Rage Iteger 2 Miimum This value is used i cojuctio with the Number of Itervals ad Width values to costruct a set of itervals ito which the umeric variables are categorized. This is the miimum value of the first iterval. Rage This value must be less tha the miimum data value. Width This value is used i cojuctio with the Number of Itervals ad Miimum values to costruct a set of itervals ito which the umeric variables are categorized. All itervals will have a width equal to this value. A data value X is i this iterval if Lower Limit < X Upper Limit. List of Iterval Upper Limits This optio allows you to specify the categories for the umeric variable by eterig a list of iterval boudaries directly, separated by blaks or commas. A iterval of the form L1 < X L2 is geerated for each iterval. The actual umber of itervals is oe more tha the umber of items specified here. For example, suppose you wat to tabulate a variable cotaiig idividual icome values ito four categories: Below 10000, 10000 to 40000, 40000 to 80000, ad Over 80000. You would set List of Iterval Upper Limits to 10000 40000 80000. Note that 10000 would be icluded i the Below 10000 iterval, but ot the 10000 to 40000 iterval. Also, 80000 would be icluded i the 40000 to 80000 iterval, ot the Over 80000 iterval. Layout Preview for Items i the Table This sectio provides a represetatio of how the results will be laid out i the table based o your item positio choices. Colors are used oly to highlight the positio of items i the table. The actual output will all be black. 201-9

Breaks, Frequecies Tab This pael lets you specify up to eight break variables ad a frequecy variable. These variables are completely optioal. Break Variables Eter up to 8 categorical break variables. The values i these variables are used to break the output up ito separate reports ad plots. A separate set of reports is geerated for each uique value (or uique combiatio of values if multiple break variables are specified). The break variables will be applied i the order that they are listed here. Frequecy Variable Specify a optioal frequecy (cout) variable. This data colum cotais itegers that represet the umber of observatios (frequecy) associated with each row of the dataset. If this optio is left blak, each dataset row has a frequecy of oe. This variable lets you modify that frequecy. This may be useful whe your data are tabulated ad you wat to eter couts. Missig Values Tab This pael lets you specify up to five missig values (besides the default of blak). For example, 0, 9, or NA may be missig values i your database. Missig Value Iclusio Specifies whether to iclude observatios with missig values i the tables. Delete All idicates that you wat the missig values totally igored. Iclude i All idicates that you wat the missig values treated just like ay other category. Missig Values Specify up to five idividual missig values here, oe per box. Report Optios Tab The followig optios cotrol the format of the reports. Group Variable Margial Totals Display Group Variable Margial Total o the Summary Tables Check to display margial totals for group variables (if used) o the tables. If o group variables are beig used the this optio is igored. Report Optios Variable Names This optio lets you select whether to display oly variable ames, variable labels, or both. Value Labels This optio lets you select whether to display oly values, value labels, or both. Use this optio if you wat the table to automatically attach labels to the values (like 1=Yes, 2=No, etc.). See the sectio o specifyig Value Labels elsewhere i this maual. 201-10

Summary Table Formattig Colum Justificatio Specify whether data colums i the tables will be left or right justified. Colum Widths Specify how the widths of colums i the cotigecy tables will be determied. The optios are Autosize to Miimum Widths Each data colum is idividually resized to the smallest width required to display the data i the colum. This usually results i colums with differet widths. This optio produces the most compact table possible, displayig the most data per page. Autosize to Equal Miimum Width The smallest width of each data colum is calculated ad the all colums are resized to the width of the widest colum. This results i the most compact table possible where all data colums have the same with. This is the default settig. Custom (User-Specified) Specify the widths (i iches) of the colums directly istead of havig the software calculate them for you. Custom Widths Eter oe or more values for the widths (i iches) of colums i the cotigecy tables. Sigle Value If you eter a sigle value, that value will be used as the width for all data colums i the table. List of Values Eter a list of values separated by spaces correspodig to the widths of each colum. The first value is used for the width of the first data colum, the secod for the width of the secod data colum, ad so forth. Extra values will be igored. If you eter fewer values tha the umber of colums, the last value i your list will be used for the remaiig colums. Type the word Autosize for ay colum to cause the program to calculate it's width for you. For example, eter 1 Autosize 0.7 to make colum 1 be 1 ich wide, colum 2 be sized by the program, ad colum 3 be 0.7 iches wide. Wrap Colum Headigs oto Two Lies Check this optio to make colum headigs wrap oto two lies. Use this optio to codese your table whe your data are spaced too far apart because of log colum headigs. Use Short Statistical Names o Reports ad Plots Normally, the ames of the statistical items i the reports ad plots are complete ames, such as Stadard Deviatio. Checkig this optio causes a shorter ame, such as SD, to be used istead so that more colums ca be displayed together i tables ad so that plot titles ad labels are ot so log. A maximum of 13 colums ca be displayed o a sigle row. 201-11

Decimal Places Item Decimal Places These decimal optios allow the user to specify the umber of decimal places for items i the output. Your choice here will ot affect calculatios; it will oly affect the format of the output. Auto If oe of the Auto optios is selected, the edig zero digits are ot show. For example, if Auto (0 to 7) is chose, 0.0500 is displayed as 0.05 1.314583689 is displayed as 1.314584 The output formattig system is ot desiged to accommodate Auto (0 to 13), ad if chose, this will likely lead to lies that ru o to a secod lie. This optio is icluded, however, for the rare case whe a very large umber of decimals is eeded. Plots Tab The optios o this pael cotrol the appearace of the plots that may be displayed. Click the plot format butto to chage the plot settigs. Show Separate Plots of each Statistic for each Table Check to display plots for each statistic i each table. This may result i several plots beig created for each table. Plots are created with a table s row item o the group axis ad the colum item as the leged variable. Whe there is oly oe colum, the sub row item is used as the leged variable. Show a Combied Plot for each Table Check to display a sigle plot for each table that cotais all of the iformatio i the table. Plots are created with a table s row item o the group axis ad the colum item as the leged variable. Whe there is oly oe colum, the sub row item is used as the leged variable. For combied plots from tables with rows, sub rows, ad colums, the rows ad sub rows are combied oto the group axis ad the colums are icluded i the leged. Display Break Variables Values as Subtitles o the Plots Specify whether to display the values of the break variables as the secod title lie o the plots. Display Group Variable Margial Totals o the Plots Check to display margial totals for group variables (if used) o the plots. If o group variables are beig used the this optio is igored. 201-12

Example 1 Basic Variable Summary Report (No Group Variables) The data used i this example are i the Resale dataset. You may follow alog here by makig the appropriate etries or load the completed template Example 1a by clickig o Ope Example Template from the File meu of the widow. 1 Ope the Resale dataset. From the File meu of the NCSS Data widow, select Ope Example Data. Click o the file Resale.NCSS. Click Ope. 2 Ope the widow. Usig the Aalysis meu or the Procedure Navigator, fid ad select the Descriptive Statistics Summary Tables procedure O the meus, select File, the New Template. This will fill the procedure with the default template. 3 Specify the variables. Select the Variables tab. For Data Variable(s), select Price, Bedrooms, Bathrooms, Garage, ad TotalSqft. 4 Specify the statistics. I the Table Statistics sectio, check Cout, Mea, Std Dev, 95% LCL, ad 95% UCL. 5 Ru the procedure. From the Ru meu, select Ru Procedure. Alteratively, just click the gree Ru butto. Summary Table Variable Statistic Price Bedrooms Bathrooms Garage TotalSqft Cout 150 150 150 150 150 Mea 174392 2.42 2.4 1.266667 1893.38 Stadard Deviatio 97656.81 0.8919476 0.8047677 0.5636252 754.2496 Lower 95% CL Mea 158636 2.276093 2.270158 1.175731 1771.689 Upper 95% CL Mea 190148 2.563908 2.529842 1.357602 2015.071 The table is created with the statistics as rows ad the data variables as colums whe the positios are both set to Auto. 201-13

Plots of Each Statistic (More Plots Follow) The plots are ot very iformative because the variables have vastly differet scales. Example 1b Adjust Item Table Positios (Data Variables i Rows ad Statistics i Colums) To rotate the table, all we have to do is chage the positio of oe of the items. Go back to the Descriptive Statistics Summary Tables procedure widow ad chage the positio for Data Variable(s) to Rows (or load the completed template Example 1b by clickig o Ope Example Template from the File meu) ad ru the procedure agai to get the results. 6 Specify the group variable. For Data Variable(s) Positio, select Rows ad re-ru the procedure. Statistic Variable Stadard Lower 95% Upper 95% Cout Mea Deviatio CL Mea CL Mea Price 150 174392 97656.81 158636 190148 Bedrooms 150 2.42 0.8919476 2.276093 2.563908 Bathrooms 150 2.4 0.8047677 2.270158 2.529842 Garage 150 1.266667 0.5636252 1.175731 1.357602 TotalSqft 150 1893.38 754.2496 1771.689 2015.071 The table is ow rotated with the data variables as rows ad the statistics as colums. Notice that the actual summary statistic values are exactly the same. 201-14

Example 2 Variable Summary Report (Oe Group Variable) The data used i this example are i the Resale dataset. You may follow alog here by makig the appropriate etries or load the completed template Example 2a by clickig o Ope Example Template from the File meu of the widow. 1 Ope the Resale dataset. From the File meu of the NCSS Data widow, select Ope Example Data. Click o the file Resale.NCSS. Click Ope. 2 Ope the widow. Usig the Aalysis meu or the Procedure Navigator, fid ad select the Descriptive Statistics Summary Tables procedure O the meus, select File, the New Template. This will fill the procedure with the default template. 3 Specify the variables. Select the Variables tab. For Data Variable(s), select Price, TotalSqft, ad LotSize. 4 Specify the statistics. I the Table Statistics sectio, check Cout, Mea, ad Std Dev. 5 Specify the group variable. Check Group Variable 1 ad select State as the variable. 6 Specify the report format. Click o the Report Optios tab. For Variable Names, select Labels. For Value Labels, select Value Labels. 7 Ru the procedure. From the Ru meu, select Ru Procedure. Alteratively, just click the gree Ru butto. 201-15

Summary Table Variable State Sales Total Area Lot Size Statistic Price (Sqft) (Sqft) Nevada Cout 88 88 88 Mea 170762.5 1881.33 8571.454 Stadard Deviatio 98665.72 788.569 2419.88 Virgiia Cout 62 62 62 Mea 179543.5 1910.484 8076.597 Stadard Deviatio 96771.49 708.6572 2301.226 Total Cout 150 150 150 Mea 174392 1893.38 8366.913 Stadard Deviatio 97656.81 754.2496 2376.334 The table is displays the group variable values as the rows, the statistics as the subrows, ad the data variables as the colums. The plots are ot show because they are ot very iformative because the variables have vastly differet scales. Totals are give for the group variable. Example 2b Adjust Item Table Positios (Data Variables i Rows, Statistics i Sub Rows, ad Group Variable i Colums) To rotate the table, simply chage the positio the items. Go back to the procedure widow ad chage the positio for Data Variable(s) to Rows (or load the completed template Example 2b by clickig o Ope Example Template from the File meu) ad ru the procedure agai to get the results. 8 Specify the group variable. For Data Variable(s) Positio, select Rows ad re-ru the procedure. State Variable Statistic Nevada Virgiia Total Sales Price Cout 88 62 150 Mea 170762.5 179543.5 174392 Stadard Deviatio 98665.72 96771.49 97656.81 Total Area (Sqft) Cout 88 62 150 Mea 1881.33 1910.484 1893.38 Stadard Deviatio 788.569 708.6572 754.2496 Lot Size (Sqft) Cout 88 62 150 Mea 8571.454 8076.597 8366.913 Stadard Deviatio 2419.88 2301.226 2376.334 The table is ow rotated with the data variables as rows ad the group variable values as colums. Notice that the actual summary statistic values are exactly the same. 201-16

Example 2c Adjust Item Table Positios (Data Variables i Rows, Group Variable i Sub Rows, ad Statistics i Colums) To chage the table so that statistics are preseted as colums with the group variable as subrows ad the data variables as rows, chage the positio of Statistics to Colums with the positio for Data Variable(s) still set to Rows (or load the completed template Example 2c by clickig o Ope Example Template from the File meu) ad ru the procedure agai to get the results. 9 Specify the statistics. For Statistics Positio, select Colums ad re-ru the procedure. Statistic Variable Stadard State Cout Mea Deviatio Sales Price Nevada 88 170762.5 98665.72 Virgiia 62 179543.5 96771.49 Total 150 174392 97656.81 Total Area (Sqft) Nevada 88 1881.33 788.569 Virgiia 62 1910.484 708.6572 Total 150 1893.38 754.2496 Lot Size (Sqft) Nevada 88 8571.454 2419.88 Virgiia 62 8076.597 2301.226 Total 150 8366.913 2376.334 The table ow has the data variables as rows ad the group variable values as subrows with the statistics as colums. 201-17

Example 3 Variable Summary Report (Two Group Variables) The data used i this example are i the Pai dataset. I this example we ll show you how to make eve more customizatios to adjust the appearace of the tables ad plots ad how easy it is to make positio adjustmets. You may follow alog here by makig the appropriate etries or load the completed template Example 3a by clickig o Ope Example Template from the File meu of the widow. 1 Ope the Pai dataset. From the File meu of the NCSS Data widow, select Ope Example Data. Click o the file Pai.NCSS. Click Ope. 2 Ope the widow. Usig the Aalysis meu or the Procedure Navigator, fid ad select the Descriptive Statistics Summary Tables procedure O the meus, select File, the New Template. This will fill the procedure with the default template. 3 Specify the variables. Select the Variables tab. For Data Variable(s), select Pai. 4 Specify the statistics. I the Table Statistics sectio, click the Ucheck All butto to ucheck all selected statistics. I the Table Statistics sectio, check Mea, Media, Miimum, Maximum, 25 th Pctile, ad 75 th Pctile. Use the up/dow arrow buttos to move the checked statistics so that the order is Mea, Miimum, 25 th Pctile, Media, 75 th Pctile, the Maximum. It does ot matter if there are uchecked statistics betwee checked statistics. Checked statistics will be output i the order they are listed. 5 Specify the group variables. Check Group Variable 1 ad select Drug as the variable. Check Group Variable 2 ad select Time as the variable. 6 Specify the report optios ad format. Click o the Report Optios tab. Ucheck Display Group Variable Margial Total o the Summary Tables so totals are ot displayed. Check Use Short Statistical Names o Reports ad Plots to fit more colums o oe row of the table. Chage the Decimal Places for Sum, Mea, CI Limits to 2 to limit the width of the displayed values. 7 Specify the plots. Click o the Plots tab. Click o the Separate Plot Format butto. O the Bar Chart Format widow, select the Numeric Axis tab ad eter 100 for Max uder Boudaries. This will make it so that all statistic plots are o the same scale for easy compariso amog plots. Click OK to save the plot settigs. Check Show a Combied Plot for Each Table. Click o the Combied Plot Format butto. O the Bar Chart Format widow, select the Group Axis tab ad click o the Layout butto for the Lower Axis Tick Label. Chage Aligmet to Right, Rotatio Agle to 45, ad Margi Above the Text to 10. Click OK to save the layout settigs ad OK agai to save the plot settigs. 201-18

8 Ru the procedure. From the Ru meu, select Ru Procedure. Alteratively, just click the gree Ru butto. Output Summary Table of Pai Time Drug Statistic 0.5 1 1.5 2 2.5 3 Kerlosi Mea 76.00 69.86 65.00 54.00 41.71 40.14 Mi 68 62 59 46 34 33 25th Pctile 71 64 61 47 36 37 Media 77 68 65 56 43 41 75th Pctile 81 77 69 57 46 45 Max 83 80 72 64 48 46 Laposec Mea 72.29 71.00 64.00 60.57 52.43 51.71 Mi 65 65 55 54 46 47 25th Pctile 68 67 60 56 47 49 Media 71 71 65 61 53 50 75th Pctile 78 77 68 65 56 56 Max 79 78 70 66 58 58 Placebo Mea 78.14 76.29 70.86 72.14 65.14 65.43 Mi 69 66 62 67 61 60 25th Pctile 71 69 64 70 63 62 Media 79 78 70 73 65 67 75th Pctile 87 82 76 73 68 68 Max 87 84 81 76 69 70 The table is displays Group Variable 1 (Drug) values as the rows, the statistics as the subrows, ad Group Variable 2 (Time) values as the colums. Plots of each Statistic for Pai (More Statistic Plots Follow) Idividual plots are created with the table row item (Group Variable 1 --- Drug ) o the group (X) axis ad the table colum item (Group Variable 2 --- Time ) as the leged variable. A separate plot is created for each statistic. These plots are very useful for seeig overall treds. From the plots show here, it is apparet that the average ad miimum pai respose is lower for both drugs tha for placebo ad that the pai cotrol is better over time. Kerlosi appears to cotrol pai the best from these results. Statistical tests would eed to be performed, however, to assert statistical sigificace i the differeces. 201-19

Combied Plot of Pai The combied plot displays all of the iformatio i the table. We rotated the group axis labels so they would ot overlap ad be readable. The table row item (Group Variable 1 --- Drug ) ad table sub row item (Statistic) are combied o the group (X) axis. The table colum item (Group Variable 2 --- Time ) is the leged variable. Example 3b Adjust Item Table Positios (Group 2 Variable i Rows, Group 1 Variable i Sub Rows, ad Statistics i Colums) To chage the orietatio o the tables ad plots, simply chage the positio the items. Let s display the Statistics as the colums ad Time as the rows. This will put Drug as the sub row. Go back to the Descriptive Statistics Summary Tables procedure widow ad chage the positio for Statistics to Colums ad the positio for Group Variable 2 (Time) to Rows (or load the completed template Example 3b by clickig o Ope Example Template from the File meu) ad ru the procedure agai to get the results. 9 Specify the statistics ad group variables. For Statistics Positio, select Colums. For Group Variable 2 Positio, select Rows ad re-ru the procedure. 201-20

Summary Table of Pai Statistic Time 25th 75th Drug Mea Mi Pctile Media Pctile Max 0.5 Kerlosi 76.00 68 71 77 81 83 Laposec 72.29 65 68 71 78 79 Placebo 78.14 69 71 79 87 87 1 Kerlosi 69.86 62 64 68 77 80 Laposec 71.00 65 67 71 77 78 Placebo 76.29 66 69 78 82 84 1.5 Kerlosi 65.00 59 61 65 69 72 Laposec 64.00 55 60 65 68 70 Placebo 70.86 62 64 70 76 81 2 Kerlosi 54.00 46 47 56 57 64 Laposec 60.57 54 56 61 65 66 Placebo 72.14 67 70 73 73 76 2.5 Kerlosi 41.71 34 36 43 46 48 Laposec 52.43 46 47 53 56 58 Placebo 65.14 61 63 65 68 69 3 Kerlosi 40.14 33 37 41 45 46 Laposec 51.71 47 49 50 56 58 Placebo 65.43 60 62 67 68 70 The table is displays Group Variable 2 (Time) values as the rows, Group Variable 1 (Drug) values as the subrows, ad the statistics as the colums. Plots of each Statistic for Pai (More Statistic Plots Follow) The idividual plots are differet ow with the table row item (Group Variable 2 --- Time ) o the group (X) axis ad the table colum item (Group Variable 1 --- Drug ) as the leged variable. A separate plot is created for each statistic. These plots are agai useful for seeig overall treds. There is a very distict reductio i pai over time. 201-21

Combied Plot of Pai Agai, the combied plot displays all of the iformatio i the table. The table row item (Group Variable 2 --- Time ) ad table sub row item (Group Variable 1 --- Drug ) are combied o the group (X) axis. The table colum item (Statistic) is the leged variable. Example 3c Adjust Item Table Positios (Creatig a Separate Table for each Data Variable ad Statistic Combiatio) It s easy to create a separate table for each data variable ad statistic combiatio (this ca oly be doe whe there is at least oe group variable). Let s display a separate table for each statistic with Time as the rows ad Drug as the colums. There will be o sub row item. Go back to the procedure widow ad chage the positio for Data Variable(s) to Tables ad the positio for Statistics to Tables as well. Leave the positio for Group Variable 2 (Time) as Rows (or load the completed template Example 3c by clickig o Ope Example Template from the File meu) ad ru the procedure agai to get the results. 10 Specify the statistics ad group variables. For Data Variable(s) Positio, select Tables. For Statistics Positio, select Tables. Leave Group Variable 2 Positio as Rows ad re-ru the procedure. 201-22

Summary Table of Mea of Pai Drug Time Kerlosi Laposec Placebo 0.5 76.00 72.29 78.14 1 69.86 71.00 76.29 1.5 65.00 64.00 70.86 2 54.00 60.57 72.14 2.5 41.71 52.43 65.14 3 40.14 51.71 65.43 Plot of Mea of Pai Summary Table of Mi of Pai Drug Time Kerlosi Laposec Placebo 0.5 68 65 69 1 62 65 66 1.5 59 55 62 2 46 54 67 2.5 34 46 61 3 33 47 60 Plot of Mi of Pai (Report cotiues with table ad plot for each Data Variable/Statistic combiatio) A separate table is created for each Data Variable/Statistic combiatio. If more tha oe data variable were etered, the report would be eve loger. There is o combied plot i the output because the combied plot is the same as the idividual plot i this case. 201-23