Descriptive Statistics Summary Lists

Transcription

1 Chapter 209 Descriptive Statistics Summary Lists Itroductio This procedure is used to summarize cotiuous data. Large volumes of such data may be easily summarized i statistical lists of meas, couts, stadard deviatios, etc. Up to 8 categorical group variables may be used to calculate summaries for idividual group combiatios. The summary lists may be output directly to a ew dataset. This procedure produces lists 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 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 Nev Vir Nev Nev Nev

2 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 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. s 2 i = 1 = ( x x ) i

3 Stadard Deviatio (Std Dev) 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. 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 = x ± t a /2, 1s x Miimum The smallest data value. Maximum The largest data value. 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

4 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 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. COD = MADM Media = i= 1 xi Media Media 209-4

5 Skewess 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 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. Numeric Data Variables to Summarize 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. Categorical Group Variables Group Variable(s) Specify up to 8 categorical group variables. The categories may be text (e.g. Low, Med, High ) or umeric (e.g. 1, 2, 3 ). Statistics are computed for each combiatio of group values from all variables etered here

6 Category Order 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. Frequecy (Cout) Variables 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. Summary Statistics 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. Summary List Storage Store the Summary List i a New NCSS Data File Whe this box is checked, the curret dataset will close ad the resultig data summary list will be writte to a ew data table. You will be prompted to save ay chages to the curret dataset before cotiuig. The ew data table with the data summary list will automatically be saved i the output file etered below. If o output file is specified, o file will be saved. You ca maually save the output data file to ay file you wish. Output File Name Eter a output file ame i which to store the data. Double-click the box or click o the file selectio butto to browse for a file or folder. The selected output file will be overwritte ad the curret database will be closed, so make sure to save all data before cotiuig. If o output file is specified, o file will be automatically saved. You ca maually save the output data file to ay file you wish. If you have chose to reope the curret dataset without eterig a output file ame, the the summary output data will be lost. Summary List Storage Storage Optios Data Variables Select how the data variables will be stored i the output file. This optio does ot affect calculatios. The optios are Store as Rows Data variable ames ad associated summary statistics are stored row-by-row i the output data table. Variable Group Cout Mea Var 1 A Var 1 B Var 2 A Var 2 B

7 Store as Colums Data variable ames ad associated summary statistics are stored colum-by-colum i the output data table. Var 1 Var 1 Var 2 Var 2 Group Cout Mea Cout Mea A B I both cases, the summary statistics for group variables (if etered) are listed row-by-row. Automatically Reope the Curret Dataset Data storage requires the curret dataset to close whe the summary data is writte to the data table. Whe this box is checked, the curret dataset will automatically reope oce the process is complete. Usaved Data Warig If you have ot saved the curret dataset to a file, the data will ot reope ad will be lost! 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. 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

8 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

9 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, is displayed as is displayed as 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 Statistic Plots Check to display a separate plot 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. If there is oly oe row i a table, the o plot is output

10 Example 1 Basic Summary List with 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 Lists 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 List Statistics Variable 95% LCL 95% UCL Cout Mea SD Mea Mea Price Bedrooms Bathrooms Garage TotalSqft The data summary list is preseted with each variable represeted o a sigle row

11 Plots of Each Statistic (More Plots Follow) The plots are ot very iformative because the variables have vastly differet scales. Example 1b Storig the Summary List i a New NCSS Data File To store the data summary list i a ew data file, simply go back to the procedure widow ad check Store the Summary List i a New NCSS Data File (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. Be careful because ay usaved data will be lost! 6 Specify the data storage. I the Summary List Storage sectio, check Store the Summary List i a New NCSS Data File. For Output File Name, eter %mydocs_ncss%\data\resalesummary.ncss. Ucheck Automatically Reope the Curret Dataset after the Save Operatio Completes so that we ca review the summary data file that has bee created. Summary List Storage Iformatio Output Data File Name: {NCSS Documets Folder}\Data\ResaleSummary.NCSS Origial Raw Data File: {Example Data Folder}\Resale.NCSS Data Variable(s): (5) Price, Bedrooms, Bathrooms, Garage, TotalSqft Group Variable(s): (0) Summary Statistic(s): (5) Cout, Mea, SD, 95% LCL Mea, 95% UCL Mea (Summary List Report ad Plots Follow) The data summary list output data file is described i this report. Go to the data table to see the ew summary data file that has bee created

12 Example 2 Summary List with Oe Group Variable The data used i this example are i the Pai 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 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 Lists 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. For Group Variable(s), select Drug. 4 Specify the statistics. I the Summary Statistics sectio, click the Ucheck All butto to ucheck all selected statistics. I the Summary 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 Ru the procedure. From the Ru meu, select Ru Procedure. Alteratively, just click the gree Ru butto. Summary List Statistics for Pai Drug 25th 75th Mea Miimum Pctile Media Pctile Maximum Kerlosi Laposec Placebo The summary list is preseted with each level of Drug represeted o a sigle row. The various statistics are listed i colums

13 Plots of Each Statistic (More Plots Follow) Idividual plots for each statistic are created with the Group Variable, Drug, o the group (X) axis. 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. 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. Example 2b Storig the Summary List i a New NCSS Data File To store the data summary list i a ew data file, simply go back to the procedure widow ad check Store the Summary List i a New NCSS Data File (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. Be careful because ay usaved data will be lost! 6 Specify the data storage. I the Summary List Storage sectio, check Store the Summary List i a New NCSS Data File. For Output File Name, eter %mydocs_ncss%\data\paidrugsummary.ncss. Ucheck Automatically Reope the Curret Dataset after the Save Operatio Completes so that we ca review the summary data file that has bee created. Summary List Storage Iformatio Output Data File Name: Origial Raw Data File: Data Variable(s): Group Variable(s): Summary Statistic(s): {NCSS Documets Folder}\Data\PaiDrugSummary.NCSS {Example Data Folder}\Pai.NCSS (1) Pai (1) Drug (6) Mea, Miimum, 25th Pctile, Media, 75th Pctile, Maximum (Summary List Report ad Plots Follow) The data summary list output data file is described i this report. Go to the data table to see the ew summary data file that has bee created

14 Example 3 Summary List with 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. 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 Lists 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 Cov ad Pai. For Group Variable(s), select Drug ad Time. 4 Specify the statistics. I the Summary Statistics sectio, check Cout, Mea, ad Std Dev. 5 Specify the report optios ad format. Click o the Report Optios tab. Ucheck Use Short Statistical Names o Reports ad Plots. Chage the Decimal Places for Sum, Mea, CI Limits to 2 to limit the width of the displayed values. Chage the Decimal Places for SD, SE, Var, MAD, MADM to 2 to limit the width of the displayed values. 6 Specify the plots. Click o the Plots tab. Click o the 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 90, ad Margi Above the Text to 10. Click OK to save the layout settigs ad OK agai to save the plot settigs. 7 Ru the procedure. From the Ru meu, select Ru Procedure. Alteratively, just click the gree Ru butto

15 Output Summary List of Cov Statistics for Cov Drug Time Stadard Cout Mea Deviatio Kerlosi Kerlosi Kerlosi Kerlosi Kerlosi Kerlosi Laposec Laposec Laposec Laposec Laposec Laposec Placebo Placebo Placebo Placebo Placebo Placebo Plots of each Statistic for Cov

16 Summary List of Pai Statistics for Pai Drug Time Stadard Cout Mea Deviatio Kerlosi Kerlosi Kerlosi Kerlosi Kerlosi Kerlosi Laposec Laposec Laposec Laposec Laposec Laposec Placebo Placebo Placebo Placebo Placebo Placebo Plots of each Statistic for Pai Summary list tables are preseted separately for the data variables, Cov ad Pai, with each combiatio of Drug ad Time represeted o a sigle row. The various statistics are listed i colums. 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

17 Example 3b Storig the Summary List i a New NCSS Data File (Row-by- Row) To store the data summary list i a ew data file row-by-row, simply go back to the Descriptive Statistics Summary Lists procedure widow ad check Store the Summary List i a New NCSS Data File (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. Be careful because ay usaved data will be lost! 8 Specify the data storage. I the Summary List Storage sectio, check Store the Summary List i a New NCSS Data File. For Output File Name, eter %mydocs_ncss%\data\paidrugtimesummary1.ncss. Ucheck Automatically Reope the Curret Dataset after the Save Operatio Completes so that we ca review the summary data file that has bee created. Summary List Storage Iformatio Output Data File Name: Origial Raw Data File: Data Variable(s): Group Variable(s): Summary Statistic(s): {NCSS Documets Folder}\PaiDrugTimeSummary1.NCSS {Example Data Folder}\Pai.NCSS (2) Cov, Pai (2) Drug, Time (3) Cout, Mea, SD (Summary List Report ad Plots Follow) The data summary list output data file is described i this report. Go to the data table to see the ew summary data file that has bee created. The summary data values are stored i PaiDrugTimeSummary1.NCSS as follows Variable Drug Time Cout Mea SD Cov Kerlosi Cov Kerlosi Cov Kerlosi Cov Kerlosi Cov Kerlosi Cov Kerlosi Cov Laposec Cov Laposec Cov Laposec Cov Laposec Cov Laposec Cov Laposec Cov Placebo Cov Placebo Cov Placebo Cov Placebo Cov Placebo Cov Placebo Pai Kerlosi Pai Kerlosi Pai Kerlosi

18 Example 3c Storig the Summary List i a New NCSS Data File (Columby-Colum) To store the data summary list i a ew data file colum-by-colum, simply go back to the Descriptive Statistics Summary Lists procedure widow ad check Store the Summary List i a New NCSS Data File (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. Be careful because ay usaved data will be lost! 9 Specify the data storage. I the Summary List Storage sectio, check Store the Summary List i a New NCSS Data File. For Output File Name, eter %mydocs_ncss%\data\paidrugtimesummary2.ncss. For Data Variable Storage, eter Store as Colums. Ucheck Automatically Reope the Curret Dataset after the Save Operatio Completes so that we ca review the summary data file that has bee created. Summary List Storage Iformatio Output Data File Name: Origial Raw Data File: Data Variable(s): Group Variable(s): Summary Statistic(s): {NCSS Documets Folder}\PaiDrugTimeSummary2.NCSS {Example Data Folder}\Pai.NCSS (2) Cov, Pai (2) Drug, Time (3) Cout, Mea, SD (Summary List Report ad Plots Follow) The data summary list output data file is described i this report. Go to the data table to see the ew summary data file that has bee created. The summary data values are stored i PaiDrugTimeSummary2.NCSS as follows Drug Time Cov_Cout Cov_Mea Cov_SD Pai_Cout Kerlosi Kerlosi Kerlosi Kerlosi Kerlosi Kerlosi Laposec Laposec Laposec Laposec Laposec Laposec Placebo Placebo Placebo Placebo Placebo Placebo