X-Git-Url: https://pintos-os.org/cgi-bin/gitweb.cgi?a=blobdiff_plain;f=doc%2Fstatistics.texi;h=3877a8d43d93db8ddd35a49aa287121ac907bd86;hb=6e80abcaeb7c361477eff4b8a578e54f1def81c4;hp=f0160f40a8a2888b626c4f61f00ca3c15758a216;hpb=5443c41f89a2b29cf8cf55f21eecb839fae08177;p=pspp diff --git a/doc/statistics.texi b/doc/statistics.texi index f0160f40a8..3877a8d43d 100644 --- a/doc/statistics.texi +++ b/doc/statistics.texi @@ -138,6 +138,7 @@ FREQUENCIES [@{FREQ,PERCENT@}] [@{NOMISSING,MISSING@}] /BARCHART=[MINIMUM(@var{x_min})] [MAXIMUM(@var{x_max})] [@{FREQ,PERCENT@}] + /ORDER=@{ANALYSIS,VARIABLE@} (These options are not currently implemented.) @@ -148,9 +149,8 @@ FREQUENCIES The @cmd{FREQUENCIES} procedure outputs frequency tables for specified variables. @cmd{FREQUENCIES} can also calculate and display descriptive statistics -(including median and mode) and percentiles, -@cmd{FREQUENCIES} can also output -histograms and pie charts. +(including median and mode) and percentiles, and various graphical representations +of the frequency distribution. The @subcmd{VARIABLES} subcommand is the only required subcommand. Specify the variables to be analyzed. @@ -197,9 +197,12 @@ For instance, @subcmd{/NTILES=4} would cause quartiles to be reported. The @subcmd{HISTOGRAM} subcommand causes the output to include a histogram for each specified numeric variable. The X axis by default ranges from the minimum to the maximum value observed in the data, but the @subcmd{MINIMUM} -and @subcmd{MAXIMUM} keywords can set an explicit range. The number of -bins are 2IQR(x)n^-1/3 according to the Freedman-Diaconis rule. (Note that -@cmd{EXAMINE} uses a different algorithm to determine bin sizes.) +and @subcmd{MAXIMUM} keywords can set an explicit range. +@footnote{The number of +bins is chosen according to the Freedman-Diaconis rule: +@math{2 \times IQR(x)n^{-1/3}}, where @math{IQR(x)} is the interquartile range of @math{x} +and @math{n} is the number of samples. Note that +@cmd{EXAMINE} uses a different algorithm to determine bin sizes.} Histograms are not created for string variables. Specify @subcmd{NORMAL} to superimpose a normal curve on the @@ -209,12 +212,26 @@ histogram. The @subcmd{PIECHART} subcommand adds a pie chart for each variable to the data. Each slice represents one value, with the size of the slice proportional to the value's frequency. By default, all non-missing values are given -slices. The @subcmd{MINIMUM} and @subcmd{MAXIMUM} keywords can be used to limit the -displayed slices to a given range of values. The @subcmd{MISSING} keyword adds -slices for missing values. - -The @subcmd{FREQ} and @subcmd{PERCENT} options on @subcmd{HISTOGRAM} and @subcmd{PIECHART} are accepted -but not currently honoured. +slices. +The @subcmd{MINIMUM} and @subcmd{MAXIMUM} keywords can be used to limit the +displayed slices to a given range of values. +The keyword @subcmd{NOMISSING} causes missing values to be omitted from the +piechart. This is the default. +If instead, @subcmd{MISSING} is specified, then a single slice +will be included representing all system missing and user-missing cases. + +@cindex bar chart +The @subcmd{BARCHART} subcommand produces a bar chart for each variable. +The @subcmd{MINIMUM} and @subcmd{MAXIMUM} keywords can be used to omit +categories whose counts which lie outside the specified limits. +The @subcmd{FREQ} option (default) causes the ordinate to display the frequency +of each category, whereas the @subcmd{PERCENT} option will display relative +percentages. + +The @subcmd{FREQ} and @subcmd{PERCENT} options on @subcmd{HISTOGRAM} and +@subcmd{PIECHART} are accepted but not currently honoured. + +The @subcmd{ORDER} subcommand is accepted but ignored. @node EXAMINE @section EXAMINE @@ -294,10 +311,9 @@ The first three can be used to visualise how closely each cell conforms to a normal distribution, whilst the spread vs.@: level plot can be useful to visualise how the variance of differs between factors. Boxplots will also show you the outliers and extreme values. - -@subcmd{HISTOGRAM} uses Sturges' rule to determine the number of -bins, as approximately 1 + log2(n). (Note that @cmd{FREQUENCIES} uses a -different algorithm to find the bin size.) +@footnote{@subcmd{HISTOGRAM} uses Sturges' rule to determine the number of +bins, as approximately @math{1 + \log2(n)}, where @math{n} is the number of samples. +Note that @cmd{FREQUENCIES} uses a different algorithm to find the bin size.} The @subcmd{SPREADLEVEL} plot displays the interquartile range versus the median. It takes an optional parameter @var{t}, which specifies how the data @@ -395,8 +411,9 @@ large quantity of output. @display GRAPH - /HISTOGRAM = @var{var} - /SCATTERPLOT [(BIVARIATE)] = @var{var1} WITH @var{var2} [BY @var{var3}] + /HISTOGRAM [(NORMAL)]= @var{var} + /SCATTERPLOT [(BIVARIATE)] = @var{var1} WITH @var{var2} [BY @var{var3}] + /BAR = @{@var{summary-function}(@var{var1}) | @var{count-function}@} BY @var{var2} [BY @var{var3}] [ /MISSING=@{LISTWISE, VARIABLE@} [@{EXCLUDE, INCLUDE@}] ] [@{NOREPORT,REPORT@}] @@ -406,11 +423,20 @@ The @cmd{GRAPH} produces graphical plots of data. Only one of the subcommands @subcmd{HISTOGRAM} or @subcmd{SCATTERPLOT} can be specified, i.e. only one plot can be produced per call of @cmd{GRAPH}. The @subcmd{MISSING} is optional. +@menu +* SCATTERPLOT:: Cartesian Plots +* HISTOGRAM:: Histograms +* BAR CHART:: Bar Charts +@end menu + +@node SCATTERPLOT +@subsection Scatterplot @cindex scatterplot -The subcommand @subcmd{SCATTERPLOT} produces an xy plot of the data. The different -values of the optional third variable @var{var3} will result in different colours and/or -markers for the plot. The following is an example for producing a scatterplot. +The subcommand @subcmd{SCATTERPLOT} produces an xy plot of the +data. The different values of the optional third variable @var{var3} +will result in different colours and/or markers for the plot. The +following is an example for producing a scatterplot. @example GRAPH @@ -421,10 +447,14 @@ This example will produce a scatterplot where @var{height} is plotted versus @va on the value of the @var{gender} variable, the colour of the datapoint is different. With this plot it is possible to analyze gender differences for @var{height} vs.@: @var{weight} relation. +@node HISTOGRAM +@subsection Histogram @cindex histogram The subcommand @subcmd{HISTOGRAM} produces a histogram. Only one variable is allowed for the histogram plot. +The keyword @subcmd{NORMAL} may be specified in parentheses, to indicate that the ideal normal curve +should be superimposed over the histogram. For an alternative method to produce histograms @pxref{EXAMINE}. The following example produces a histogram plot for the variable @var{weight}. @@ -433,6 +463,60 @@ GRAPH /HISTOGRAM = @var{weight}. @end example +@node BAR CHART +@subsection Bar Chart +@cindex bar chart + +The subcommand @subcmd{BAR} produces a bar chart. +This subcommand requires that a @var{count-function} be specified (with no arguments) or a @var{summary-function} with a variable @var{var1} in parentheses. +Following the summary or count function, the keyword @subcmd{BY} should be specified and then a catagorical variable, @var{var2}. +The values of the variable @var{var2} determine the labels of the bars to be plotted. +Optionally a second categorical variable @var{var3} may be specified in which case a clustered (grouped) bar chart is produced. + +Valid count functions are +@table @subcmd +@item COUNT +The weighted counts of the cases in each category. +@item PCT +The weighted counts of the cases in each category expressed as a percentage of the total weights of the cases. +@item CUFREQ +The cumulative weighted counts of the cases in each category. +@item CUPCT +The cumulative weighted counts of the cases in each category expressed as a percentage of the total weights of the cases. +@end table + +The summary function is applied to @var{var1} across all cases in each category. +The recognised summary functions are: +@table @subcmd +@item SUM +The sum. +@item MEAN +The arithmetic mean. +@item MAXIMUM +The maximum value. +@item MINIMUM +The minimum value. +@end table + +The following examples assume a dataset which is the results of a survey. +Each respondent has indicated annual income, their sex and city of residence. +One could create a bar chart showing how the mean income varies between of residents of different cities, thus: +@example +GRAPH /BAR = MEAN(@var{income}) BY @var{city}. +@end example + +This can be extended to also indicate how income in each city differs between the sexes. +@example +GRAPH /BAR = MEAN(@var{income}) BY @var{city} BY @var{sex}. +@end example + +One might also want to see how many respondents there are from each city. This can be achieved as follows: +@example +GRAPH /BAR = COUNT BY @var{city}. +@end example + +Bar charts can also be produced using the @ref{FREQUENCIES} and @ref{CROSSTABS} commands. + @node CORRELATIONS @section CORRELATIONS @@ -514,6 +598,7 @@ CROSSTABS ASRESIDUAL,ALL,NONE@} /STATISTICS=@{CHISQ,PHI,CC,LAMBDA,UC,BTAU,CTAU,RISK,GAMMA,D, KAPPA,ETA,CORR,ALL,NONE@} + /BARCHART (Integer mode.) /VARIABLES=@var{var_list} (@var{low},@var{high})@dots{} @@ -656,8 +741,15 @@ some statistics are calculated only in integer mode. @samp{/STATISTICS} without any settings selects CHISQ. If the @subcmd{STATISTICS} subcommand is not given, no statistics are calculated. +@cindex bar chart +The @samp{/BARCHART} subcommand produces a clustered bar chart for the first two +variables on each table. +If a table has more than two variables, the counts for the third and subsequent levels +will be aggregated and the chart will be produces as if there were only two variables. + + @strong{Please note:} Currently the implementation of @cmd{CROSSTABS} has the -following bugs: +following limitations: @itemize @bullet @item @@ -685,6 +777,8 @@ FACTOR VARIABLES=@var{var_list} [ /METHOD = @{CORRELATION, COVARIANCE@} ] + [ /ANALYSIS=@var{var_list} ] + [ /EXTRACTION=@{PC, PAF@}] [ /ROTATION=@{VARIMAX, EQUAMAX, QUARTIMAX, PROMAX[(@var{k})], NOROTATE@}] @@ -703,7 +797,10 @@ FACTOR VARIABLES=@var{var_list} The @cmd{FACTOR} command performs Factor Analysis or Principal Axis Factoring on a dataset. It may be used to find common factors in the data or for data reduction purposes. -The @subcmd{VARIABLES} subcommand is required. It lists the variables which are to partake in the analysis. +The @subcmd{VARIABLES} subcommand is required. It lists the variables +which are to partake in the analysis. (The @subcmd{ANALYSIS} +subcommand may optionally further limit the variables that +participate; it is not useful and implemented only for compatibility.) The @subcmd{/EXTRACTION} subcommand is used to specify the way in which factors (components) are extracted from the data. If @subcmd{PC} is specified, then Principal Components Analysis is used. @@ -1413,7 +1510,7 @@ of variable preceding @subcmd{WITH} against variable following @display T-TEST /MISSING=@{ANALYSIS,LISTWISE@} @{EXCLUDE,INCLUDE@} - /CRITERIA=CIN(@var{confidence}) + /CRITERIA=CI(@var{confidence}) (One Sample mode.) @@ -1618,8 +1715,9 @@ The default is 0.05. @display QUICK CLUSTER @var{var_list} - [/CRITERIA=CLUSTERS(@var{k}) [MXITER(@var{max_iter})]] + [/CRITERIA=CLUSTERS(@var{k}) [MXITER(@var{max_iter})] CONVERGE(@var{epsilon}) [NOINITIAL]] [/MISSING=@{EXCLUDE,INCLUDE@} @{LISTWISE, PAIRWISE@}] + [/PRINT=@{INITIAL@} @{CLUSTERS@}] @end display The @cmd{QUICK CLUSTER} command performs k-means clustering on the @@ -1629,11 +1727,29 @@ of similar values and you already know the number of clusters. The minimum specification is @samp{QUICK CLUSTER} followed by the names of the variables which contain the cluster data. Normally you will also want to specify @subcmd{/CRITERIA=CLUSTERS(@var{k})} where @var{k} is the -number of clusters. If this is not given, then @var{k} defaults to 2. +number of clusters. If this is not specified, then @var{k} defaults to 2. + +If you use @subcmd{/CRITERIA=NOINITIAL} then a naive algorithm to select +the initial clusters is used. This will provide for faster execution but +less well separated initial clusters and hence possibly an inferior final +result. -The command uses an iterative algorithm to determine the clusters for -each case. It will continue iterating until convergence, or until @var{max_iter} -iterations have been done. The default value of @var{max_iter} is 2. + +@cmd{QUICK CLUSTER} uses an iterative algorithm to select the clusters centers. +The subcommand @subcmd{/CRITERIA=MXITER(@var{max_iter})} sets the maximum number of iterations. +During classification, @pspp{} will continue iterating until until @var{max_iter} +iterations have been done or the convergence criterion (see below) is fulfilled. +The default value of @var{max_iter} is 2. + +If however, you specify @subcmd{/CRITERIA=NOUPDATE} then after selecting the initial centers, +no further update to the cluster centers is done. In this case, @var{max_iter}, if specified. +is ignored. + +The subcommand @subcmd{/CRITERIA=CONVERGE(@var{epsilon})} is used +to set the convergence criterion. The value of convergence criterion is @var{epsilon} +times the minimum distance between the @emph{initial} cluster centers. Iteration stops when +the mean cluster distance between one iteration and the next +is less than the convergence criterion. The default value of @var{epsilon} is zero. The @subcmd{MISSING} subcommand determines the handling of missing variables. If @subcmd{INCLUDE} is set, then user-missing values are considered at their face @@ -1648,6 +1764,12 @@ clustering variables contain missing values. Otherwise it is clustered on the basis of the non-missing values. The default is @subcmd{LISTWISE}. +The @subcmd{PRINT} subcommand requests additional output to be printed. +If @subcmd{INITIAL} is set, then the initial cluster memberships will +be printed. +If @subcmd{CLUSTERS} is set, the cluster memberships of the individual +cases will be displayed (potentially generating lengthy output). + @node RANK @section RANK