1 @alias prompt = sansserif
8 PSPP is a tool for the statistical analysis of sampled data.
9 You can use it to discover patterns in the data,
10 to explain differences in one subset of data in terms of another subset
12 whether certain beliefs about the data are justified.
13 This chapter does not attempt to introduce the theory behind the
15 but it shows how such analysis can be performed using PSPP.
17 For the purposes of this tutorial, it is assumed that you are using PSPP in its
18 interactive mode from the command line.
19 However, the example commands can also be typed into a file and executed in
20 a post-hoc mode by typing @samp{pspp @var{filename}} at a shell prompt,
21 where @var{filename} is the name of the file containing the commands.
22 Alternatively, from the graphical interface, you can select
23 @clicksequence{File @click{} New @click{} Syntax} to open a new syntax window
24 and use the @clicksequence{Run} menu when a syntax fragment is ready to be
26 Whichever method you choose, the syntax is identical.
28 When using the interactive method, PSPP tells you that it's waiting for your
29 data with a string like @prompt{PSPP>} or @prompt{data>}.
30 In the examples of this chapter, whenever you see text like this, it
31 indicates the prompt displayed by PSPP, @emph{not} something that you
34 Throughout this chapter reference is made to a number of sample data files.
35 So that you can try the examples for yourself,
36 you should have received these files along with your copy of PSPP.@c
37 @footnote{These files contain purely fictitious data. They should not be used
38 for research purposes.}
39 @note{Normally these files are installed in the directory
40 @file{@value{example-dir}}.
41 If however your system administrator or operating system vendor has
42 chosen to install them in a different location, you will have to adjust
43 the examples accordingly.}
47 * Preparation of Data Files::
48 * Data Screening and Transformation::
49 * Hypothesis Testing::
52 @node Preparation of Data Files
53 @section Preparation of Data Files
56 Before analysis can commence, the data must be loaded into PSPP and
57 arranged such that both PSPP and humans can understand what
59 There are two aspects of data:
62 @item The variables --- these are the parameters of a quantity
63 which has been measured or estimated in some way.
64 For example height, weight and geographic location are all variables.
65 @item The observations (also called `cases') of the variables ---
66 each observation represents an instance when the variables were measured
71 For example, a data set which has the variables @var{height}, @var{weight}, and
72 @var{name}, might have the observations:
79 The following sections explain how to define a dataset.
82 * Defining Variables::
84 * Reading data from a text file::
85 * Reading data from a pre-prepared PSPP file::
86 * Saving data to a PSPP file.::
87 * Reading data from other sources::
90 @node Defining Variables
91 @subsection Defining Variables
94 Variables come in two basic types, @i{viz}: @dfn{numeric} and @dfn{string}.
95 Variables such as age, height and satisfaction are numeric,
96 whereas name is a string variable.
97 String variables are best reserved for commentary data to assist the
99 However they can also be used for nominal or categorical data.
102 @ref{data-list} defines two variables @var{forename} and @var{height},
103 and reads data into them by manual input.
105 @float Example, data-list
108 @prompt{PSPP>} data list list /forename (A12) height.
109 @prompt{PSPP>} begin data.
110 @prompt{data>} Ahmed 188
111 @prompt{data>} Bertram 167
112 @prompt{data>} Catherine 134.231
113 @prompt{data>} David 109.1
114 @prompt{data>} end data
118 @caption{Manual entry of data using the @cmd{DATA LIST} command.
120 @var{forename} and @var{height} are defined and subsequently filled
121 with manually entered data.}
124 There are several things to note about this example.
128 The words @samp{data list list} are an example of the @cmd{DATA LIST}
129 command. @xref{DATA LIST}.
130 It tells PSPP to prepare for reading data.
131 The word @samp{list} intentionally appears twice.
132 The first occurrence is part of the @cmd{DATA LIST} call,
134 tells PSPP that the data is to be read as free format data with
138 The @samp{/} character is important. It marks the start of the list of
139 variables which you wish to define.
142 The text @samp{forename} is the name of the first variable,
143 and @samp{(A12)} says that the variable @var{forename} is a string
144 variable and that its maximum length is 12 bytes.
145 The second variable's name is specified by the text @samp{height}.
146 Since no format is given, this variable has the default format.
147 For more information on data formats, @pxref{Input and Output Formats}.
151 Normally, PSPP displays the prompt @prompt{PSPP>} whenever it's
153 However, when it's expecting data, the prompt changes to @prompt{data>}
154 so that you know to enter data and not a command.
157 At the end of every command there is a terminating @samp{.} which tells
158 PSPP that the end of a command has been encountered.
159 You should not enter @samp{.} when data is expected (@i{ie.} when
160 the @prompt{data>} prompt is current) since it is appropriate only for
161 terminating commands.
164 @node Listing the data
165 @subsection Listing the data
168 Once the data has been entered,
171 @prompt{PSPP>} list /format=numbered.
175 The optional text @samp{/format=numbered} requests the case numbers to be
176 shown along with the data.
177 It should show the following output:
180 Case# forename height
181 ----- ------------ --------
189 Note that the numeric variable @var{height} is displayed to 2 decimal
190 places, because the format for that variable is @samp{F8.2}.
191 For a complete description of the @cmd{LIST} command, @pxref{LIST}.
193 @node Reading data from a text file
194 @subsection Reading data from a text file
197 The previous example showed how to define a set of variables and to
198 manually enter the data for those variables.
199 Manual entering of data is tedious work, and often
200 a file containing the data will be have been previously
202 Let us assume that you have a file called @file{mydata.dat} containing the
215 You can can tell the @cmd{DATA LIST} command to read the data directly from
216 this file instead of by manual entry, with a command like:
218 @prompt{PSPP>} data list file='mydata.dat' list /forename (A12) height.
221 Notice however, that it is still necessary to specify the names of the
222 variables and their formats, since this information is not contained
224 It is also possible to specify the file's character encoding and other
226 For full details refer to @pxref{DATA LIST}.
228 @node Reading data from a pre-prepared PSPP file
229 @subsection Reading data from a pre-prepared PSPP file
233 When working with other PSPP users, or users of other software which
234 uses the PSPP data format, you may be given the data in
235 a pre-prepared PSPP file.
236 Such files contain not only the data, but the variable definitions,
237 along with their formats, labels and other meta-data.
238 Conventionally, these files (sometimes called ``system'' files)
239 have the suffix @file{.sav}, but that is
241 The following syntax loads a file called @file{my-file.sav}.
243 @prompt{PSPP>} get file='my-file.sav'.
246 You will encounter several instances of this in future examples.
249 @node Saving data to a PSPP file.
250 @subsection Saving data to a PSPP file.
254 If you want to save your data, along with the variable definitions so
255 that you or other PSPP users can use it later, you can do this with
256 the @cmd{SAVE} command.
258 The following syntax will save the existing data and variables to a
259 file called @file{my-new-file.sav}.
261 @prompt{PSPP>} save outfile='my-new-file.sav'.
264 If @file{my-new-file.sav} already exists, then it will be overwritten.
265 Otherwise it will be created.
268 @node Reading data from other sources
269 @subsection Reading data from other sources
270 @cindex comma separated values
274 Sometimes it's useful to be able to read data from comma
275 separated text, from spreadsheets, databases or other sources.
276 In these instances you should
277 use the @cmd{GET DATA} command (@pxref{GET DATA}).
280 @node Data Screening and Transformation
281 @section Data Screening and Transformation
284 @cindex transformation
286 Once data has been entered, it is often desirable, or even necessary,
287 to transform it in some way before performing analysis upon it.
288 At the very least, it's good practice to check for errors.
291 * Identifying incorrect data::
292 * Dealing with suspicious data::
293 * Inverting negatively coded variables::
294 * Testing data consistency::
295 * Testing for normality ::
298 @node Identifying incorrect data
299 @subsection Identifying incorrect data
300 @cindex erroneous data
301 @cindex errors, in data
303 Data from real sources is rarely error free.
304 PSPP has a number of procedures which can be used to help
305 identify data which might be incorrect.
307 The @cmd{DESCRIPTIVES} command (@pxref{DESCRIPTIVES}) is used to generate
308 simple linear statistics for a dataset. It is also useful for
309 identifying potential problems in the data.
310 The example file @file{physiology.sav} contains a number of physiological
311 measurements of a sample of healthy adults selected at random.
312 However, the data entry clerk made a number of mistakes when entering
314 @ref{descriptives} illustrates the use of @cmd{DESCRIPTIVES} to screen this
315 data and identify the erroneous values.
317 @float Example, descriptives
320 @prompt{PSPP>} get file='@value{example-dir}/physiology.sav'.
321 @prompt{PSPP>} descriptives sex, weight, height.
326 DESCRIPTIVES. Valid cases = 40; cases with missing value(s) = 0.
327 +--------#--+-------+-------+-------+-------+
328 |Variable# N| Mean |Std Dev|Minimum|Maximum|
329 #========#==#=======#=======#=======#=======#
330 |sex #40| .45| .50| .00| 1.00|
331 |height #40|1677.12| 262.87| 179.00|1903.00|
332 |weight #40| 72.12| 26.70| -55.60| 92.07|
333 +--------#--+-------+-------+-------+-------+
336 @caption{Using the @cmd{DESCRIPTIVES} command to display simple
337 summary information about the data.
338 In this case, the results show unexpectedly low values in the Minimum
339 column, suggesting incorrect data entry.}
342 In the output of @ref{descriptives},
343 the most interesting column is the minimum value.
344 The @var{weight} variable has a minimum value of less than zero,
345 which is clearly erroneous.
346 Similarly, the @var{height} variable's minimum value seems to be very low.
347 In fact, it is more than 5 standard deviations from the mean, and is a
348 seemingly bizarre height for an adult person.
349 We can examine the data in more detail with the @cmd{EXAMINE}
350 command (@pxref{EXAMINE}):
352 In @ref{examine} you can see that the lowest value of @var{height} is
353 179 (which we suspect to be erroneous), but the second lowest is 1598
355 we know from the @cmd{DESCRIPTIVES} command
356 is within 1 standard deviation from the mean.
357 Similarly the @var{weight} variable has a lowest value which is
358 negative but a plausible value for the second lowest value.
359 This suggests that the two extreme values are outliers and probably
360 represent data entry errors.
362 @float Example, examine
364 [@dots{} continue from @ref{descriptives}]
366 @prompt{PSPP>} examine height, weight /statistics=extreme(3).
371 #===============================#===========#=======#
372 # #Case Number| Value #
373 #===============================#===========#=======#
374 #Height in millimetres Highest 1# 14|1903.00#
377 # ----------#-----------+-------#
378 # Lowest 1# 30| 179.00#
381 # ----------#-----------+-------#
382 #Weight in kilograms Highest 1# 13| 92.07#
385 # ----------#-----------+-------#
386 # Lowest 1# 38| -55.60#
389 #===============================#===========#=======#
392 @caption{Using the @cmd{EXAMINE} command to see the extremities of the data
393 for different variables. Cases 30 and 38 seem to contain values
394 very much lower than the rest of the data.
395 They are possibly erroneous.}
398 @node Dealing with suspicious data
399 @subsection Dealing with suspicious data
402 @cindex recoding data
403 If possible, suspect data should be checked and re-measured.
404 However, this may not always be feasible, in which case the researcher may
405 decide to disregard these values.
406 PSPP has a feature whereby data can assume the special value `SYSMIS', and
407 will be disregarded in future analysis. @xref{Missing Observations}.
408 You can set the two suspect values to the `SYSMIS' value using the @cmd{RECODE}
411 PSPP> recode height (179 = SYSMIS).
412 PSPP> recode weight (LOWEST THRU 0 = SYSMIS).
415 The first command says that for any observation which has a
416 @var{height} value of 179, that value should be changed to the SYSMIS
418 The second command says that any @var{weight} values of zero or less
419 should be changed to SYSMIS.
420 From now on, they will be ignored in analysis.
421 For detailed information about the @cmd{RECODE} command @pxref{RECODE}.
423 If you now re-run the @cmd{DESCRIPTIVES} or @cmd{EXAMINE} commands in
424 @ref{descriptives} and @ref{examine} you
425 will see a data summary with more plausible parameters.
426 You will also notice that the data summaries indicate the two missing values.
428 @node Inverting negatively coded variables
429 @subsection Inverting negatively coded variables
432 @cindex Inverting data
433 Data entry errors are not the only reason for wanting to recode data.
434 The sample file @file{hotel.sav} comprises data gathered from a
435 customer satisfaction survey of clients at a particular hotel.
436 In @ref{reliability}, this file is loaded for analysis.
437 The line @code{display dictionary.} tells PSPP to display the
438 variables and associated data.
439 The output from this command has been omitted from the example for the sake of clarity, but
440 you will notice that each of the variables
441 @var{v1}, @var{v2} @dots{} @var{v5} are measured on a 5 point Likert scale,
442 with 1 meaning ``Strongly disagree'' and 5 meaning ``Strongly agree''.
443 Whilst variables @var{v1}, @var{v2} and @var{v4} record responses
444 to a positively posed question, variables @var{v3} and @var{v5} are
445 responses to negatively worded questions.
446 In order to perform meaningful analysis, we need to recode the variables so
447 that they all measure in the same direction.
448 We could use the @cmd{RECODE} command, with syntax such as:
450 recode v3 (1 = 5) (2 = 4) (4 = 2) (5 = 1).
453 However an easier and more elegant way uses the @cmd{COMPUTE}
454 command (@pxref{COMPUTE}).
455 Since the variables are Likert variables in the range (1 @dots{} 5),
456 subtracting their value from 6 has the effect of inverting them:
458 compute @var{var} = 6 - @var{var}.
461 @ref{reliability} uses this technique to recode the variables
462 @var{v3} and @var{v5}.
463 After applying @cmd{COMPUTE} for both variables,
464 all subsequent commands will use the inverted values.
467 @node Testing data consistency
468 @subsection Testing data consistency
473 A sensible check to perform on survey data is the calculation of
475 This gives the statistician some confidence that the questionnaires have been
476 completed thoughtfully.
477 If you examine the labels of variables @var{v1}, @var{v3} and @var{v5},
478 you will notice that they ask very similar questions.
479 One would therefore expect the values of these variables (after recoding)
480 to closely follow one another, and we can test that with the @cmd{RELIABILITY}
481 command (@pxref{RELIABILITY}).
482 @ref{reliability} shows a PSPP session where the user (after recoding
483 negatively scaled variables) requests reliability statistics for
484 @var{v1}, @var{v3} and @var{v5}.
486 @float Example, reliability
489 @prompt{PSPP>} get file='@value{example-dir}/hotel.sav'.
490 @prompt{PSPP>} display dictionary.
491 @prompt{PSPP>} * recode negatively worded questions.
492 @prompt{PSPP>} compute v3 = 6 - v3.
493 @prompt{PSPP>} compute v5 = 6 - v5.
494 @prompt{PSPP>} reliability v1, v3, v5.
497 Output (dictionary information omitted for clarity):
499 1.1 RELIABILITY. Case Processing Summary
500 #==============#==#======#
502 #==============#==#======#
503 #Cases Valid #17|100.00#
506 #==============#==#======#
508 1.2 RELIABILITY. Reliability Statistics
509 #================#==========#
510 #Cronbach's Alpha#N of Items#
511 #================#==========#
513 #================#==========#
516 @caption{Recoding negatively scaled variables, and testing for
517 reliability with the @cmd{RELIABILITY} command. The Cronbach Alpha
518 coefficient suggests a high degree of reliability among variables
519 @var{v1}, @var{v2} and @var{v5}.}
522 As a rule of thumb, many statisticians consider a value of Cronbach's Alpha of
523 0.7 or higher to indicate reliable data.
524 Here, the value is 0.86 so the data and the recoding that we performed
528 @node Testing for normality
529 @subsection Testing for normality
530 @cindex normality, testing
532 Many statistical tests rely upon certain properties of the data.
533 One common property, upon which many linear tests depend, is that of
534 normality --- the data must have been drawn from a normal distribution.
535 It is necessary then to ensure normality before deciding upon the
536 test procedure to use. One way to do this uses the @cmd{EXAMINE} command.
538 In @ref{normality}, a researcher was examining the failure rates
539 of equipment produced by an engineering company.
540 The file @file{repairs.sav} contains the mean time between
541 failures (@var{mtbf}) of some items of equipment subject to the study.
542 Before performing linear analysis on the data,
543 the researcher wanted to ascertain that the data is normally distributed.
545 A normal distribution has a skewness and kurtosis of zero.
546 Looking at the skewness of @var{mtbf} in @ref{normality} it is clear
547 that the mtbf figures have a lot of positive skew and are therefore
548 not drawn from a normally distributed variable.
549 Positive skew can often be compensated for by applying a logarithmic
551 This is done with the @cmd{COMPUTE} command in the line
553 compute mtbf_ln = ln (mtbf).
556 Rather than redefining the existing variable, this use of @cmd{COMPUTE}
557 defines a new variable @var{mtbf_ln} which is
558 the natural logarithm of @var{mtbf}.
559 The final command in this example calls @cmd{EXAMINE} on this new variable,
560 and it can be seen from the results that both the skewness and
561 kurtosis for @var{mtbf_ln} are very close to zero.
562 This provides some confidence that the @var{mtbf_ln} variable is
563 normally distributed and thus safe for linear analysis.
564 In the event that no suitable transformation can be found,
565 then it would be worth considering
566 an appropriate non-parametric test instead of a linear one.
567 @xref{NPAR TESTS}, for information about non-parametric tests.
569 @float Example, normality
572 @prompt{PSPP>} get file='@value{example-dir}/repairs.sav'.
573 @prompt{PSPP>} examine mtbf
574 /statistics=descriptives.
575 @prompt{PSPP>} compute mtbf_ln = ln (mtbf).
576 @prompt{PSPP>} examine mtbf_ln
577 /statistics=descriptives.
582 1.2 EXAMINE. Descriptives
583 #====================================================#=========#==========#
584 # #Statistic|Std. Error#
585 #====================================================#=========#==========#
586 #mtbf Mean # 8.32 | 1.62 #
587 # 95% Confidence Interval for Mean Lower Bound# 4.85 | #
588 # Upper Bound# 11.79 | #
589 # 5% Trimmed Mean # 7.69 | #
591 # Variance # 39.21 | #
592 # Std. Deviation # 6.26 | #
594 # Maximum # 26.47 | #
596 # Interquartile Range # 5.83 | #
597 # Skewness # 1.85 | .58 #
598 # Kurtosis # 4.49 | 1.12 #
599 #====================================================#=========#==========#
601 2.2 EXAMINE. Descriptives
602 #====================================================#=========#==========#
603 # #Statistic|Std. Error#
604 #====================================================#=========#==========#
605 #mtbf_ln Mean # 1.88 | .19 #
606 # 95% Confidence Interval for Mean Lower Bound# 1.47 | #
607 # Upper Bound# 2.29 | #
608 # 5% Trimmed Mean # 1.88 | #
611 # Std. Deviation # .74 | #
615 # Interquartile Range # .92 | #
616 # Skewness # -.16 | .58 #
617 # Kurtosis # -.09 | 1.12 #
618 #====================================================#=========#==========#
621 @caption{Testing for normality using the @cmd{EXAMINE} command and applying
622 a logarithmic transformation.
623 The @var{mtbf} variable has a large positive skew and is therefore
624 unsuitable for linear statistical analysis.
625 However the transformed variable (@var{mtbf_ln}) is close to normal and
626 would appear to be more suitable.}
630 @node Hypothesis Testing
631 @section Hypothesis Testing
633 @cindex Hypothesis testing
635 @cindex null hypothesis
637 One of the most fundamental purposes of statistical analysis
638 is hypothesis testing.
639 Researchers commonly need to test hypotheses about a set of data.
640 For example, she might want to test whether one set of data comes from
641 the same distribution as another,
643 whether the mean of a dataset significantly differs from a particular
645 This section presents just some of the possible tests that PSPP offers.
647 The researcher starts by making a @dfn{null hypothesis}.
648 Often this is a hypothesis which he suspects to be false.
649 For example, if he suspects that @var{A} is greater than @var{B} he will
650 state the null hypothesis as @math{ @var{A} = @var{B}}.@c
651 @footnote{This example assumes that it is already proven that @var{B} is
652 not greater than @var{A}.}
654 The @dfn{p-value} is a recurring concept in hypothesis testing.
655 It is the highest acceptable probability that the evidence implying a
656 null hypothesis is false, could have been obtained when the null
657 hypothesis is in fact true.
658 Note that this is not the same as ``the probability of making an
659 error'' nor is it the same as ``the probability of rejecting a
660 hypothesis when it is true''.
665 * Testing for differences of means::
666 * Linear Regression::
669 @node Testing for differences of means
670 @subsection Testing for differences of means
675 A common statistical test involves hypotheses about means.
676 The @cmd{T-TEST} command is used to find out whether or not two separate
677 subsets have the same mean.
679 @ref{t-test} uses the file @file{physiology.sav} previously
681 A researcher suspected that the heights and core body
682 temperature of persons might be different depending upon their sex.
683 To investigate this, he posed two null hypotheses:
685 @item The mean heights of males and females in the population are equal.
686 @item The mean body temperature of males and
687 females in the population are equal.
690 For the purposes of the investigation the researcher
691 decided to use a p-value of 0.05.
693 In addition to the T-test, the @cmd{T-TEST} command also performs the
694 Levene test for equal variances.
695 If the variances are equal, then a more powerful form of the T-test can be used.
696 However if it is unsafe to assume equal variances,
697 then an alternative calculation is necessary.
698 PSPP performs both calculations.
700 For the @var{height} variable, the output shows the significance of the
701 Levene test to be 0.33 which means there is a
702 33% probability that the
703 Levene test produces this outcome when the variances are unequal.
704 Such a probability is too high
705 to assume that the variances are equal so the row
706 for unequal variances should be used.
707 Examining this row, the two tailed significance for the @var{height} t-test
708 is less than 0.05, so it is safe to reject the null hypothesis and conclude
709 that the mean heights of males and females are unequal.
711 For the @var{temperature} variable, the significance of the Levene test
712 is 0.58 so again, it is unsafe to use the row for equal variances.
713 The unequal variances row indicates that the two tailed significance for
714 @var{temperature} is 0.19. Since this is greater than 0.05 we must reject
715 the null hypothesis and conclude that there is insufficient evidence to
716 suggest that the body temperature of male and female persons are different.
718 @float Example, t-test
721 @prompt{PSPP>} get file='@value{example-dir}/physiology.sav'.
722 @prompt{PSPP>} recode height (179 = SYSMIS).
723 @prompt{PSPP>} t-test group=sex(0,1) /variables = height temperature.
727 1.1 T-TEST. Group Statistics
728 #==================#==#=======#==============#========#
729 # sex | N| Mean |Std. Deviation|SE. Mean#
730 #==================#==#=======#==============#========#
731 #height Male |22|1796.49| 49.71| 10.60#
732 # Female|17|1610.77| 25.43| 6.17#
733 #temperature Male |22| 36.68| 1.95| .42#
734 # Female|18| 37.43| 1.61| .38#
735 #==================#==#=======#==============#========#
736 1.2 T-TEST. Independent Samples Test
737 #===========================#=========#=============================== =#
738 # # Levene's| t-test for Equality of Means #
739 # #----+----+------+-----+------+---------+- -#
741 # # | | | |Sig. 2| | #
742 # # F |Sig.| t | df |tailed|Mean Diff| #
743 #===========================#====#====#======#=====#======#=========#= =#
744 #height Equal variances# .97| .33| 14.02|37.00| .00| 185.72| ... #
745 # Unequal variances# | | 15.15|32.71| .00| 185.72| ... #
746 #temperature Equal variances# .31| .58| -1.31|38.00| .20| -.75| ... #
747 # Unequal variances# | | -1.33|37.99| .19| -.75| ... #
748 #===========================#====#====#======#=====#======#=========#= =#
751 @caption{The @cmd{T-TEST} command tests for differences of means.
752 Here, the @var{height} variable's two tailed significance is less than
753 0.05, so the null hypothesis can be rejected.
754 Thus, the evidence suggests there is a difference between the heights of
755 male and female persons.
756 However the significance of the test for the @var{temperature}
757 variable is greater than 0.05 so the null hypothesis cannot be
758 rejected, and there is insufficient evidence to suggest a difference
759 in body temperature.}
762 @node Linear Regression
763 @subsection Linear Regression
764 @cindex linear regression
767 Linear regression is a technique used to investigate if and how a variable
768 is linearly related to others.
769 If a variable is found to be linearly related, then this can be used to
770 predict future values of that variable.
772 In example @ref{regression}, the service department of the company wanted to
773 be able to predict the time to repair equipment, in order to improve
774 the accuracy of their quotations.
775 It was suggested that the time to repair might be related to the time
776 between failures and the duty cycle of the equipment.
777 The p-value of 0.1 was chosen for this investigation.
778 In order to investigate this hypothesis, the @cmd{REGRESSION} command
780 This command not only tests if the variables are related, but also
781 identifies the potential linear relationship. @xref{REGRESSION}.
784 @float Example, regression
787 @prompt{PSPP>} get file='@value{example-dir}/repairs.sav'.
788 @prompt{PSPP>} regression /variables = mtbf duty_cycle /dependent = mttr.
789 @prompt{PSPP>} regression /variables = mtbf /dependent = mttr.
793 1.3(1) REGRESSION. Coefficients
794 #=============================================#====#==========#====#=====#
795 # # B |Std. Error|Beta| t #
796 #========#====================================#====#==========#====#=====#
797 # |(Constant) #9.81| 1.50| .00| 6.54#
798 # |Mean time between failures (months) #3.10| .10| .99|32.43#
799 # |Ratio of working to non-working time#1.09| 1.78| .02| .61#
801 #========#====================================#====#==========#====#=====#
803 1.3(2) REGRESSION. Coefficients
804 #=============================================#============#
806 #========#====================================#============#
808 # |Mean time between failures (months) # .00#
809 # |Ratio of working to non-working time# .55#
811 #========#====================================#============#
812 2.3(1) REGRESSION. Coefficients
813 #============================================#=====#==========#====#=====#
814 # # B |Std. Error|Beta| t #
815 #========#===================================#=====#==========#====#=====#
816 # |(Constant) #10.50| .96| .00|10.96#
817 # |Mean time between failures (months)# 3.11| .09| .99|33.39#
819 #========#===================================#=====#==========#====#=====#
821 2.3(2) REGRESSION. Coefficients
822 #============================================#============#
824 #========#===================================#============#
826 # |Mean time between failures (months)# .00#
828 #========#===================================#============#
831 @caption{Linear regression analysis to find a predictor for
833 The first attempt, including @var{duty_cycle}, produces some
834 unacceptable high significance values.
835 However the second attempt, which excludes @var{duty_cycle}, produces
836 significance values no higher than 0.06.
837 This suggests that @var{mtbf} alone may be a suitable predictor
841 The coefficients in the first table suggest that the formula
842 @math{@var{mttr} = 9.81 + 3.1 \times @var{mtbf} + 1.09 \times @var{duty_cycle}}
843 can be used to predict the time to repair.
844 However, the significance value for the @var{duty_cycle} coefficient
845 is very high, which would make this an unsafe predictor.
846 For this reason, the test was repeated, but omitting the
847 @var{duty_cycle} variable.
848 This time, the significance of all coefficients no higher than 0.06,
849 suggesting that at the 0.06 level, the formula
850 @math{@var{mttr} = 10.5 + 3.11 \times @var{mtbf}} is a reliable
851 predictor of the time to repair.
854 @c LocalWords: PSPP dir itemize noindent var cindex dfn cartouche samp xref
855 @c LocalWords: pxref ie sav Std Dev kilograms SYSMIS sansserif pre pspp emph
856 @c LocalWords: Likert Cronbach's Cronbach mtbf npplot ln myfile cmd NPAR Sig
857 @c LocalWords: vindex Levene Levene's df Diff clicksequence mydata dat ascii
858 @c LocalWords: mttr outfile