+@c PSPP - a program for statistical analysis.
+@c Copyright (C) 2017, 2020 Free Software Foundation, Inc.
+@c Permission is granted to copy, distribute and/or modify this document
+@c under the terms of the GNU Free Documentation License, Version 1.3
+@c or any later version published by the Free Software Foundation;
+@c with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.
+@c A copy of the license is included in the section entitled "GNU
+@c Free Documentation License".
+@c
@alias prompt = sansserif
@include tut.texi
to explain differences in one subset of data in terms of another subset
and to find out
whether certain beliefs about the data are justified.
-This chapter does not attempt to introduce the theory behind the
+This chapter does not attempt to introduce the theory behind the
statistical analysis,
but it shows how such analysis can be performed using @pspp{}.
-For the purposes of this tutorial, it is assumed that you are using @pspp{} in its
+For the purposes of this tutorial, it is assumed that you are using @pspp{} in its
interactive mode from the command line.
-However, the example commands can also be typed into a file and executed in
-a post-hoc mode by typing @samp{pspp @var{filename}} at a shell prompt,
-where @var{filename} is the name of the file containing the commands.
+However, the example commands can also be typed into a file and executed in
+a post-hoc mode by typing @samp{pspp @var{file-name}} at a shell prompt,
+where @var{file-name} is the name of the file containing the commands.
Alternatively, from the graphical interface, you can select
@clicksequence{File @click{} New @click{} Syntax} to open a new syntax window
-and use the @clicksequence{Run} menu when a syntax fragment is ready to be
+and use the @clicksequence{Run} menu when a syntax fragment is ready to be
executed.
Whichever method you choose, the syntax is identical.
When using the interactive method, @pspp{} tells you that it's waiting for your
data with a string like @prompt{PSPP>} or @prompt{data>}.
In the examples of this chapter, whenever you see text like this, it
-indicates the prompt displayed by @pspp{}, @emph{not} something that you
+indicates the prompt displayed by @pspp{}, @emph{not} something that you
should type.
Throughout this chapter reference is made to a number of sample data files.
@menu
-* Preparation of Data Files::
-* Data Screening and Transformation::
-* Hypothesis Testing::
+* Preparation of Data Files::
+* Data Screening and Transformation::
+* Hypothesis Testing::
@end menu
@node Preparation of Data Files
For example height, weight and geographic location are all variables.
@item The observations (also called `cases') of the variables ---
each observation represents an instance when the variables were measured
- or observed.
+ or observed.
@end itemize
@noindent
-For example, a data set which has the variables @var{height}, @var{weight}, and
-@var{name}, might have the observations:
+For example, a data set which has the variables @exvar{height}, @exvar{weight}, and
+@exvar{name}, might have the observations:
@example
1881 89.2 Ahmed
1192 107.01 Frank
The following sections explain how to define a dataset.
@menu
-* Defining Variables::
-* Listing the data::
-* Reading data from a text file::
-* Reading data from a pre-prepared PSPP file::
-* Saving data to a PSPP file.::
-* Reading data from other sources::
+* Defining Variables::
+* Listing the data::
+* Reading data from a text file::
+* Reading data from a pre-prepared PSPP file::
+* Saving data to a PSPP file.::
+* Reading data from other sources::
+* Exiting PSPP::
@end menu
@node Defining Variables
Variables come in two basic types, @i{viz}: @dfn{numeric} and @dfn{string}.
Variables such as age, height and satisfaction are numeric,
whereas name is a string variable.
-String variables are best reserved for commentary data to assist the
+String variables are best reserved for commentary data to assist the
human observer.
However they can also be used for nominal or categorical data.
+The following example defines two variables @exvar{forename} and @exvar{height},
+and reads data into them by manual input:
-@ref{data-list} defines two variables @var{forename} and @var{height},
-and reads data into them by manual input.
-
-@float Example, data-list
-@cartouche
@example
@prompt{PSPP>} data list list /forename (A12) height.
@prompt{PSPP>} begin data.
@prompt{data>} end data
@prompt{PSPP>}
@end example
-@end cartouche
-@caption{Manual entry of data using the @cmd{DATA LIST} command.
-Two variables
-@var{forename} and @var{height} are defined and subsequently filled
-with manually entered data.}
-@end float
There are several things to note about this example.
@item
The text @samp{forename} is the name of the first variable,
-and @samp{(A12)} says that the variable @var{forename} is a string
+and @samp{(A12)} says that the variable @exvar{forename} is a string
variable and that its maximum length is 12 bytes.
The second variable's name is specified by the text @samp{height}.
Since no format is given, this variable has the default format.
locales which use a period (@samp{.}) as the decimal separator.
However if you are using a system with a locale which uses the comma (@samp{,})
as the decimal separator, then you should in the subsequent lines substitute
-@samp{.} with @samp{,}.
-Alternatively, you could explicitly tell @pspp{} that the @var{height}
+@samp{.} with @samp{,}.
+Alternatively, you could explicitly tell @pspp{} that the @exvar{height}
variable is to be read using a period as its decimal separator by appending the
text @samp{DOT8.3} after the word @samp{height}.
For more information on data formats, @pxref{Input and Output Formats}.
@item
At the end of every command there is a terminating @samp{.} which tells
@pspp{} that the end of a command has been encountered.
-You should not enter @samp{.} when data is expected (@i{ie.} when
+You should not enter @samp{.} when data is expected (@i{ie.} when
the @prompt{data>} prompt is current) since it is appropriate only for
terminating commands.
@end itemize
@end example
@noindent
to list the data.
-The optional text @samp{/format=numbered} requests the case numbers to be
+The optional text @samp{/format=numbered} requests the case numbers to be
shown along with the data.
It should show the following output:
-@example
-@group
-Case# forename height
------ ------------ --------
- 1 Ahmed 188.00
- 2 Bertram 167.00
- 3 Catherine 134.23
- 4 David 109.10
-@end group
-@end example
+@psppoutput {tutorial1}
@noindent
-Note that the numeric variable @var{height} is displayed to 2 decimal
+Note that the numeric variable @exvar{height} is displayed to 2 decimal
places, because the format for that variable is @samp{F8.2}.
For a complete description of the @cmd{LIST} command, @pxref{LIST}.
@subsection Reading data from a text file
@cindex reading data
-The previous example showed how to define a set of variables and to
+The previous example showed how to define a set of variables and to
manually enter the data for those variables.
Manual entering of data is tedious work, and often
-a file containing the data will be have been previously
+a file containing the data will be have been previously
prepared.
Let us assume that you have a file called @file{mydata.dat} containing the
ascii encoded data:
@example
-Ahmed 188.00
-Bertram 167.00
-Catherine 134.23
-David 109.10
+Ahmed 188.00
+Bertram 167.00
+Catherine 134.23
+David 109.10
@ .
@ .
@ .
Notice however, that it is still necessary to specify the names of the
variables and their formats, since this information is not contained
in the file.
-It is also possible to specify the file's character encoding and other
+It is also possible to specify the file's character encoding and other
parameters.
For full details refer to @pxref{DATA LIST}.
a pre-prepared @pspp{} file.
Such files contain not only the data, but the variable definitions,
along with their formats, labels and other meta-data.
-Conventionally, these files (sometimes called ``system'' files)
+Conventionally, these files (sometimes called ``system'' files)
have the suffix @file{.sav}, but that is
not mandatory.
The following syntax loads a file called @file{my-file.sav}.
@cindex spreadsheets
@cindex databases
-Sometimes it's useful to be able to read data from comma
+Sometimes it's useful to be able to read data from comma
separated text, from spreadsheets, databases or other sources.
In these instances you should
use the @cmd{GET DATA} command (@pxref{GET DATA}).
-
+@node Exiting PSPP
+@subsection Exiting PSPP
+
+Use the @cmd{FINISH} command to exit PSPP:
+@example
+@prompt{PSPP>} finish.
+@end example
+
@node Data Screening and Transformation
@section Data Screening and Transformation
At the very least, it's good practice to check for errors.
@menu
-* Identifying incorrect data::
-* Dealing with suspicious data::
-* Inverting negatively coded variables::
-* Testing data consistency::
-* Testing for normality ::
+* Identifying incorrect data::
+* Dealing with suspicious data::
+* Inverting negatively coded variables::
+* Testing data consistency::
+* Testing for normality ::
@end menu
@node Identifying incorrect data
@cindex errors, in data
Data from real sources is rarely error free.
-@pspp{} has a number of procedures which can be used to help
+@pspp{} has a number of procedures which can be used to help
identify data which might be incorrect.
The @cmd{DESCRIPTIVES} command (@pxref{DESCRIPTIVES}) is used to generate
measurements of a sample of healthy adults selected at random.
However, the data entry clerk made a number of mistakes when entering
the data.
-@ref{descriptives} illustrates the use of @cmd{DESCRIPTIVES} to screen this
-data and identify the erroneous values.
+The following example illustrates the use of @cmd{DESCRIPTIVES} to screen this
+data and identify the erroneous values:
-@float Example, descriptives
-@cartouche
@example
@prompt{PSPP>} get file='@value{example-dir}/physiology.sav'.
@prompt{PSPP>} descriptives sex, weight, height.
@end example
-Output:
-@example
-DESCRIPTIVES. Valid cases = 40; cases with missing value(s) = 0.
-+--------#--+-------+-------+-------+-------+
-|Variable# N| Mean |Std Dev|Minimum|Maximum|
-#========#==#=======#=======#=======#=======#
-|sex #40| .45| .50| .00| 1.00|
-|height #40|1677.12| 262.87| 179.00|1903.00|
-|weight #40| 72.12| 26.70| -55.60| 92.07|
-+--------#--+-------+-------+-------+-------+
-@end example
-@end cartouche
-@caption{Using the @cmd{DESCRIPTIVES} command to display simple
-summary information about the data.
-In this case, the results show unexpectedly low values in the Minimum
-column, suggesting incorrect data entry.}
-@end float
-
-In the output of @ref{descriptives},
-the most interesting column is the minimum value.
-The @var{weight} variable has a minimum value of less than zero,
+@noindent For this example, PSPP produces the following output:
+@psppoutput {tutorial2a}
+
+The most interesting column in the output is the minimum value.
+The @exvar{weight} variable has a minimum value of less than zero,
which is clearly erroneous.
-Similarly, the @var{height} variable's minimum value seems to be very low.
-In fact, it is more than 5 standard deviations from the mean, and is a
+Similarly, the @exvar{height} variable's minimum value seems to be very low.
+In fact, it is more than 5 standard deviations from the mean, and is a
seemingly bizarre height for an adult person.
-We can examine the data in more detail with the @cmd{EXAMINE}
-command (@pxref{EXAMINE}):
-In @ref{examine} you can see that the lowest value of @var{height} is
+We can look deeper into these discrepancies by issuing an additional
+@cmd{EXAMINE} command:
+
+@example
+@prompt{PSPP>} examine height, weight /statistics=extreme(3).
+@end example
+
+@noindent This command produces the following additional output (in part):
+@psppoutput {tutorial2b}
+
+@noindent
+From this new output, you can see that the lowest value of @exvar{height} is
179 (which we suspect to be erroneous), but the second lowest is 1598
which
-we know from the @cmd{DESCRIPTIVES} command
+we know from @cmd{DESCRIPTIVES}
is within 1 standard deviation from the mean.
-Similarly the @var{weight} variable has a lowest value which is
-negative but a plausible value for the second lowest value.
-This suggests that the two extreme values are outliers and probably
-represent data entry errors.
-
-@float Example, examine
-@cartouche
-[@dots{} continue from @ref{descriptives}]
-@example
-@prompt{PSPP>} examine height, weight /statistics=extreme(3).
-@end example
+Similarly, the lowest value of @exvar{weight} is
+negative, but its second lowest value is plausible.
+This suggests that the two extreme values are outliers and probably
+represent data entry errors.
-Output:
-@example
-#===============================#===========#=======#
-# #Case Number| Value #
-#===============================#===========#=======#
-#Height in millimetres Highest 1# 14|1903.00#
-# 2# 15|1884.00#
-# 3# 12|1801.65#
-# ----------#-----------+-------#
-# Lowest 1# 30| 179.00#
-# 2# 31|1598.00#
-# 3# 28|1601.00#
-# ----------#-----------+-------#
-#Weight in kilograms Highest 1# 13| 92.07#
-# 2# 5| 92.07#
-# 3# 17| 91.74#
-# ----------#-----------+-------#
-# Lowest 1# 38| -55.60#
-# 2# 39| 54.48#
-# 3# 33| 55.45#
-#===============================#===========#=======#
-@end example
-@end cartouche
-@caption{Using the @cmd{EXAMINE} command to see the extremities of the data
-for different variables. Cases 30 and 38 seem to contain values
-very much lower than the rest of the data.
-They are possibly erroneous.}
-@end float
+The output also identifies the case numbers for each extreme value,
+so we can see that
+cases 30 and 38 are the ones with the erroneous values.
@node Dealing with suspicious data
@subsection Dealing with suspicious data
@end example
@noindent
The first command says that for any observation which has a
-@var{height} value of 179, that value should be changed to the SYSMIS
+@exvar{height} value of 179, that value should be changed to the SYSMIS
value.
-The second command says that any @var{weight} values of zero or less
+The second command says that any @exvar{weight} values of zero or less
should be changed to SYSMIS.
From now on, they will be ignored in analysis.
For detailed information about the @cmd{RECODE} command @pxref{RECODE}.
-If you now re-run the @cmd{DESCRIPTIVES} or @cmd{EXAMINE} commands in
-@ref{descriptives} and @ref{examine} you
-will see a data summary with more plausible parameters.
+If you now re-run the @cmd{DESCRIPTIVES} or @cmd{EXAMINE} commands from
+the previous section,
+you will see a data summary with more plausible parameters.
You will also notice that the data summaries indicate the two missing values.
@node Inverting negatively coded variables
@cindex Likert scale
@cindex Inverting data
Data entry errors are not the only reason for wanting to recode data.
-The sample file @file{hotel.sav} comprises data gathered from a
+The sample file @file{hotel.sav} comprises data gathered from a
customer satisfaction survey of clients at a particular hotel.
-In @ref{reliability}, this file is loaded for analysis.
-The line @code{display dictionary.} tells @pspp{} to display the
-variables and associated data.
-The output from this command has been omitted from the example for the sake of clarity, but
-you will notice that each of the variables
-@var{v1}, @var{v2} @dots{} @var{v5} are measured on a 5 point Likert scale,
+The following commands load the file and display its
+variables and associated data:
+
+@example
+@prompt{PSPP>} get file='@value{example-dir}/hotel.sav'.
+@prompt{PSPP>} display dictionary.
+@end example
+
+@noindent It yields the following output:
+
+@psppoutput {tutorial3}
+
+The output shows that all of the variables @exvar{v1} through @exvar{v5} are measured on a 5 point Likert scale,
with 1 meaning ``Strongly disagree'' and 5 meaning ``Strongly agree''.
-Whilst variables @var{v1}, @var{v2} and @var{v4} record responses
-to a positively posed question, variables @var{v3} and @var{v5} are
-responses to negatively worded questions.
-In order to perform meaningful analysis, we need to recode the variables so
+However, some of the questions are positively worded (@exvar{v1}, @exvar{v2}, @exvar{v4}) and others are negatively worded (@exvar{v3}, @exvar{v5}).
+To perform meaningful analysis, we need to recode the variables so
that they all measure in the same direction.
We could use the @cmd{RECODE} command, with syntax such as:
@example
compute @var{var} = 6 - @var{var}.
@end example
@noindent
-@ref{reliability} uses this technique to recode the variables
-@var{v3} and @var{v5}.
+The following section uses this technique to recode the variables
+@exvar{v3} and @exvar{v5}.
After applying @cmd{COMPUTE} for both variables,
all subsequent commands will use the inverted values.
A sensible check to perform on survey data is the calculation of
reliability.
-This gives the statistician some confidence that the questionnaires have been
+This gives the statistician some confidence that the questionnaires have been
completed thoughtfully.
-If you examine the labels of variables @var{v1}, @var{v3} and @var{v5},
+If you examine the labels of variables @exvar{v1}, @exvar{v3} and @exvar{v4},
you will notice that they ask very similar questions.
-One would therefore expect the values of these variables (after recoding)
-to closely follow one another, and we can test that with the @cmd{RELIABILITY}
+One would therefore expect the values of these variables (after recoding)
+to closely follow one another, and we can test that with the @cmd{RELIABILITY}
command (@pxref{RELIABILITY}).
-@ref{reliability} shows a @pspp{} session where the user (after recoding
-negatively scaled variables) requests reliability statistics for
-@var{v1}, @var{v3} and @var{v5}.
+The following example shows a @pspp{} session where the user recodes
+negatively scaled variables and then requests reliability statistics for
+@exvar{v1}, @exvar{v3}, and @exvar{v4}.
-@float Example, reliability
-@cartouche
@example
@prompt{PSPP>} get file='@value{example-dir}/hotel.sav'.
-@prompt{PSPP>} display dictionary.
-@prompt{PSPP>} * recode negatively worded questions.
@prompt{PSPP>} compute v3 = 6 - v3.
@prompt{PSPP>} compute v5 = 6 - v5.
-@prompt{PSPP>} reliability v1, v3, v5.
+@prompt{PSPP>} reliability v1, v3, v4.
@end example
-Output (dictionary information omitted for clarity):
-@example
-1.1 RELIABILITY. Case Processing Summary
-#==============#==#======#
-# # N| % #
-#==============#==#======#
-#Cases Valid #17|100.00#
-# Excluded# 0| .00#
-# Total #17|100.00#
-#==============#==#======#
-
-1.2 RELIABILITY. Reliability Statistics
-#================#==========#
-#Cronbach's Alpha#N of Items#
-#================#==========#
-# .86# 3#
-#================#==========#
-@end example
-@end cartouche
-@caption{Recoding negatively scaled variables, and testing for
-reliability with the @cmd{RELIABILITY} command. The Cronbach Alpha
-coefficient suggests a high degree of reliability among variables
-@var{v1}, @var{v2} and @var{v5}.}
-@end float
-
-As a rule of thumb, many statisticians consider a value of Cronbach's Alpha of
+@noindent This yields the following output:
+@psppoutput {tutorial4}
+
+As a rule of thumb, many statisticians consider a value of Cronbach's Alpha of
0.7 or higher to indicate reliable data.
-Here, the value is 0.86 so the data and the recoding that we performed
-are vindicated.
+
+Here, the value is 0.81, which suggests a high degree of reliability
+among variables @exvar{v1}, @exvar{v3} and @exvar{v4}, so the data and
+the recoding that we performed are vindicated.
-@node Testing for normality
+@node Testing for normality
@subsection Testing for normality
-@cindex normality, testing
+@cindex normality, testing
Many statistical tests rely upon certain properties of the data.
One common property, upon which many linear tests depend, is that of
It is necessary then to ensure normality before deciding upon the
test procedure to use. One way to do this uses the @cmd{EXAMINE} command.
-In @ref{normality}, a researcher was examining the failure rates
+In the following example, a researcher was examining the failure rates
of equipment produced by an engineering company.
The file @file{repairs.sav} contains the mean time between
-failures (@var{mtbf}) of some items of equipment subject to the study.
-Before performing linear analysis on the data,
+failures (@exvar{mtbf}) of some items of equipment subject to the study.
+Before performing linear analysis on the data,
the researcher wanted to ascertain that the data is normally distributed.
+@example
+@prompt{PSPP>} get file='@value{example-dir}/repairs.sav'.
+@prompt{PSPP>} examine mtbf
+ /statistics=descriptives.
+@end example
+
+@noindent This produces the following output:
+@psppoutput {tutorial5a}
+
A normal distribution has a skewness and kurtosis of zero.
-Looking at the skewness of @var{mtbf} in @ref{normality} it is clear
+The skewness of @exvar{mtbf} in the output above makes it clear
that the mtbf figures have a lot of positive skew and are therefore
not drawn from a normally distributed variable.
-Positive skew can often be compensated for by applying a logarithmic
-transformation.
-This is done with the @cmd{COMPUTE} command in the line
-@example
-compute mtbf_ln = ln (mtbf).
-@end example
-@noindent
-Rather than redefining the existing variable, this use of @cmd{COMPUTE}
-defines a new variable @var{mtbf_ln} which is
-the natural logarithm of @var{mtbf}.
-The final command in this example calls @cmd{EXAMINE} on this new variable,
-and it can be seen from the results that both the skewness and
-kurtosis for @var{mtbf_ln} are very close to zero.
-This provides some confidence that the @var{mtbf_ln} variable is
-normally distributed and thus safe for linear analysis.
-In the event that no suitable transformation can be found,
-then it would be worth considering
-an appropriate non-parametric test instead of a linear one.
-@xref{NPAR TESTS}, for information about non-parametric tests.
+Positive skew can often be compensated for by applying a logarithmic
+transformation, as in the following continuation of the example:
-@float Example, normality
-@cartouche
@example
-@prompt{PSPP>} get file='@value{example-dir}/repairs.sav'.
-@prompt{PSPP>} examine mtbf
- /statistics=descriptives.
@prompt{PSPP>} compute mtbf_ln = ln (mtbf).
@prompt{PSPP>} examine mtbf_ln
/statistics=descriptives.
@end example
-Output:
+@noindent which produces the following additional output:
+@psppoutput {tutorial5b}
+
+The @cmd{COMPUTE} command in the first line above performs the
+logarithmic transformation:
@example
-1.2 EXAMINE. Descriptives
-#====================================================#=========#==========#
-# #Statistic|Std. Error#
-#====================================================#=========#==========#
-#mtbf Mean # 8.32 | 1.62 #
-# 95% Confidence Interval for Mean Lower Bound# 4.85 | #
-# Upper Bound# 11.79 | #
-# 5% Trimmed Mean # 7.69 | #
-# Median # 8.12 | #
-# Variance # 39.21 | #
-# Std. Deviation # 6.26 | #
-# Minimum # 1.63 | #
-# Maximum # 26.47 | #
-# Range # 24.84 | #
-# Interquartile Range # 5.83 | #
-# Skewness # 1.85 | .58 #
-# Kurtosis # 4.49 | 1.12 #
-#====================================================#=========#==========#
-
-2.2 EXAMINE. Descriptives
-#====================================================#=========#==========#
-# #Statistic|Std. Error#
-#====================================================#=========#==========#
-#mtbf_ln Mean # 1.88 | .19 #
-# 95% Confidence Interval for Mean Lower Bound# 1.47 | #
-# Upper Bound# 2.29 | #
-# 5% Trimmed Mean # 1.88 | #
-# Median # 2.09 | #
-# Variance # .54 | #
-# Std. Deviation # .74 | #
-# Minimum # .49 | #
-# Maximum # 3.28 | #
-# Range # 2.79 | #
-# Interquartile Range # .92 | #
-# Skewness # -.16 | .58 #
-# Kurtosis # -.09 | 1.12 #
-#====================================================#=========#==========#
+compute mtbf_ln = ln (mtbf).
@end example
-@end cartouche
-@caption{Testing for normality using the @cmd{EXAMINE} command and applying
-a logarithmic transformation.
-The @var{mtbf} variable has a large positive skew and is therefore
-unsuitable for linear statistical analysis.
-However the transformed variable (@var{mtbf_ln}) is close to normal and
-would appear to be more suitable.}
-@end float
-
+@noindent
+Rather than redefining the existing variable, this use of @cmd{COMPUTE}
+defines a new variable @exvar{mtbf_ln} which is
+the natural logarithm of @exvar{mtbf}.
+The final command in this example calls @cmd{EXAMINE} on this new variable.
+The results show that both the skewness and
+kurtosis for @exvar{mtbf_ln} are very close to zero.
+This provides some confidence that the @exvar{mtbf_ln} variable is
+normally distributed and thus safe for linear analysis.
+In the event that no suitable transformation can be found,
+then it would be worth considering
+an appropriate non-parametric test instead of a linear one.
+@xref{NPAR TESTS}, for information about non-parametric tests.
@node Hypothesis Testing
@section Hypothesis Testing
The researcher starts by making a @dfn{null hypothesis}.
Often this is a hypothesis which he suspects to be false.
-For example, if he suspects that @var{A} is greater than @var{B} he will
+For example, if he suspects that @var{A} is greater than @var{B} he will
state the null hypothesis as @math{ @var{A} = @var{B}}.@c
@footnote{This example assumes that it is already proven that @var{B} is
not greater than @var{A}.}
@menu
-* Testing for differences of means::
-* Linear Regression::
+* Testing for differences of means::
+* Linear Regression::
@end menu
@node Testing for differences of means
@vindex T-TEST
A common statistical test involves hypotheses about means.
-The @cmd{T-TEST} command is used to find out whether or not two separate
+The @cmd{T-TEST} command is used to find out whether or not two separate
subsets have the same mean.
-@ref{t-test} uses the file @file{physiology.sav} previously
-encountered.
-A researcher suspected that the heights and core body
+A researcher suspected that the heights and core body
temperature of persons might be different depending upon their sex.
-To investigate this, he posed two null hypotheses:
+To investigate this, he posed two null hypotheses based on the data
+from @file{physiology.sav} previously encountered:
@itemize @bullet
@item The mean heights of males and females in the population are equal.
@item The mean body temperature of males and
For the purposes of the investigation the researcher
decided to use a p-value of 0.05.
-In addition to the T-test, the @cmd{T-TEST} command also performs the
+In addition to the T-test, the @cmd{T-TEST} command also performs the
Levene test for equal variances.
If the variances are equal, then a more powerful form of the T-test can be used.
However if it is unsafe to assume equal variances,
then an alternative calculation is necessary.
@pspp{} performs both calculations.
-For the @var{height} variable, the output shows the significance of the
-Levene test to be 0.33 which means there is a
-33% probability that the
+For the @exvar{height} variable, the output shows the significance of the
+Levene test to be 0.33 which means there is a
+33% probability that the
Levene test produces this outcome when the variances are equal.
Had the significance been less than 0.05, then it would have been unsafe to assume that
the variances were equal.
However, because the value is higher than 0.05 the homogeneity of variances assumption
is safe and the ``Equal Variances'' row (the more powerful test) can be used.
-Examining this row, the two tailed significance for the @var{height} t-test
+Examining this row, the two tailed significance for the @exvar{height} t-test
is less than 0.05, so it is safe to reject the null hypothesis and conclude
that the mean heights of males and females are unequal.
-For the @var{temperature} variable, the significance of the Levene test
+For the @exvar{temperature} variable, the significance of the Levene test
is 0.58 so again, it is safe to use the row for equal variances.
The equal variances row indicates that the two tailed significance for
-@var{temperature} is 0.20. Since this is greater than 0.05 we must reject
-the null hypothesis and conclude that there is insufficient evidence to
+@exvar{temperature} is 0.20. Since this is greater than 0.05 we must reject
+the null hypothesis and conclude that there is insufficient evidence to
suggest that the body temperature of male and female persons are different.
-@float Example, t-test
-@cartouche
+The syntax for this analysis is:
@example
@prompt{PSPP>} get file='@value{example-dir}/physiology.sav'.
@prompt{PSPP>} recode height (179 = SYSMIS).
@prompt{PSPP>} t-test group=sex(0,1) /variables = height temperature.
@end example
-Output:
-@example
-1.1 T-TEST. Group Statistics
-#==================#==#=======#==============#========#
-# sex | N| Mean |Std. Deviation|SE. Mean#
-#==================#==#=======#==============#========#
-#height Male |22|1796.49| 49.71| 10.60#
-# Female|17|1610.77| 25.43| 6.17#
-#temperature Male |22| 36.68| 1.95| .42#
-# Female|18| 37.43| 1.61| .38#
-#==================#==#=======#==============#========#
-1.2 T-TEST. Independent Samples Test
-#===========================#=========#=============================== =#
-# # Levene's| t-test for Equality of Means #
-# #----+----+------+-----+------+---------+- -#
-# # | | | | | | #
-# # | | | |Sig. 2| | #
-# # F |Sig.| t | df |tailed|Mean Diff| #
-#===========================#====#====#======#=====#======#=========#= =#
-#height Equal variances# .97| .33| 14.02|37.00| .00| 185.72| ... #
-# Unequal variances# | | 15.15|32.71| .00| 185.72| ... #
-#temperature Equal variances# .31| .58| -1.31|38.00| .20| -.75| ... #
-# Unequal variances# | | -1.33|37.99| .19| -.75| ... #
-#===========================#====#====#======#=====#======#=========#= =#
-@end example
-@end cartouche
-@caption{The @cmd{T-TEST} command tests for differences of means.
-Here, the @var{height} variable's two tailed significance is less than
+
+PSPP produces the following output for this syntax:
+@psppoutput {tutorial6}
+
+The @cmd{T-TEST} command tests for differences of means.
+Here, the @exvar{height} variable's two tailed significance is less than
0.05, so the null hypothesis can be rejected.
Thus, the evidence suggests there is a difference between the heights of
-male and female persons.
-However the significance of the test for the @var{temperature}
+male and female persons.
+However the significance of the test for the @exvar{temperature}
variable is greater than 0.05 so the null hypothesis cannot be
rejected, and there is insufficient evidence to suggest a difference
-in body temperature.}
-@end float
+in body temperature.
@node Linear Regression
@subsection Linear Regression
@cindex linear regression
@vindex REGRESSION
-Linear regression is a technique used to investigate if and how a variable
+Linear regression is a technique used to investigate if and how a variable
is linearly related to others.
-If a variable is found to be linearly related, then this can be used to
+If a variable is found to be linearly related, then this can be used to
predict future values of that variable.
-In example @ref{regression}, the service department of the company wanted to
+In the following example, the service department of the company wanted to
be able to predict the time to repair equipment, in order to improve
the accuracy of their quotations.
It was suggested that the time to repair might be related to the time
This command not only tests if the variables are related, but also
identifies the potential linear relationship. @xref{REGRESSION}.
+A first attempt includes @exvar{duty_cycle}:
-@float Example, regression
-@cartouche
@example
@prompt{PSPP>} get file='@value{example-dir}/repairs.sav'.
@prompt{PSPP>} regression /variables = mtbf duty_cycle /dependent = mttr.
-@prompt{PSPP>} regression /variables = mtbf /dependent = mttr.
-@end example
-Output:
-@example
-1.3(1) REGRESSION. Coefficients
-#=============================================#====#==========#====#=====#
-# # B |Std. Error|Beta| t #
-#========#====================================#====#==========#====#=====#
-# |(Constant) #9.81| 1.50| .00| 6.54#
-# |Mean time between failures (months) #3.10| .10| .99|32.43#
-# |Ratio of working to non-working time#1.09| 1.78| .02| .61#
-# | # | | | #
-#========#====================================#====#==========#====#=====#
-
-1.3(2) REGRESSION. Coefficients
-#=============================================#============#
-# #Significance#
-#========#====================================#============#
-# |(Constant) # .10#
-# |Mean time between failures (months) # .00#
-# |Ratio of working to non-working time# .55#
-# | # #
-#========#====================================#============#
-2.3(1) REGRESSION. Coefficients
-#============================================#=====#==========#====#=====#
-# # B |Std. Error|Beta| t #
-#========#===================================#=====#==========#====#=====#
-# |(Constant) #10.50| .96| .00|10.96#
-# |Mean time between failures (months)# 3.11| .09| .99|33.39#
-# | # | | | #
-#========#===================================#=====#==========#====#=====#
-
-2.3(2) REGRESSION. Coefficients
-#============================================#============#
-# #Significance#
-#========#===================================#============#
-# |(Constant) # .06#
-# |Mean time between failures (months)# .00#
-# | # #
-#========#===================================#============#
@end example
-@end cartouche
-@caption{Linear regression analysis to find a predictor for
-@var{mttr}.
-The first attempt, including @var{duty_cycle}, produces some
-unacceptable high significance values.
-However the second attempt, which excludes @var{duty_cycle}, produces
-significance values no higher than 0.06.
-This suggests that @var{mtbf} alone may be a suitable predictor
-for @var{mttr}.}
-@end float
-
-The coefficients in the first table suggest that the formula
+
+@noindent This attempt yields the following output (in part):
+@psppoutput {tutorial7a}
+
+The coefficients in the above table suggest that the formula
@math{@var{mttr} = 9.81 + 3.1 \times @var{mtbf} + 1.09 \times @var{duty_cycle}}
can be used to predict the time to repair.
However, the significance value for the @var{duty_cycle} coefficient
is very high, which would make this an unsafe predictor.
For this reason, the test was repeated, but omitting the
-@var{duty_cycle} variable.
-This time, the significance of all coefficients no higher than 0.06,
+@exvar{duty_cycle} variable:
+
+@example
+@prompt{PSPP>} regression /variables = mtbf /dependent = mttr.
+@end example
+
+@noindent
+This second try produces the following output (in part):
+@psppoutput {tutorial7b}
+
+This time, the significance of all coefficients is no higher than 0.06,
suggesting that at the 0.06 level, the formula
@math{@var{mttr} = 10.5 + 3.11 \times @var{mtbf}} is a reliable
predictor of the time to repair.
projects / pspp / blobdiff