Autor des Abschnitts: Danielle J. Navarro and David R. Foxcroft

Logische Ausdrücke in jamovi

A key concept that a lot of data transformations in jamovi rely on is the idea of a logical value. A logical value is an assertion about whether something is true or false. This is implemented in jamovi in a pretty straightforward way. There are two logical values, namely TRUE and FALSE. Despite the simplicity, logical values are very useful things. Let us see how they work.

Beurteilen mathematischer Wahrheiten

In George Orwell’s classic book 1984 one of the slogans used by the totalitarian Party was “two plus two equals five”. The idea being that the political domination of human freedom becomes complete when it is possible to subvert even the most basic of truths. It is a terrifying thought, especially when the protagonist Winston Smith finally breaks down under torture and agrees to the proposition. “Man is infinitely malleable”, the book says. I am pretty sure that this is not true of humans[1] and it is definitely not true of jamovi. jamovi is not infinitely malleable, it has rather firm opinions on the topic of what is and is not true, at least as regards basic mathematics. If I ask it to calculate 2 + 2,[2] it always gives the same answer, and it is not 5!

Of course, so far jamovi is just doing the calculations. I have not asked it to explicitly assert that 2 + 2 = 4 is a true statement. If I want jamovi to make an explicit judgement, I can use a command like this: 2 + 2 == 4

What I have done here is use the equality operator, ==, to force jamovi to make a “TRUE or FALSE” judgement.[3] Okay, let us see what jamovi thinks of the Party slogan, so type this into the compute new variable Formula-box:

2 + 2 == 5

And what do you get? It should be a whole set of FALSE values in the spreadsheet column for your newly computed variable. It was worth having a look at what happens if I try to force jamovi to believe that two plus two is five by making a statement like 2 + 2 = 5. I know that if I do this in another program, say R, then it throws up an error message. But wait, if you do this in jamovi you get a whole set of FALSE values. So what is going on? Well, it seems that jamovi is being pretty smart and realises that you are testing whether it is TRUE or FALSE that 2 + 2 = 5, regardless of whether you use the correct equality operator, ==, or the equals sign =.

Logische Operationen

So now we have seen logical operations at work. But so far we have only seen the simplest possible example. You probably will not be surprised to discover that we can combine logical operations with other operations and functions in a more complicated way, like this:

3 * 3 + 4 * 4 == 5 * 5

oder so:

SQRT(25) == 5

Not only that, but as Tab. 3 illustrates, there are several other logical operators that you can use corresponding to some basic mathematical concepts. Hopefully these are all pretty self-explanatory. For example, the less than operator < checks to see if the number on the left is less than the number on the right. If it is less, then jamovi returns an answer of TRUE, but if the two numbers are equal, or if the one on the right is larger, then jamovi returns an answer of FALSE.

Tab. 3 Some logical operators. Technically I should be calling these “binary relational operators”, but quite frankly I do not want to. It is my book so no-one can make me.

Operation	Operator	Beispiel-Eingabe	Ausgabe
weniger als	<	2 < 3	TRUE
kleiner als oder gleich	<=	2 <= 2	TRUE
größer als	>	2 > 3	FALSE
größer als oder gleich	>=	2 >= 2	TRUE
gleich	==	2 == 3	FALSE
ungleich	!=	2 != 3	TRUE

In contrast, the less than or equal to operator <= will do exactly what it says. It returns a value of TRUE if the number of the left-hand side is less than or equal to the number on the right-hand side. At this point I hope it is pretty obvious what the greater than operator > and the greater than or equal to operator >= do!

Next on the list of logical operators is the not equal to operator != which, as with all the others, does what it says it does. It returns a value of TRUE when things on either side are not identical to each other. Therefore, since 2 + 2 is not equal to 5 we would get TRUE as the value for our newly computed variable. Try it and see:

2 + 2 != 5

We are not quite done yet. There are three more logical operations that are worth knowing about, listed in Tab. 4. These are the not operator !, the and-operator and, and the or-operator or. Like the other logical operators, their behaviour is more or less exactly what you would expect given their names. For instance, if I ask you to assess the claim that “either 2 + 2 = 4 or 2 + 2 = 5” you would say that it is true. Since it is an “either-or” statement, all we need is for one of the two parts to be true. That is what the or operator does:[4]

(2 + 2 == 4) or (2 + 2 == 5)

Tab. 4 Einige weitere logische Operatoren.

Operation	Operator	Beispiel-Eingabe	Ausgabe
not (nicht)	NOT	NOT(1 == 1)	FALSE
or (oder)	or	(1 == 1) or (2 == 3)	TRUE
and (und)	and	(1 == 1) and (2 == 3)	FALSE

On the other hand, if I ask you to assess the claim that “both 2 + 2 = 4 and 2 + 2 = 5” you would say that it is false. Since this is an and statement we need both parts to be true. And that is what the and operator does:

(2 + 2 == 4) and (2 + 2 == 5)

Finally, there is the not operator, which is simple but annoying to describe in English. If I ask you to assess my claim that “it is not true that 2 + 2 = 5” then you would say that my claim is true, because actually my claim is that “2 + 2 = 5 is false”. And I am right. If we write this in jamovi we use this:

NOT(2 + 2 == 5)

In other words, since 2 + 2 == 5 is a FALSE statement, it must be the case that NOT(2 + 2 == 5) is a TRUE one. Essentially, what we have really done is claim that “not false” is the same thing as “true”. Obviously, this is not really quite right in real life. But jamovi lives in a much more black or white world. For jamovi everything is either TRUE or FALSE. No shades of grey are allowed.

Of course, in our 2 + 2 = 5 example, we did not really need to use the “not” operator NOT and the “equals to” operator == as two separate operators. We could have just used the “not equals to” operator != like this:

2 + 2 != 5

Logische Operationen auf Text anwenden

I also want to briefly point out that you can apply these logical operators to text as well as to logical data. It is just that we need to be a bit more careful in understanding how jamovi interprets the different operations. In this section I will talk about how the equal to operator == applies to text, since this is the most important one. Obviously, the not equal to operator != gives the exact opposite answers to == so I am implicitly talking about that one too, but I will not give specific commands showing the use of !=.

Okay, let us see how it works. In one sense, it is very simple. For instance, I can ask jamovi if the word cat is the same as the word dog, like this:

"cat" == "dog"

That is pretty obvious, and it is good to know that even jamovi can figure that out. Similarly, jamovi does recognise that a cat is a cat:

"cat" == "cat"

Again, that is exactly what we would expect. However, what you need to keep in mind is that jamovi is not at all tolerant when it comes to grammar and spacing. If two strings differ in any way whatsoever, jamovi will say that they are not equal to each other, as with the following:

" cat" == "cat"
"cat" == "CAT"
"cat" == "c a t"

You can also use other logical operators too. For instance jamovi also allows you to use the < and > operators to determine which of two text “strings” comes first, alphabetically speaking. Sort of. Actually, it is a bit more complicated than that, but let us start with a simple example:

"cat" < "dog"

In jamovi wird dieses Beispiel als TRUE ausgewertet. Das liegt daran, dass cat alphabetisch vor dog steht, so dass jamovi die Aussage für wahr hält. Wenn wir jedoch jamovi bitten, uns zu sagen, ob cat vor anteater steht, dann wird es den Ausdruck als FALSE bewerten. So weit, so gut. Aber Textdaten sind ein bisschen komplizierter, als das Wörterbuch vermuten lässt. Was ist mit cat und CAT? Welcher dieser Ausdrücke kommt zuerst? Probieren Sie es aus und finden Sie es heraus:

"CAT" < "cat"

Dies ergibt in der Tat TRUE. Mit anderen Worten: jamovi geht davon aus, dass Großbuchstaben vor Kleinbuchstaben kommen. Das ist in Ordnung. Das wird wohl niemanden überraschen. Was Sie vielleicht überraschen könnte, ist, dass jamovi davon ausgeht, dass alle Großbuchstaben vor allen Kleinbuchstaben kommen. Das heißt, während "anteater" < "zebra" eine wahre Aussage ist, und das Äquivalent in Großbuchstaben "ANTEATER" < "ZEBRA" ebenfalls wahr ist, ist es nicht wahr, zu sagen, dass "anteater" < "ZEBRA", wie der folgende Auszug zeigt. Versuchen Sie dies:

"anteater" < "ZEBRA"

Die Auswertung ergibt FALSE, was etwas kontraintuitiv erscheinen mag. Vor diesem Hintergrund kann es hilfreich sein, einen kurzen Blick auf die verschiedenen Textzeichen in der Reihenfolge zu werfen, in der sie von jamovi verarbeitet werden:

! " # $ % & ' ( ) * + , - . /  0 1 2 3 4 5 6 7 8 9 : ; < = > ? @
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z [ \ ]  ^ _ `
a b c d e f g h i j k l m n o p q r s t u v w x y z } | {

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[1]

I offer up my teenage attempts to be “cool” as evidence that some things just can not be done.

[2]

You can do this in the Compute new variable panel, though just calculating 2 + 2 for every cell of a new variable is not very useful!

[3]

Note that this is a very different operator to the equals operator =. A common typo that people make when trying to write logical commands in jamovi (or other languages, since the “= versus ==” distinction is important in many computer and statistical programs) is to accidentally type = when you really mean ==. Be especially cautious with this, I have been programming in various languages since I was a teenager and I still screw this up a lot. Hmm. I think I see why I was not cool as a teenager. And why I am still not cool.

[4]

Now, here is a quirk in jamovi. When you have simple logical expressions like the ones we have already met, e.g., 2 + 2 == 5 then jamovi neatly states FALSE (or TRUE) in the corresponding spreadsheet column. Underneath the hood, jamovi stores FALSE as 0 and TRUE as 1. When we have more complex logical expressions, such as (2 + 2 == 4) or (2 + 2 == 5), then jamovi just displays either 0 or 1, depending whether the logical expression is evaluated as false, or true.