Section author: Danielle J. Navarro and David R. Foxcroft

Logical expressions 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’s see how they work.

Assessing mathematical truths

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’s 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’m pretty sure that this isn’t true of humans[1] and it’s definitely not true of jamovi. jamovi is not infinitely malleable, it has rather firm opinions on the topic of what is and isn’t true, at least as regards basic mathematics. If I ask it to calculate 2 + 2,[2] it always gives the same answer, and it’s not bloody 5!

Of course, so far jamovi is just doing the calculations. I haven’t 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’ve done here is use the equality operator, ==, to force jamovi to make a “TRUE or FALSE” judgement.[3] Okay, let’s 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. Booyah! Freedom and ponies for all! Or something like that. Anyway, 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 =.

Logical operations

So now we’ve seen logical operations at work. But so far we’ve only seen the simplest possible example. You probably won’t 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

or this

SQRT(25) == 5

Not only that, but as Table 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’s 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.

Table 3 Some logical operators. Technically I should be calling these “binary relational operators”, but quite frankly I don’t want to. It’s my book so no-one can make me.

operation	operator	example input	answer
less than	<	2 < 3	TRUE
less than or equal to	<=	2 <= 2	TRUE
greater than	>	2 > 3	FALSE
greater than or equal to	>=	2 >= 2	TRUE
equal to	==	2 == 3	FALSE
not equal to	!=	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’s 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 isn’t equal to 5 we would get TRUE as the value for our newly computed variable. Try it and see:

2 + 2 != 5

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

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

Table 4 Some more logical operators.

operation	operator	example input	answer
not	NOT	NOT(1==1)	FALSE
or	or	(1==1) or (2==3)	TRUE
and	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’d say that it’s false. Since this is an and statement we need both parts to be true. And that’s what the and operator does:

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

Finally, there’s 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’m 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’ve really done is claim that “not false” is the same thing as “true”. Obviously, this isn’t 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 didn’t 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

Applying logical operation to text

I also want to briefly point out that you can apply these logical operators to text as well as to logical data. It’s just that we need to be a bit more careful in understanding how jamovi interprets the different operations. In this section I’ll 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’m implicitly talking about that one too, but I won’t give specific commands showing the use of !=.

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

"cat" == "dog"

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

"cat" == "cat"

Again, that’s exactly what we’d 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’re 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’s a bit more complicated than that, but let’s start with a simple example:

"cat" < "dog"

In jamovi, this example evaluates to TRUE. This is because cat does does come before dog alphabetically, so jamovi judges the statement to be true. However, if we ask jamovi to tell us if cat comes before anteater then it will evaluate the expression as FALSE. So far, so good. But text data is a bit more complicated than the dictionary suggests. What about cat and CAT? Which of these comes first? Try it and find out:

"CAT" < "cat"

This in fact evaluates to TRUE. In other words, jamovi assumes that uppercase letters come before lowercase ones. Fair enough. No-one is likely to be surprised by that. What you might find surprising is that jamovi assumes that all uppercase letters come before all lowercase ones. That is, while "anteater" < "zebra" is a true statement, and the uppercase equivalent "ANTEATER" < "ZEBRA" is also true, it is not true to say that "anteater" < "ZEBRA", as the following extract illustrates. Try this:

"anteater" < "ZEBRA"

This evaluates to FALSE, and this may seem slightly counterintuitive. With that in mind, it may help to have a quick look at the various text characters in the order that jamovi processes them:

! " # $ % & ' ( ) * + , - . /  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 } | {

---

[1]	I offer up my teenage attempts to be “cool” as evidence that some things just can’t be done.

[2]	You can do this in the Compute new variable screen, 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’ve 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 wasn’t cool as a teenager. And why I’m still not cool.

[4]

Now, here’s 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.