SPSS paired samples t-test is a procedure for testing whether the means of two metric variables are equal in some population. Both variables have been measured on the same cases. Although “paired samples” suggests that multiple samples are involved, there's really only one sample and two variables. The screenshot below illustrates the basic idea.

## SPSS Paired Samples T-Test Example

A behavioral scientist wants to know whether drinking a single glass of beer affects reaction times. She has 30 participants perform some tasks before and after having a beer and records their reaction times. For each participant she calculates the average reaction time over tasks both before and after the beer, resulting in reaction_times.sav. Can we conclude from these data that a single beer affects reaction time? We'll first open the data by running the syntax below.

***1. Set default directory.**

cd 'd:downloaded'. /*or wherever data file is located.

***2. Open data.**

get file "reaction_times.sav".

## Quick Data Check

We first just want to know what the data look like. We could do so by taking a look at the histograms of the two variables. However, a nice alternative for two variables measured on the same respondents is a scatter plot. The screenshots below walk you through.

We first navigate to

We then move `reac_1`

and `reac_2`

to and . Clicking results in the syntax below.

***Run scatter plot.**

GRAPH

/SCATTERPLOT(BIVAR)=reac_2 WITH reac_1

/MISSING=LISTWISE.

Normal reactions times are between 800 and 1500 ms (= milliseconds). Neither variable has any values that are way out of this normal range so the data seem plausible.

We also see a substantial positive correlation between the variables; respondents who were fast on the first task tend to be fast on the second task as well. The graph seems to suggest that the mean reaction time before a beer is somewhere near 1100 ms (vertical axis) and after a beer perhaps 1300 ms (horizontal axis).

One respondent (right top corner, denoted “outlier”) is remarkably slow compared to the others. However, we decide that its scores are not extreme enough to justify removing it from the data.

## 2. Assumptions Paired Samples T-Test

SPSS will happily provide us with test results but we can only take those seriously insofar as the assumptions for our test are met. For the paired samples t-test, these are

**independent observations**or, more precisely, independent and identically distributed variables;- the difference scores between the two variables must be
**normally distributed**in our population.

The first assumption is often satisfied if each case (row of data values) holds a distinct person or other unit of analysis. The normality assumption is mostly relevant for small sample sizes (say N < 30). If it's violated, consider a Wilcoxon signed-ranks test instead of a t-test. However, our data seems to meet both assumptions so we'll proceed to the t-test.

## 3. Run SPSS Paired Samples T-Test

We'll first navigate to

.
Select both variables and

move them into the box.

Clicking results in the syntax below.

***Run paired samples t-test.**

T-TEST PAIRS=reac_1 WITH reac_2 (PAIRED)

/CRITERIA=CI(.9500)

/MISSING=ANALYSIS.

## 4. SPSS Paired Samples T-Test Output

The first table (“**Paired Samples Statistics**”) presents the descriptive statistics we'll report. (Do not use the `DESCRIPTIVES`

command for obtaining these.The reason for this is that the significance test is (necessarily) limited to cases without any missing values on the test variables. Cases with a missing value on one of the test variables should therefore be excluded from the descriptives as well. This holds for the descriptives from the paired samples t-test but not for `DESCRIPTIVES`

.)

Since N = 30, we don't have any missing values on the test variables and

as expected, the mean reaction time before a beer (1166 ms) is lower than after a beer (1288 ms).

On average, respondents slow down some 122 ms. We could have calculated this from the first table ourselves.

The p-value denoted by “Sig. (2-tailed)” is 0. (If we double-click it, we'll see it's precisely 0.000083, meaning a .0083 % chance.) So if the population means are equal, there's a 0% chance of finding this result. We therefore reject the null hypothesis. Even a single beer slows people down on the given tasks.

Note that the p-value is **two-sided**. This means that the p-value consists of a .00415% chance of finding a difference < -122 ms and another .00415% chance of finding a difference > 122 ms.

## 5.Reporting a Paired Samples T-Test

As we mentioned before, we'll always report the descriptive statistics obtained from the paired samples t-test. For the significance test, we may write something like ** “Participants became slower after drinking a single beer, t(29) = -4.6, p = 0.00”**.

## This tutorial has 18 comments

## By Ruben Geert van den Berg on March 28th, 2020

Hi Patrick, thanks for your feedback!

We actually started rewriting this tutorial from scratch yesterday because we've some more issues with it:

-it doesn't test the normality assumption required for this test -only needed for small sample sizes (say N < 25 or so);

-it doesn't mention Cohen’s D, the effect size for this test.

But anyway, we think APA recommendations usually suck and they should also be rewritten from scratch after serious debate with some good statisticians.

Regarding p-values, our view is that more accurate is always better than less accurate. You're technically right that neither the normal distribution nor the t-distribution ever comes up with exact zero probabilities because they both run from -∞ to +∞.

However, we didn't say

exactlyzero: taking rounding into regard, 0.00 may be any value between (exactly) 0 and 0.0049. That is, we don't use 0, 0.0, 0.00 and 0.000 interchangeably. Perhaps scientific notation would be appropriate here.In any case, we feel that effect size and confidence intervals deserve more attention than p-values and most researchers -as well as the APA- do a very poor job there.

Have a great weekend!

SPSS tutorials

## By Patrick Guziewicz on March 27th, 2020

Nice overview! Only comment would be that in standard nomenclature (at least for APA) would be not to use p=.00, it would be p<.001 since a normal distribution never touches zero. Best and thank you!

## By kidest on January 23rd, 2020

Good one it helps me