- Assumptions for Confidence Intervals for Means
- Any Confidence Level - All Cases
- 95% Confidence Level - Separate Groups
- Any Confidence Level - Separate Groups
- Bonferroni Corrected Confidence Intervals

Confidence intervals for means are among the most essential statistics for reporting. Sadly, they're pretty well hidden in SPSS. This tutorial quickly walks you through the best (and worst) options for obtaining them. We'll use adolescents_clean.sav -partly shown below- for all examples.

## Assumptions for Confidence Intervals for Means

Computing confidence intervals for means requires

- independent observations and
- normality: our variables must be normally distributed in the population represented by our sample.

1. A visual inspection of our data suggests that each case represents a distinct respondent so it seems safe to assume these are independent observations.

2. Second, the normality assumption is only required for small samples of N < 25 or so. For larger samples, the central limit theorem ensures that the sampling distributions for means, sums and proportions approximate normal distributions. In short,
our example data meet both assumptions.

## Any Confidence Level - All Cases I

If we want to analyze all cases as a single group, our best option is the one sample t-test dialog.

The final output will include confidence intervals for the differences between our test value and our sample means. Now, if we use 0 as the test value, these differences will be exactly equal to our sample means.

Clicking syntax below. Let's run it.

results in the***Obtain 99% CI's for means of iq to wellb over all cases.**

T-TEST

/TESTVAL=0

/MISSING=ANALYSIS

/VARIABLES=iq depr anxi soci wellb

/CRITERIA=CI(.99).

## Result

- as long as we use 0 as the test value, mean differences are equal to the actual means. This holds for their confidence intervals as well;
- the table indirectly includes the sample sizes: df = N - 1 and therefore N = df + 1.

## Any Confidence Level - All Cases II

An alternative -but worse- option for obtaining these same confidence intervals is from Any Confidence Level - Separate Groups II. They result in the syntax below.

We'll discuss these dialogs and their output in a minute under***Obtain 95% CI's for means of iq to wellb over all cases.**

EXAMINE VARIABLES=iq depr anxi soci wellb

/PLOT NONE

/STATISTICS DESCRIPTIVES

/CINTERVAL 95

/MISSING PAIRWISE

**/*IMPORTANT!*/**

/NOTOTAL.

***Minimal syntax - returns 95% CI's by default.**

examine iq depr anxi soci wellb

/missing pairwise

**/*IMPORTANT!*/**.

## 95% Confidence Level - Separate Groups

In many situations, analysts report statistics for separate groups such as male and female respondents. If these statistics include 95% confidence intervals for means, the way to go is the One-Way ANOVA dialog.

Now, sex is a dichotomous variable so we compare these 2 means with a t-test rather than an ANOVA -even though the significance levels are identical for these tests. However, the dialogs below result in a much nicer -and technically correct- descriptives table than the t-test dialogs.

Descriptives includes 95% CI's for means but other confidence levels aren't available.

Clicking results in the syntax below. Let's run it.

***Obtain 95% CI's for means of iq to wellb by sex.**

ONEWAY iq depr anxi soci wellb BY sex

/STATISTICS DESCRIPTIVES .

## Result

The resulting table has a **nice layout** that comes pretty close to the APA recommended format. It includes

- sample sizes;
- sample means;
- standard deviations and
- 95% CI's for means.

As mentioned, this method is restricted to 95% CI's. So let's look into 2 alternatives for other confidence levels.

## Any Confidence Level - Separate Groups I

So how to obtain other confidence intervals for separate groups? The best option is adding a SPLIT FILE to the One Sample T-Test method. Since we discussed these dialogs and output under Any Confidence Level - All Cases I, we'll now just present the modified syntax.

***SPLIT FILE -succeeding output is created for males and females separately.**

sort cases by sex.

split file layered by sex.

***Obtain 95% CI's for means of iq to wellb.**

T-TEST

/TESTVAL=0

/MISSING=ANALYSIS

/VARIABLES=iq depr anxi soci wellb

/CRITERIA=CI(.95).

***Switch off SPLIT FILE for succeeding output.**

split file off.

## Any Confidence Level - Separate Groups II

A last option we should mention is the Explore dialog as shown below.

We mostly discuss it for the sake of completeness because
SPSS’ Explore dialog is a real showcase of stupidity

and poor UX design.
Just a few of its shortcomings are that

- you can select “statistics” but not
**which**statistics; - if you do so, you always get a
**tsunami**of statistics -the vast majority of which you don't want; - what you probably
*do*want are**sample sizes**but these are not available; - the sample sizes that are actually used may be different than you think: in contrast to similar dialogs, Explore uses
**listwise exclusion**of missing values by default; - what you probably
*do*want, is exclusion of missing values by analysis or variable. This is available but**mislabeled**“pairwise” exclusion. - the Explore dialog generates an EXAMINE command so many users think these are 2 separate procedures.

For these reasons, I personally only use Explore for

These tests are under

But anyway, the steps shown below result in confidence intervals for means for males and females separately.

Clicking

generates the syntax below.***Obtain 95% CI's for means of iq to wellb for males and females separately.**

EXAMINE VARIABLES=iq depr anxi soci wellb BY sex

/PLOT NONE

/STATISTICS DESCRIPTIVES

/CINTERVAL 95

/MISSING PAIRWISE

**/*IMPORTANT!*/**

/NOTOTAL.

***Minimal syntax - returns 95% CI's by default.**

examine iq depr anxi soci wellb by sex

/missing pairwise

**/*IMPORTANT!*/**

/nototal.

## Result

## Bonferroni Corrected Confidence Intervals

All examples in this tutorial used 5 outcome variables measured on the same sample of respondents. Now, a 95% confidence interval has a 5% chance of *not* enclosing the population parameter we're after. So for 5 such intervals, there's a (1 - 0.95^{5} =) 0.226 probability that at least one of them is wrong.

Some analysts argue that this problem should be fixed by applying a Bonferroni correction. Some procedures in SPSS have this as an option as shown below.

But what about basic confidence intervals? The easiest way is probably to adjust the confidence levels manually by
$$level_{adj} = 100\% - \frac{100\% - level_{unadj}}{N_i}$$

where \(N_i\) denotes the number of intervals calculated on the same sample. So some Bonferroni adjusted confidence levels are

**95.00%**if you calculate**1**(95%) confidence interval;**97.50%**if you calculate**2**(95%) confidence intervals;**98.33%**if you calculate**3**(95%) confidence intervals;**98.75%**if you calculate**4**(95%) confidence intervals;**99.00%**if you calculate**5**(95%) confidence intervals;

and so on.

Well, I think that should do. I can't think of anything else I could write on this topic. If you do, please throw us a comment below.

**Thanks for reading!**

## THIS TUTORIAL HAS 5 COMMENTS:

## By Chelsey on March 11th, 2020

Thank you! These are very useful topics.

## By Jon K Peck on March 31st, 2020

Examine (EXPLORE) gives you in one place the basic stats that one might want to look at. It's hardly a tsunami. It can include some robust stats along with the basic ones, and you can specify the CI level.

The simplest way to get CI's along with the other particular stats you want is to use Custom Tables. And you can specify the CI level there and get a Bonferroni or Benjamini-Hochberg correction in a multiple testing situation.

Examine, t tests, descriptives, and oneway all support bootstrapping, which can be important.

## By Ruben Geert van den Berg on April 1st, 2020

Hi Jon!

CTABLES is a good suggestion and I'll perhaps cover it in the first update of this tutorial. I'm currently not licensed for CTABLES. Also, I'm generally not a big fan of its interface (too many clicks) and its verbose and error sensitive syntax. Nevertheless, I'll look into it because it does have some nice options.

On a personal note, I often prefer MEANS:

-I can choose precisely which statistics I want in which order

-I may or may include 1+ between-subjects factors

-the syntax is super clean

-the output table is simple and clean -no nested column headers which complicate removing columns in WORD

-it includes medians

I find it surprising that MEANS doesn't come up with CI's. More generally, functionality is often scattered and duplicated over a myriad of commands which differ only so slightly...

## By Jon K Peck on April 1st, 2020

CTABLES is designed to give you a lot of control over the layout and format of the output, so the syntax is necessarily more complex than for some other commands, but it can be pretty simple. For example, for means and CIs, it could be just this.

CTABLES

/TABLE (prevexp + salary + salbegin) [MEAN.LCL, MEAN, MEAN.UCL].

The gui panel syntax generator often generates more complex syntax than necessary, unfortunately, but the syntax logic is pretty regular.

## By Ruben Geert van den Berg on April 1st, 2020

Totally agree. I had a CTABLES project about a year ago and I skipped the GUI altogether. Honestly, I think the same goes for OUTPUT MODIFY: I did amazing stuff from syntax but I had huge trouble getting anything done from the GUI.

P.s. for something totally different: you sent me some .py file for Cohen’s D some time ago. Are you aware of any full-blown extension for it? Ideally, I'd like to show my users something that creates a full-blown APA t-test table with 3 mouse clicks or so. I searched for "cohen" in the extension hub but nothing came up.