# No value or "."returned for Mauchly's Test of Sphericity in SPSS

I am learning how to do a Two-Way Repeated Measures ANOVA in SPSS but when I try to check the Mauchly's Test of Sphericity Significance value it only displays a single decimal point. It is also missing the Approx. Chi-Square value.

The experiment was a 9x9 Within Subject Incomplete Counterbalanced Measures Design

The data was collected to measure the effect of common distortions across multiple websites.

                           Mauchly's Test of Sphericity
Measure:   MEASURE_1
Within Subjects | Mauchly's W| Approx.    |   df |  Sig.|             Epsilon
Effect          |            |            |      |      |----------------------------
|            | Chi-Square |      |      |Greenhouse-|  Huynh-| Lower
|            |            |      |      |Geisser    |  Feldt | bound
website         |        .024|      41.546|   35 |  .247|       .579|    .900| .125
distortions     |        .111|      24.430|   35 |  .925|       .655|   1.000| .125                     |            |            |      |      |           |        |
website *       |            |            |      |      |           |        |
distortions     |        .000|          . | 2079 |    . |       .180|   1.000| .016


I understand from this question/answer and this question/answer that this might happen when there are only 2 factors with 2 levels but in my case there are 2 factors (website, distortion) each with 9 levels. Each of these levels has 15 data observations.

Alternatively I also note from this Laerd Statistics guide "the greater the number of repeated measures, the greater the potential for the violation of sphericity". Maybe 9x9 is too much and/or the value is uncomputable?

I understand that if Mauchly's Test returns a Sig value <.05 I should turn to the Greenhouse-Geisser and Huynh-Feldt values and that the lower these values are the greater the violations of sphericity. However, the Huynh-Feldt value of 1 indicates perfect sphericity while my Greenhouse-Geisser is .180 indicating there is an issue.

Has anybody else experienced this problem? And what does it mean? Am I to assume that there is an issue with Sphericity? Which correction should I use?

EDIT: Memory?

So after some investigation it looks like the test is simply too complicated, possibly for my machine.

When I did the same test with a small sample of the same data, a 3x3 design each with 6 data observations the test worked. Both the Approx. Chi-Square value and the Sig value were visible.

4x4 with 12 data observations also works

However, when I did it with a more complex 5x5 design, each with 15 data observations it would no longer give me either value.

EDIT 2: Not Memory

To increase the memory allocations to SPSS simply:

• Open a new Syntax window. File > Open > Syntax.
• Type SHOW WORKSPACE and click run to show the current memory allocation
• This was 24576 in my case (memory shown in KB)
• To increase your memory type SET WORKSPACE= 49150 and click run
• Note: I read somewhere that it should be increased by X2 each time

I increased this all the way to 3145600 kb (yup 3.14 GB) and it still did not work so it must not be a memory issue.

• Did you look for an answer in 1) SPSS Command Syntax Reference, 2) SPSS Algorithms document? Aug 31, 2016 at 11:51
• SPSS Command Syntax Reference only appears to mention Mauchly's test in passing. The SPSS Algoritms document only explains how Mauchly's test is preformed, it does not mention any limitation on size etc. Aug 31, 2016 at 15:13
• I also noticed that R function anova_test doesn't support Mauchly's test results in some cases. Maybe the reason is as follows? As part of Mauchly's Test calculation, you need to have an Eigenvalues vector of a matrix based on the covariance matrix. In some cases, there are no Eigenvalues (the algorithm to calculate eigenvalues doesn't convergent)
– OB1
Aug 15, 2022 at 12:46
• It would be surprising if any decent software were subject to this problem and, if it were, it did not issue an error message.
– whuber
Aug 15, 2022 at 17:06