Need help interpreting Standard Error and Standard Deviation


In another post on SPSS forum I discussed Order effects where I split file on SPSS by order and conducted an independent t test looking at the effects of group on the DV.

I found that the original result was only evident in order 1 and not order 2... however on the second order one of the experimental groups has mean: 5.82, SD=3.401 and SE= 1.025. all the other descriptive stats have standard errors below zero.

Of course, I have checked that the data is normally distributed using skewness and kurtosis z scores as well as Shapiro-Wilk tests.

I was wondering if it can be interpreted that the variation around the mean is large and as such the mean does not reliably reflect the population mean despite being within the bounds of statistical such the lack of effect coupled with the large variation in score within one experimental group makes conclusions about its nonsignificance problematic. The mean differences for order 1 effects of experimental group on DV= 2.091 and Order 2= 2.000.

I don't know if I can introduce that interpretation because I'm not sure if it's viable or too much open to interpretation...

Any help would be greatly appreciated!


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You confuse me when you keep using the word order, j cant follow what you are actually examining.

With attest you have to test the equality of variance between the two groups, did you do that?

Also please provide more details.
Firstly, thank you for responding! :)

When I am referring to Order, it relates to the order of two tasks within my experiment. My experiment investigated the effect of motivational state (IV-two levels)on categorisation and probabilistic reasoning. One task relates to categorisation DV and one to probabilistic reasoning.

I found an effect of experimental group on categorisation, specifically category inclusion of non-prototypic items (sum of yes responses). However, if I split my SPSS data file by Order (order 1=categorisation task first, order 2=probabilistic reasoning task first), I find that the significance only lies within order 1. The mean difference between experimental groups for order 1 split is 2.091, for order 2=2.

However, looking at order 2 data, the descriptive statistics for one experimental group look like there is a lot of variation around the mean [as reported in pervious post], such that it may be unreliable. I did look at levene's test for both order 1 and order 2 comparisons- it was significant for order 2 so I wrote down (temporarily) the equal variances not assumed inferential stats.

I also looked at box plots and interquartile range- the interquartile range for the experimental group with descriptive stats variability was 6 compared to 2's and 3's for all other plots, it also has a rather long whisker representing the top 25% upper quartile range.

I am not sure if I can interpret much from this regarding whether there is any statistical vulnerability here which I might discuss further in discussion?

What may be of interest or further confusion I don't know. If I remove split file, so analysis incorporates all data and perform a two way ANOVA with order and group being two fixed factors and categorisation as dependent variable I find no significant interaction, suggesting (I think) that the effects of group on the dependent variable are not different for order 1 compared to order 2... but as discussed above, when I split file by order and perform independent t tests looking at the effects of group on categorisation, I find that order 1 find a significant difference in categorisation score between groups and order 2 does not.

I am confusing myself, I think I am clearly misinterpreting or missing something here. Any help you can provide would be incredibly useful at this point!

Thanks again for your initial response and I look forward to hearing from you soon, I hope :)
Firstly, thank you for responding!

I have posted my reply in a separate message on the thread I think, so just replying here so that you're notified. Sorry, new to this :/
I should also mention that regarding the two way ANOVA the Levene's test was significant... Does that mean, with that assumption violated and unlike the t test (where I can instead report equal variances not assumed stats) I should not report those stats first and go straight into reporting t tests? (I have read about bootstrapping, trimming and mean estimators etc. but I have not been taught those on my undergraduate course and after reading the text book I wouldn't feel comfortable attempting it...I have successfully computed several square root with reflection transformations for some of my other variables, however the variable in question has normal skewness and kurtosis z scores however as mentioned before SD and standard error of means for one group in Order 2 are large (according to the t test) and it is the same Order that the levene's test was violated.

I hope you understand some of what I am writing because I am managing to confuse myself so I'm guessing no one is going to be able to follow my ramblings :/ Sorry :(