ANOVA and t-test are not testing the same thing from the data, and the two tests are not being conducted on the same data set. The F-statistic represents the ratio of treatment variance to error variance, whereas the paired-samples t-statistic represents the ratio of the mean difference and the standard error of difference scores. Thus, you should not use the result of one to make a decision about the result of the other.

While it's still common practice to follow-up ANOVA with t-tests, this practice really makes no sense.

Yes I know that, but how to conduct pairwise comparisons if I have significant interaction. There is no option for post hoc test, because I have 2 levels.

See this video (time 8:19) https://www.youtube.com/watch?v=IxMdfoklcnM&t=590s

Don't bother with t-tests. In the repeated measures ANOVA dialogue box, click on "EM Means". Move your factors (including the interaction term) to the box on the right where it reads "Display Means For". Check the box next to "Compare Main Effects". Specify a Confidence Interval Adjustment. I suggest either LSD or Bonferroni. Click OK.

You can use post hoc tests even controlling for "subject". R, for instance, provides the function glht() from the package multcomp.

Apart from that, you do NOT have contradictory results. The direction of the interaction is conclusive but the data is not sufficient to make conclusions about the direction of the simple or the main effects. You could only talk about a contradiction when the simple effects were also significant but leading to the opposite direction of the interaction (what is logically impossible).

Correction - that should be the "EM Means" button, not "Options".

Dear Blaine,

Thank you for your suggestion. I already did it, but again, there are no p values for pairwise comparisons in SPSS output. I have only the main effect of time, limb, and interaction.

A one-way ANOVA was used to compare the group categories of a specific variable (e.g. biological samples), for the mean values of continuous variables (e.g. trace element levels). The main purpose of using one-way ANOVA is to examine whether there are significant differences in the mean values of trace elements across groups. In general, an F-value test is calculated which represents the variance between the groups divided by the variance within the group at the level of significance (P < 0.05). The values of Sig. and F are used to evaluate whether the differences between the levels of trace elements over study groups are significant. If the Sig. value is less than 0.05, then there is a significant difference among the mean values of the trace elements across the groups.

Reference:

1- Field, A. (2009). Discuvering statistics using SPSS. 3th Edition, SAGE Publication Ltd., Los Angeles, USA, 1-780.

2- Hair, J.F., Black, W.C., Babin, B.J. & Anderson, R.E. (2010). Multivariate data analysis, a global perspective. 7th Edition, Person Education, Inc., New Jersey.

3- Miller, J.N. & Miller, J.C. (2010). Statistics and Chemometrics for Analytical Chemistry. 4th Edition, Pearson Education Limited, England, 1-272.

Emilija Stojanović If you've set up the data correctly in SPSS, you should see a table in the output labeled "Pairwise Comparisons" beneath the Time*Limb interaction term with a column in the table labeled "Sig". Unfortunately, I can't see how your data were entered. Could you share a screen shot of your data in the Data view tab?

Blaine Tomkins,

Please find attached. Thank you for your efforts on this one.

Dear Emilija,

I hope the comments of the others researchers were useful.

About the possibility of post doc in the interaction and 2 levels, maybe you can ask the post hoc changing the sintaxe on SPSS. In the repeated measures analyses, before run the analysis, click on "paste". and define the posthoc.

For example, in an analysis considering 3 moments and 3 groups, I also don't have the post-hoc of the interaction sport_group*factor1[time]. So in the sintaxe of interaction I define the post doc:

/EMMEANS=TABLES(Sport_group*factor1[time])

I change for

/EMMEANS=TABLES(Sport_group*factor1[time]) COMPARE (Sport_group) ADJ(BONFERRONI)

or

/EMMEANS=TABLES(Sport_group*factor1[time]) COMPARE (factor1) ADJ(BONFERRONI)

Emilija Stojanović Thank you for sharing the output. I see the issue now. This older version of SPSS (v.19) doesn't have the post hoc option for interactions in repeated-measures ANOVA included.

I'm not sure which version of SPSS included this additional feature ("EM Means"). More recent versions have post hoc analysis for interactions included in rANOVA as you can see in this example (see Section 4 & 10):

https://statistics.laerd.com/spss-tutorials/two-way-repeated-measures-anova-using-spss-statistics.php

If you are unable to update SPSS to a more recent version, I second Jochen's suggestion to use R (which is free).

What is your response variable? Did you do something between time 1 and time 2, and do you have an expectation for how that might affect the response variable? For example, if the response variable is time and you expect the intervention to halve (or some scalar) the time taken, the procedure you describe would not be appropriate.

Dear Daniel Wright,

Thank you for your response. I have within subjects limb to limb (injured vs. non-injured) differences in peak torque recorded across two time points (pre and post-intervention).

Regards

Thanks Emilija, This is not an area I know about, so excuse this if it is naive, but suppose the limb to limb pre measurement is 100cm and 50cm for two people. Would you expect the intervention to say add 10cm to these (so expected values of 110cm and 50cm), increase it by some amount, so 10% (so expected values of 110cm and 55cm), or something else (like pre score times some unknown multiplier plus a constant)? What I am thinking about is there subtracting the scores is the right way for comparing them. Most of the other responders are assuming this, so this may be the norm in this area, but it is worth me asking. And if I am wrong I get to learn! Dan

Thanks Daniel for your efforts.

As I said, we have within subject design.

E.g.

pre intervention values - Injured leg 30 cm, non-injured 45 cm for the same subject

post-intervention values - Injured leg 42 cm, non-injured 45 cm for the same subject

So we expect improvement only on the injured leg (interaction effect). We do not have mixed ANOVA [with between subject factor (control and exp) and within (pre vs. post)]

Emilija Stojanović

>I have within subjects limb to limb (injured vs. non-injured) differences in peak torque recorded across two time points (pre and post-intervention).

Intervention acts on both legs (injured and non-injured) ?

Dear Olga,

Thank you for your interest. No on both, intervention acts on the injured leg.

Hi Emilija Stojanović , so you expect no change for the control limbs, but my question is not whether you predict any improvement, but if you if you predict the improvement to be related with the pre amount and how. By using the difference (post-pre) you are making assumptions about that, but I was just asking how you choose this over alternatives, like the intervention's improvement would be something different, like an increase of X%.