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Following experimental design was done and some data as shown in table below was obtained:

pretest> intervention1> intervention2> posttest > perception survey

Number of students=60

Number of Students subjected to intervention=20

Independant variable is "Intervention2" which possible influences posttest .Perception survey is the students own evaluation of the intervention, lower the better.

pretest posttest intervention1 intervention2 perceptionrank

37  35  10  10  4.2
38  28  8   10  2
20  30  8   10  #N/A
34  22  10  10  1.7
28  21  10  10  3.2
23  19  8   10  3.5
14  8   10  10  2
26  33  7   8   3.2
24  35  8   8   2.2
33  21  7   8   1.8
29  25  7   8   2
36  20  7   8   2.9

The subjects were students in the same classroom, the interventions were also evaluated , the score for which is also tabulated above. What I am interested to find the causality between intervention2 and posttest scores.

How should I go about solving this problem , should I use t-test , correlation and how?

Update:

I forgot to add that the control group is the students who did not receive the interventions , so I have their pretest and post test scores.

Moreover I also have perception survey scores for the students who received the intervention.

stats101
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  • Are interventions 1 & 2 different experimental conditions to which the students were randomly assigned? Is one a [control condition](http://en.wikipedia.org/wiki/Treatment_and_control_groups)? – Nick Stauner Jan 09 '14 at 07:57
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    I updated the answer @NickStauner , interventions 1,2 are similar interventions to randomly assigned students. – stats101 Jan 09 '14 at 09:44
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    Please tell us your complete design. Who got which intervention? How was that determined? Why did you measure perception rank? What is your N? What are you trying to find out? (Causality can only be established in some very limited circumstances). – Peter Flom Jan 09 '14 at 11:48
  • @PeterFlom updated in the question – stats101 Jan 09 '14 at 11:57

2 Answers2

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If you didn't have a control group, you can't really establish causality (as far as I know, though you might be able to rule it out to whatever extent your results show no relationship at all). If you edit your question or respond to my comment with clarification of whether you did, I'll edit my answer to suit.

Correlations estimate the (strength and direction) of relationships; $t$-tests estimate , and thus involve . I suspect you'll want to do all of the above to squeeze as much info as you can out of your data, but you don't really have to just to "find [some information about] the [potential] causality."

You should probably look a little further into the differences between effect size estimation and significance testing, and develop more specific questions about the potentially causal relationship(s) in question. Some of the tags on your question can help you browse related topics here, and the tag wikis themselves contain nice, brief summary intros to the topics in general. Again, if you can edit your question to be a little more specific, leave a comment to let me know, and I'll try to edit to follow up.

Nick Stauner
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    The control group is simply the one who did not recieve the treatment , in my case about 20 students from a class of 60 received the treatment. – stats101 Jan 09 '14 at 09:48
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    I have added a sample perception ranks – stats101 Jan 09 '14 at 10:39
  • What do you want to do with those? – Nick Stauner Jan 09 '14 at 10:40
  • may be help in strengthening causality if it is there ? – stats101 Jan 09 '14 at 11:12
  • `perceptionrank` is a separate variable, so I'd need to know how it relates to the other variables to use it in analyzing any relationships among the other variables; otherwise it's going to entail separate questions that need their own answers. – Nick Stauner Jan 09 '14 at 11:15
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    perception rank is the users own evaluation of the positive effect of the intervention, lower the better. – stats101 Jan 09 '14 at 11:24
  • You're interested in some effect on the `pre`/`posttest` variables though, right? Their subjective evaluations won't necessarily help establish a causal relationship between group membership and change in test scores, unless the test scores somehow incorporate the information from their evaluations...? – Nick Stauner Jan 09 '14 at 11:27
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    some effect on posttest only, and I cant understand " the test scores somehow incorporate the information from their evaluations...?" – stats101 Jan 09 '14 at 11:44
  • Then you would probably want to run separate analyses on `perceptionrank` and leave it out of the analysis of `posttest`. – Nick Stauner Jan 09 '14 at 11:45
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    Both correlations and t-tests can be used to both test statistical hypotheses and as measures of effect size. They measure/test different things. – Peter Flom Jan 09 '14 at 11:46
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    @PeterFlom: wait a sec...didn't you agree with JeromyAnglim that $t$ is not [purely] an effect size [here](http://stats.stackexchange.com/a/59154/32036)? Did you change your mind? Please update that answer if you did! This seems valuable for definitional clarity. As for $r$, didn't you imply that a correlation must be combined with some information about sample size to test a hypothesis [here](http://stats.stackexchange.com/a/33092/32036)? I'd take that to mean a correlation alone (without distinct info on sample size) can't test a hypothesis, wouldn't you? "Can be used [with $n$]," of course. – Nick Stauner Jan 09 '14 at 13:17
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    Good point, @NickStauner. You are right, t is not purely a measure of effect size. It is impurely one! :-) . More precisely, the quantity measured by a t-test (differences in means, standardized) is an effect size. – Peter Flom Jan 09 '14 at 13:56
  • As you know, the pure effect size measured there would be [one of these](http://en.wikipedia.org/wiki/Effect_size#Effect_sizes_based_on_means_or_distances_between.2Famong_means) :) I find it useful conceptually to keep my effect sizes separated from significance tests until I really have a hypothesis worth testing, at which point an $r$ or a $d$ gets mixed with $n$ or $df$ to give me something different like a $t$. Then again, I'm probably the kind of person who would [object to someone getting peanut butter on my chocolate](http://youtu.be/DJLDF6qZUX0), unless I specifically wanted a Reese's! – Nick Stauner Jan 09 '14 at 14:36
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As a rule of thumb, testing for correlation will be done if you have one sample with two metric outcomes. Then you consider the alternative hypothesis "the lower one outcome the higher (lower) the other". Correlation alone is never causality.

Here, you have two samples (students with intervention2 and intervention1) with one outcome (posttest score). You would consider the alternative hypothesis: "Is the score due to intervention2 different from the score after intervention1?" This should be tested by a Wilcoxon test, the t-test's brother for not metrically scaled data (scores) --assuming you don't have to compare the change from pre- to posttest score. Otherwise you have a 2x2 nonparametric split plot design. But that's another question.

If the students have been assigned properly to the intervention groups, you may in fact infer causality.

Horst Grünbusch
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  • thanks,can you explain what is "nonparametric split plot design" – stats101 Jan 10 '14 at 12:57
  • Split plot design means that you have independent groups of subjects and dependent measurements (pre/post) per subject that you compare altogether (pre1-post1>pre2-post2). Nonparametric means that your data cannot be evaluated by metric methods (e.g. t-test, ANOVA), mostly because they are only ordinal or the distribution is completely unknown. – Horst Grünbusch Jan 10 '14 at 13:14
  • I only have two groups\subjects first who recieved the intervention and the other who did not – stats101 Jan 10 '14 at 13:22
  • Generally, if you want to compare the change of the two scores between intervention group 1 and intervention group 2, it's a 2x2 split plot. If you just want to compare the post scores between two groups, it's a usual 2-sample test (Wilcoxon, t-test). I hope this helps you and others. If you are still not sure about your particular data set, a statistical consultant might have a confidential look at it. – Horst Grünbusch Jan 10 '14 at 13:54