Comparing Data Sets Basics I'm posing a question on behalf of my daughter who is participating in an elementary school science fair.
She has two sets of data, A and B. Both are test scores given to students. The B set are scores of the students writing the test under certain special conditions. This experiment is to measure the effect of those conditions (ie, make it more or less favorable to writing a test).
The number of students in A and B are the same.
Her question is what is the best way to compare the data of A and B to determine whether there is a significant difference created by the conditions.
She is in grade 7, and I have never studied stats, so please be detailed in your answer. 
Thanks in advance.
 A: 
Her question is what is the best way to compare the data of A and B to determine whether there is a significant difference created by the conditions.

In the case where you are dealing with a student in Grade 7, I would recommend that it is best not to concern yourself with the best statistical technique available (which will be far above her year level), and instead focus on what a person in that grade level can implement with a proper understanding of what she is doing.  In this kind of problem there are five main things a professional scientist/statistician would do, and your daughter can reasonably be expected to do the first four of them (though not to the level of a professional).


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*1. Structure the report in the standard format for a scientific paper: It would be a good idea for your daughter to explain her experiment and its results in the standard format used in scientific papers: introduction; method; results; discussion.  There are a number of online resources that describe this format.  The important thing is to be strict, and not to allow these sections to bleed into each other.  She should start by introducing the research question, then describe the methodology, then describe the data and the results, then discuss the inferences she is making from that data and her conclusions with respect to the research question.

*2. Describe the experiment clearly, using appropriate statistical/experimental terms:  To do this, I would recommend that your daughter read some basic material on experimental design, and learn about "controlled experiments", "randomisation", the "control group" and the "treatment group".  (Here is an example pitched at High School students.)  She will need to consider how the students were allocated to the groups (where they randomly allocated, or allocated by some other procedure?) and why this matters.  She will also need to understand the distinction between a "causal relationship" between the variables, and a "statistical association".  Her explanation should explain what she is trying to learn from the experiment and how the method allows her to learn that.

*3. Plot the data in an appropriate way: The best way to get an understanding of the data is through a picture that allows the reader to properly visualise what has happened in the experiment.  You have said in your comment (accidentally posted as an answer) that groups A and B are two separate groups of students.  This gives you two separate groups of numbers, so it is usual to plot these either as a pair of histograms or as a pair of densities (e.g., in a violin plot).  Ideally these should be plotted side-by-side so that the viewer can easily see if one set of numbers is higher (or more spread out) than the other.  Note that a histogram is a simple plot that can be constructed manually, so your daughter could draw this herself, so long as she takes care to measure her lines and right-angles carefully.  A density plot (and violin plot) is more complicated, and would have to be drawn by a computer; the actual construction of this plot might be more complicated than she can fully understand, but she should be able to roughly understand the result.  Whatever plot she chooses, it should be one that makes it easy for the viewer to visualise the results.  (Make sure she remembers to include a title, axis labels and units, and clear numbers on the plot.)

*4. Report some basic descriptive statistics: For this kind of data, in combination with a good plot of the data, it would probably be sufficient for your daughter to calculate and report the sample mean and sample standard deviation of the data.  (Here is a simple explanation with examples.)  This information could be included in an appropriate place on your plot, or reported separately in a clear and simple way.  This quantitative information will augment the plot of the data, and it should allow the reader/viewer to get a good understanding of the location and spread of the two groups of data.

*5. Hypothesis test/confidence interval/modelling (probably beyond high-school level): With this kind of data a statistician would normally conduct a "hypothesis test" to test whether the treatment has increased the underlying mean score, or construct a "confidence interval" of the underlying mean difference.$^\dagger$  These are relatively simple tests that are usually taught in the first-year of an undergraduate degree, but they are above the level that would normally be taught to a high-school student.  It might be possible for your daughter to conduct a test of this kind using online tools that do it automatically, but it is unlikely that she will be able to understand how this test is derived and why it works the way it does.  For a high-school level project, I would personally consider this unnecessary, but you could seek clarification from the teacher if needed.
Given that this is a high-school level project, I would recommend that your daughter create a report/poster (or whatever is the required output) that uses the standard format for a scientific report, and clearly explains the research question, the experimental methodology, the results, and her discussion of those results.  In the absence of formal statistical testing, her discussion would have to involve some speculation of whether the difference between the groups looks "big enough" to be more than just random variation (which is what a formal test is checking).  I am not a high-school teacher, so I cannot say what the expected level is here (the youngest students I teach are first-year undergraduates at university).  Notwithstanding this, I would imagine that at a high-school level it should be sufficient to give a good description of the experiment, and show the data with a good plot and basic descriptive statistics.  A university student would be expected to conduct some "modelling" of the data, which would implement statistical methods to make inferences about the underlying means of groups going beyond the actual observed cases, but these are techniques that could only be understood superficially (at best) by someone in Grade 7.

$^\dagger$ Incidentally, one technical point on your question.  You say that she wants "to determine whether there is a significant difference created by the conditions".  The idea of a "significant difference" is a misleading way to talk about it.  Statistical "significance" refers to the magnitude of evidence for a non-zero difference between groups, not to the magnitude of the actual difference.  To avoid confusion, when using terms like "significance" or "statistical significance" one should always refer to "significant evidence of a difference" rather than to a "significant difference".
