Test of Significance advice needed

[SomeGuy]

I'm currently in high school doing my IB. I've been sifting through hundreds of CAT scans and x-rays that have been kindly donated to me by various hospitals and I am in need of some help. I've come to the hardest part, the statistics

I'm going to give a hypothetical example of what I'm investigating and wonder if anyone can help.

I've collected a large amount of data with measures the anatomical distance between the inferior anterior border of the maxilla to the inferior aspect of the nasal bone. I have around 900 instances of it being 2cm and the remaining 200 being around the +- 1.5cm region. While this may appear statistically significant it may not be clinically significant which is another issue all together. BUT I'm wondering what test I should use to should that these results are significant? If you link to any tutorials in addition I would be extremely appreciative.

Thanks in advance.


EDIT example of my data:

DISTANCE
2.0
2.0
2.0
2.0
1.5
2.0
2.0
2.0
2.5
1.5
2.0
2.0
2.5
3.0
2.0
2.0


1

[oparairoegbu]

I assume that the data you have are measures of anatomical distance between the "inferior anterior border of the maxilla to the inferior aspect of the nasal bone". The data set consists of 1100 data points (900+200). You talked of test of significance. Before one conducts a statistical test, there must be a hypothesis (or claim) you or someone is making about the distance you are measuring. For instance, the claim could be something like 'the mean distance of the inferior anterior border of the maxilla to the inferior aspect of the nasal bone is.....'
If there is such a claim, it is then possible to conduct a test to show whether the claim is true or false: in other words, test of significance. oparairoegbu

[SomeGuy]

I assume that the data you have are measures of anatomical distance between the "inferior anterior border of the maxilla to the inferior aspect of the nasal bone". The data set consists of 1100 data points (900+200). You talked of test of significance. Before one conducts a statistical test, there must be a hypothesis (or claim) you or someone is making about the distance you are measuring. For instance, the claim could be something like 'the mean distance of the inferior anterior border of the maxilla to the inferior aspect of the nasal bone is.....'
If there is such a claim, it is then possible to conduct a test to show whether the claim is true or false: in other words, test of significance. oparairoegbu

Hey, sorry but I do have a hyptothesis that is:

H0 = Distances recorded are by chance
H1 = The mean distance of the inferior anterior border of the maxilla to the inferior aspect of the nasal bone is 2.0cm

[SomeGuy]

I decided on performing Chi Square test then comparing the individual x^2 results. If anyone has any other suggestions feel free to post them :P

[jbc165]

I wouldn't use a chi-square test. I think a one sample t-test would be best.

This tests the hypothesis that the mean value of a group is not different than some specified value. In your case, 2 cm.

JBC

[Dason]

To be honest you can't actually test the hypothesis that are listed. It's a lot harder to show that there isn't a difference than to show that there is a difference. You would be interested in looking up what is known as equivalence testing.

[oparairoegbu]

Based on the data you have, if you set up hypotheses like these:
H0 = The mean distance of the inferior anterior border of the maxilla to the inferior aspect of the nasal bone is 2.0cm
H1 = The mean distance of the inferior anterior border of the maxilla to the inferior aspect of the nasal bone is not equal to 2.0cm,
it is testable using Z test (owing to large sample size) for a single mean, either for the entire 1100 measurements or for the 200 that were deviating from 2.0.
Or if your concern is to show that the measurements are purely random, then there has to be an additional assumption that the measurements follow a certain distribution before you can do a chi-squared goodness-of-fit test.

[SomeGuy]

To be honest you can't actually test the hypothesis that are listed. It's a lot harder to show that there isn't a difference than to show that there is a difference. You would be interested in looking up what is known as equivalence testing.

To clarify are you saying I should do a test of equivalence, they will fail the test as they are not equivalent and therefore that will demonstrate that the results are significant?