# Paper Helicopter Experiment Doubt

##### New Member
I have to do a Statistics homework related to the “Paper Helicopter Experiment”.
Well, one of the most problematic questions is the last one:

Compare two different helicopters, one exactly equal to the model of figure 12.1 and one that has two clips at the base instead of one. Release them alternately 30 times from a height of 8 feet, recording the duration of each flight. Verify if there are diferences between the duration of flight of the two helicopters.

I used two different methods, without and with Bootstrap.

What I really want to know is what is the best method that should be used without using Bootstrap. Is the Empirical CDF a good choice?

Thanks!

#### Miner

##### TS Contributor
A simple 2-sample t-test would be appropriate provided the assumptions have been met.

A t-test?

##### New Member
Thanks, Miner. Let me analyse it carefully. And what about the Bootstrap, is it ok?

Edit: Well, the t-test assesses whether the means of two groups are statistically different from each other, so this analysis is appropriate whenever I want to compare the means of two groups and especially appropriate as the analysis for the posttest-only two-group randomized experimental design... as this case, right?

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#### Miner

##### TS Contributor
Out of curiousity, what class is this? I am surprised they did not teach you the t-test before bootstrapping.

Bootstrapping is not appropriate in this situation unless they simply want you to perform the test as a learning tool. Bootstrapping is typically used in three situations:
1. The distribution is unknown or complex. These data are normally distributed.
2. The sample size is too small. Your sample size was definitely sufficient.
3. You need to perform power calculations using a small pilot sample to determine the appropriate sample size for the study. That was not your situation.

Your bootstrapping did not calculate the interval for the two helicopters, so it was incomplete. You can infer differences if the two intervals do not overlap. But standard confidence intervals may overlap up to 30% and there still be a difference.

The t-test is appropriate for a two group randomized experimental design provided the groups are independent. If you perform a pre-test and post-test on the same subjects, you would use a paired t-test.

##### New Member
My teacher just gave a brief explanation about the t-test. And if I had N=10 (small sample size) for each helicopter? Would be Bootstrap appropriate? [your point 2]

#### Miner

##### TS Contributor
You would definitely be moving into a direction where the effectivity of the t-test would be strongly impacted by the difference in means that you want to detect as well as the standard deviation of the samples. I have not used bootstrapping enough to know how well they perform at those sample sizes.

##### New Member
Ok... to build the table, you used Analysis ToolPak, right?

This is what I concluded:

"The t-test evaluates if the means of these two groups are statistically different with each other.

H0
µ1=µ2

H1
µ1≠µ2

This situation defines a two-tail test, in which the rejection zone is distributed equally in both distribution tails.

t-stat> t critical two-tail
P(T<=t) two-tail=4,35448E-12<0,05

In these conditions, H0 is rejected so we can conclude that, with a significance level of 5%, that the means of the 2 groups are different."

#### Miner

##### TS Contributor
Correct. I used Analysis ToolPak.

##### New Member
Nice. The thing that is problematic is how to use bootstrap in this case (because the teacher suggested that). Thanks a lot, Miner!

##### New Member
My teacher said that a location test could be used for this. A t-test is included in this group, right?

#### hlsmith

##### Omega Contributor
Miner,

I agree with the first part of this, but the 30% seems fairly large and specific. Is there literature out there that cites this approximate number or close to it?

You can infer differences if the two intervals do not overlap. But standard confidence intervals may overlap up to 30% and there still be a difference.

#### Miner

##### TS Contributor
My teacher said that a location test could be used for this. A t-test is included in this group, right?
A location test is a hypothesis test performed using the location parameter of a distribution. It's a pretty broad class of tests, which does include the t-test.

#### Miner

##### TS Contributor
Miner,

I agree with the first part of this, but the 30% seems fairly large and specific. Is there literature out there that cites this approximate number or close to it?
Don't overlook a key phrase "may overlap up to 30%", specifically the words may, and up to. I am not implying that this happens all the time, but can happen under certain circumstances.

The following is a reference from Cornell University on how CIs may overlap and the difference still be significant.

This reference contains an example of a 24% overlap from American Society for Quality.

##### New Member
Hi, again.

My teacher said that I can't use t-test because the conditions of application aren't verified. I really don't know why he said that: my samples are independent and big (N=30). :\

Would be MANN-WHITNEY-WILCOXON test appropriate?

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#### Miner

##### TS Contributor
Your teacher probably means the assumption of normality and equal variances. Test for those assumptions. The t-test is robust for non-normality with sample sizes > 30. If the variances are not equal, there is another version of the t-test that does not assume equal variances.

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#### Miner

##### TS Contributor
What did the tests for normality and equal variances show?