Estimated effects may be unbalanced

General
1

Is this going to affect the outcome of my data analysis? It shows I only have 44 degrees of freedom when my dataset has 45 data points and 5 factors (see upload). If so, do you have any suggestions to correct it?

2021HelicopterPlanWithResponseData.pdf (44.0 KB)

Here is my code:
copter<-(aov(hang.time.in.seconds~Wing.Length,data=data))
copter

Here is the output:
Call:
aov(formula = hang.time.in.seconds ~ Wing.Length, data = data)

Terms:
Wing.Length Residuals
Sum of Squares 3.430733 4.388044
Deg. of Freedom 4 40

Residual standard error: 0.3312116
Estimated effects may be unbalanced

2

what is the statistical question or goal that you are investigating that this data and attempted aov approach is in aid of ?

3

I have no idea what the professor is looking for as we used paper helicopters to run the experiment and collect the data. Any help you can give me in this matter is greatly appreciated.
The assignment requires us:

  • Perform ANOVA on the data. Interpret the results.

  • Check the ANOVA assumptions. Are they satisfied? Explain. Be sure to address each one using appropriate tests and graphs.

  • Run Fisher's, Tukey's, the Student-Newman-Keuls, and Dunnett's multiple comparison procedures and report the results and conclusions. For Dunnett's, use the treatment with the smallest wingspan as the control group.

  • Check if there is a significant linear or quadratic trend in the flight times as a function of wing length.

4

This seems pretty clear as far as instructions for you to follow. I would guess that addressing them, means considering the assumptions and assessing whether they are held or violated...
The error does seem to point to the truth that your data is unbalanced, violating at least that assumption.
So isn't that the end of the matter on that point ?

5

No, I asked if there was a way to correct it.

6

I dont see how you could correct that your data is not balanced, and that balanced data is an assumption for AOV
I can only think that you might gather more data under a balanced experimental design so that you have balanced data. I'll be interested myself to see if Stats experts see this thread and offer other alternatives.

7

So, let's start with the question what it means when your data is unbalanced? Once you can define what that means, you can say whether you can "fix" it.

8

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