Two-Way ANOVA without replication

[#1]

Hey all

I have the data table as mentioned here below.

Factor A is Day/Night

Factor B is Depth

the dependent factor is Distance per hour.

When I try to do Two-Way ANOVA without replication, I get these tables:

What I'm doing wrong? Why do I get LostDf's?

[#2]

I'm trying to write results section, something like:

The two-way ANOVA was performed to analyze the effect of the diurnal cycle and depth on the distance A. bannwarthi pass every hour. the test revealed that there [was or was not] a statistically significant interaction between the effects of diurnal cycle and depth (F(df interaction, df within) = [F-value], p = [p-value]). Simple main effects analysis showed that diurnal cycle [did or did not] have a statistically significant effect on the distance A. bannwarthi pass every hour (p = [p-value]). Simple main effects analysis showed that depth [did or did not] have a statistically significant effect on the distance A. bannwarthi pass every hour (p = [p-value]).

but I can't the info needed to answer it (or the info is in the screenshot but I don't understand it)

[#3]

Welcome to the community.  You are getting lost DF's because you don't have enough DF's for the model you have entered.  Since you have Depth as a nominal data type, it has many levels and as such has "consumed" all of the DF's.  Try setting Depth to continuous and re-run the fit model.  Note, I wrote this reply prior to your explanation and it is best to just attach your data table rather than a screen shot of it.

[#4]

this is what I get now:

If I understand correctly:

The two-way ANOVA was performed to analyze the effect of the diurnal cycle and depth on the distance A. bannwarthi pass every hour. the test revealed that there was not a statistically significant interaction between the effects of diurnal cycle and depth (F(1,39) = 3.6247, p = 0.0649). Simple main effects analysis showed that diurnal cycle did have a statistically significant effect on the distance A. bannwarthi pass every hour (p = 0.0479). Simple main effects analysis showed that depth did not have a statistically significant effect on the distance A. bannwarthi pass every hour (p = 0.7226).

I've attached the data table as a file.

[#5]

Here are my thoughts:

1. First, before you do any statistics, you should determine if the data is meaningful from a subject matter perspective.  How much of a change in the response distance/hour is of practical value to you the SME?

2. How was the data acquired? (e.g., Is this data from a directed sampling plan, randomly acquired or from an experiment?)

3. Visualize the data using graphical methods (e.g., Graph Builder).  Are there any unusual data points?  It appears there is more variation within Day/Night than between and the within Day is more than within Night?  Why?

4. When you run fit model, you can look at the Prediction Profiler.  Grab the vertical Red line for the Day factor and move it to night, watch how the effects on Depth change.  This is a visual of the interaction.

5. Always assess your model.  Look at residuals.  They appear to be quite "funky" (Non-constant variance, and potentially some outliers) meaning you should re-evaluate your model.

Be careful of just using p-values.  They are meaningless unless you understand the sources of variation used to estimate the mean squares for the terms in the model and most importantly the MSerror.

I re-attached your data table with some scripts to get you started.

[#6]

First of all, thank you for your answers!

I'm a marine biology master's student, and unfortunately, we didn't learn biostatistics to a reasonable level.

1. can you please explain what you mean?

2. the data was acquired through dives and measurements in the field throughout six dives (two night dives tagged as day and two day dives tagged as night).

3. There was one unusual point for the day when I did the box plot chart.

4. I don't know how, but I'll try to find out.

5. I don't know how to read what I get from JMP except for very few things. Things like residuals and such are not things I've learned.

We mostly learned how to calculate the tests by hand; in Excel, we didn't learn the essential things.

And once again, thank you for your help!

[#7]

In addition to @statman 's excellent points...this is not a two way ANOVA.  It is an ANCOVA model (Analysis of Covariance) with Depth as the covariate (regressor). This model, with the interaction term and term for Day/Night, is basically fitting a different regression line (different slopes and intercepts) for each level of Day/Night (one line or Day, and one line for Night). If you remove the interaction based on its p-value, the lines are parallel but with differing intercepts. In the full interaction model you show, the slope for day is 0.107+0.57, the slope for Night is 0.107-0.57. In the "estimates" menu (red triangle in Fit Model results) choose Show Prediction Expression to understand what you are looking at wrt parameter estimates so you can communicate results more effectively.