Random treatment for same # in each category?

[DynV]

At the start of the lesson for 2 categories ANOVA, it seemingly made a reference to the previous lesson with 1 category (ANOVA), which the translation is

As a reminder, one-way ANOVA uses a completely randomized experimental design. A treatment (i.e., one of the levels of the tested factor) is randomly assigned to each of the experimental units. Here, the experimental unit depends on the experiment, but can be made up of a patient, a client surveyed by telephone, a quadrat, an aquarium, or a site, for example.

I've read a bit about random treatment and it seems like it's for cases in which the category can't be figured out ahead of time. This doesn't seem to be the case for this course. Both in the previous lesson, and I've just checked the examples of this lesson, all categories, including combinations of them, had the same # of samples and it very much look like the analysis was made knowing the category.

Could it be that the professor was confused, thinking the previous lesson has different # of sample in categories and that he'd be doing examples with different ones in this lesson (which all had same # of samples) ? In either case I'm having a hard time the previous quote about the lesson for 1 category ANOVA as well as the following about this lesson

In a two-factor experiment, we will assign randomly a combination of the two factors at each experimental unit.

I'd appreciate if the quotes were explained to me.

 

[BigBeachBanana]

At the start of the lesson for 2 categories ANOVA, it seemingly made a reference to the previous lesson with 1 category (ANOVA), which the translation is

I've read a bit about random treatment and it seems like it's for cases in which the category can't be figured out ahead of time. This doesn't seem to be the case for this course. Both in the previous lesson, and I've just checked the examples of this lesson, all categories, including combinations of them, had the same # of samples and it very much look like the analysis was made knowing the category.

Could it be that the professor was confused, thinking the previous lesson has different # of sample in categories and that he'd be doing examples with different ones in this lesson (which all had same # of samples) ? In either case I'm having a hard time the previous quote about the lesson for 1 category ANOVA as well as the following about this lesson


I'd appreciate if the quotes were explained to me.

A concrete example might help:

Suppose the researchers want to investigate the effect of different fertilizers and the impact of two watering regimes (Regular watering vs. Infrequent watering). Now, each experimental unit (pot) will receive a combination of a fertilizer type and a watering regime.

Each pot is randomly assigned a type of fertilizer (A, B, or C) and a watering regime (Regular or Infrequent).

A two-way ANOVA will be used to analyze the data. This statistical method allows the researchers to determine whether there are significant differences in plant growth based on the type of fertilizer used and whether there are any interactions between fertilizer type and watering regime. An interaction would indicate that the effect of one factor (e.g., fertilizer) depends on the level of another factor (e.g., watering regime).

 

[DynV]

So the part of the 2nd quote

[...] we will assign randomly [...]

only mean that we keep the order of the experiment, which supposition is that samples are to be random? That it we don't sort--between--the experiment and its analysis?

 

[BigBeachBanana]

So the part of the 2nd quote

only mean that we keep the order of the experiment, which supposition is that samples are to be random? That it we don't sort--between--the experiment and its analysis?

I interpret that phrase as a random allocation of treatments to the experimental units.
In experimental design, random assignment ensures that each experimental unit has an equal chance of receiving any particular treatment, thereby minimizing the potential for bias. Researchers do not pre-determine which treatment will be applied to each experimental unit. By randomizing the assignment of treatments, researchers can assume that any differences observed between treatment groups are due to the treatments and not to other factors.

 

[DynV]

I interpret that phrase as a random allocation of treatments to the experimental units.

What does that mean exactly? Maybe we can take for example 4 groups of 2 categories (eg 1st category letters, 2nd category numbers), with 5 samples per group (4x5=20) ? If you want an order, you can go to https://www.random.org/lists/ and paste

A1
B1
A2
B2

5X then click the Randomize button. Or maybe you have a better example?

 

[BigBeachBanana]

Start simple first don't want to get into sampling yet. It's another topic on its own.
Suppose you have 100 plants, 3 types of fertilize, and 2 water treatments. How do you pick which plant get which combination of fertilize and water treatments?

 

[DynV]

I'd put a label on each plant in order (eg for a square top to bottom, left to right), an ID # then the 2 categories (3 item per label), counting all the groups while doing so (a table for R language), then highlight the smallest of the 6 groups count. I'd then make 6 different storage spaces for plants of the size of the highlighted count, then keep rolling a 100 die (2X d10) picking the plant of that # if it's still in the initial location*, look at its label, then see if there's a storage space for it and if so put it there otherwise discard it, doing so until all 6 storage spaces are filled.
* 3 locations: initial, storage, discarded.

PS: I think I misunderstood you, I thought you meant all 100 had already been changed. If I'm to figure what to do with unchanged plants, I'd split them in 2 groups, then splitting each in 3 (or course there's no part of a plant so running floor() on that #), then assign each group to a different change.

 

[BigBeachBanana]

An approach the professor is hinting at is instead of dividing by groups just roll a dice.
Roll a 3-sided dice for each plant to determine the fertilizer, and flip a 2-sided coin to determine the water treatment. Based on independent events, you'd achieve roughly 1/3 of plants with different fertilizers and half with different the 2 water treatments.