Question

1) Bootstrap sampling. Its importantance and usefulness
2) Explain Factorial Experiment , with understandable example, interaction , contrast etc everything related to factorial.. I don't have any idea

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Answer 1

1 BOOTSTRAP SAMPLING

It is a resampling method by independently sampling with replacement from an existing sample data with same sample size , and performing inference among these resampled data. Bootstrapping and use samples to draw inferences about populations.These procedures treat the single sample that a study obtains as only one of many random samples that the study could have collected.

IMPORTANCE & USEFULNESS

If you are doing inferences about the mean of the population, than you can rely on central limit theorem and build a statistic for that. The same for variance. Bootstrap works for any kind of statistic, this is where it lies its power. It's simple, and does require only minimal assumptions.

It works in the limit. For small samples it can go wrong more often.

It is very useful because you can build not only estimates of the population parameters, but also estimations for confidence intervals of p-values

it helps sample or assumptions if inferences produces too different results, it makes you think or re-evaluate your setup.

2 Factorial Experiment

Factorial experiment is an experiment whose design consists of two or more factors, each with discrete possible values or "levels", and whose experimental units take on all possible combinations of these levels across all such factors. experiment allows the investigator to study the effect of each factor on the response variable, as well as the effects of interactions between factors on the response variable.

The simplest factorial experiment contains two levels for each of two factors. Suppose an engineer wishes to study the total power used by each of two different motors, A and B, running at each of two different speeds, 2000 or 3000 RPM. The factorial experiment would consist of four experimental units: motor A at 2000 RPM, motor B at 2000 RPM, motor A at 3000 RPM, and motor B at 3000 RPM. Each combination of a single level selected from every factor is present once.This experiment is an example of a 22 (or 2×2) factorial experiment, so named because it considers two levels (the base) for each of two factors , producing 22=4 factorial points.

A factorial experiment allows for estimation of experimental error in two ways. The experiment can be replicated principle can often be exploited. Replication is more common for small experiments and is a very reliable way of assessing experimental error. When the number of factors is large (typically more than about 5 factors), replication of the design can become operationally difficult. In these cases, it is common to only run a single replicate of the design, and to assume that factor interactions of more than a certain order (say, between three or more factors) are negligible.