# Dicken bettinger three principles of experimental design

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The formula above tells us that statistical power increases with sample size but decreases with variability standard deviation. One benefit to this type of statistical analysis is that it gives you a way to quantify what kind of sample size or statistical power your experiment needs in order for you to detect an effect if there actually is one, and how much statistical noise variability you are willing put up with given your resources. A more common method of reporting results is by using regression experimental design, where treatment effects are estimated as simple regressions on x variables representing factors related to treatments.

The important assumption behind these types of designs is that each factor has only additive effects on the response variable — instead of interactions between two or more factors, which can complicate predictions about treatment responses without additional information from experiments specifically designed to test these interactions.

Another statistical approach to designing experiments is the use of factorial designs, where two or more factors are simultaneously varied in order to study their effects on an output response and then fit a statistical model that explains how each factor affects the response variable. The main assumption behind this design type is that all possible combinations of factor levels have been used which may not be feasible for many applications especially when there are several factors affecting responses; however, it can provide valuable information about individual influences between factor variables or collinearities by studying both main effects and interaction terms at different settings of other independent variables.

It will also help you identify possible sources of bias that can lead to undesirable results. Finally, it will help you provide recommendations to make future studies more efficient. The Three Rs of Experimental Design An experiment involves one or more treatments, each with two or more conditions.

The defining characteristic of an experiment is that the researcher is able to assign subjects to treatment groups. There are three principles that underlie any experiment. In this experiment, a researcher assigned each subject to one of two different exercise training groups. The goal of this experiment is to compare their time to run a mile after training for four weeks. Randomization Randomization is the assignment of the subjects in the study to treatment groups in a random way.

This is one of the most important aspects of an experiment. It ensures that the only systematic difference in groups is the treatment condition. In the training experiment, this would mean that any difference in the outcomes between the two groups is due to the training. In other words, random assignment allows you to demonstrate causation.

Suppose the researcher did not randomize, and assigned men to one group and women to the other group. Randomization is the only sure way to avoid accidental confounding and its resulting bias. Replication Replication refers to having multiple subjects in each group.

The more subjects in each group, the easier to determine whether any differences between the groups are due to the treatment and not the characteristics of individuals in the groups. Suppose the training study had limited resources. Would it be enough to recruit only two people, and compare their times after training? The difference in outcomes would depend as much on those two people as it would on the training method. There are many considerations that go into determining sample size.

Generally, though, more subjects per group means more statistical confidence in the outcomes. Too few subjects in a group makes it very hard to find differences in the outcomes between treatment groups. Reduction of Variance Reduction of variance refers to removing or accounting for systematic difference among subjects.

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A more common method of reporting results is by using regression experimental design, where treatment effects are estimated as simple regressions on x variables representing factors related to treatments. The important assumption behind these types of designs is that each factor has only additive effects on the response variable — instead of interactions between two or more factors, which can complicate predictions about treatment responses without additional information from experiments specifically designed to test these interactions.

Another statistical approach to designing experiments is the use of factorial designs, where two or more factors are simultaneously varied in order to study their effects on an output response and then fit a statistical model that explains how each factor affects the response variable. The main assumption behind this design type is that all possible combinations of factor levels have been used which may not be feasible for many applications especially when there are several factors affecting responses; however, it can provide valuable information about individual influences between factor variables or collinearities by studying both main effects and interaction terms at different settings of other independent variables.

A third method commonly employed during experimental planning involves screening designs that allow experimenters to test larger numbers of treatments than they would typically be able to test under other designs. Statistical testing is conducted on the data resulting from each factor combination by examining whether it supports any of the hypotheses about its main effects and interaction terms.

It ensures that the only systematic difference in groups is the treatment condition. In the training experiment, this would mean that any difference in the outcomes between the two groups is due to the training. In other words, random assignment allows you to demonstrate causation. Suppose the researcher did not randomize, and assigned men to one group and women to the other group.

Randomization is the only sure way to avoid accidental confounding and its resulting bias. Replication Replication refers to having multiple subjects in each group. The more subjects in each group, the easier to determine whether any differences between the groups are due to the treatment and not the characteristics of individuals in the groups.

Suppose the training study had limited resources. Would it be enough to recruit only two people, and compare their times after training? The difference in outcomes would depend as much on those two people as it would on the training method. There are many considerations that go into determining sample size. Generally, though, more subjects per group means more statistical confidence in the outcomes. Too few subjects in a group makes it very hard to find differences in the outcomes between treatment groups.

Reduction of Variance Reduction of variance refers to removing or accounting for systematic difference among subjects. This allows you to measure the differences due to the treatment more precisely. There are multiple ways to approach this. One way is to limit the population of the study so the subjects are more similar. Another way is to incorporate covariates into the analysis. These are variables outside of the experimental design that you can measure. A third way is blocking.

This refers to identifying related subjects and randomly assigning them to different treatments. In the training experiment, not accounting for gender could make it more difficult to estimate the effects of training. There are at least three ways to account for it in the design and data collection.

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