Statistics: How It is Used in Experiments

Statistics has demanded a lot. Unlike algebra or geometry, this specialty of mathematics has no single approach; where as the other fields can utilize foolproof formulas to solve a problem, with no side effects unless the applicant misinterprets the formula or utilizes it inappropriately. However, every increment of a statistics problem (or experiment or trial in a long-term study) must be applied correctly, or the data the researcher collects is rendered futile. It is also about knowing how to manipulate the data to your advantage. There is some important vocabulary included when sampling, because there is a lot of vocabulary included in statistics.

An important term within statistics is population, defined as the total group the researcher is interested in. Units are the individual elements of the population, and population size is the total number of units. A sample, on the other hand, is a subset of the population being researched. There are also distinctions within the realm of gathering data. A survey, for instance, is the information received from the members of a sample. Meanwhile, a census is a survey of the entire population, usually conducted systematically (by a set number of years). One important caveat when conducting with samples like these is to avoid bias.

A sampling method is biased if it gives rise to a sample where some characteristics of the population are represented too much or too little. An important rule to remember, though, is that the method of gathering the samples (not the samples themselves) is biased. This problem can occur when the procedure to generate samples systematically results in samples that constantly over or underestimate numerical characteristics (known as statistics in a sample, parameters in a population). There are several types of bias. A size bias occurs when the method favors units of one size or another. Voluntary response biases usually favor the population within the sample size that is interested in a researcher's study, not the average human. This bias can be amended with follow-ups from those who failed to respond. A convenience sample bias usually gathers samples within proximity, which also distorts the analysis of the data. However, problems can occur within personnel also. A judgment bias is when the expert you assign to gather the samples places his or her own biases in the experiment, causing distortion of the collected data. Fortunately, there are ways to avoid such trouble.

In the unbiased sampling method, every unit in the population has an equal chance of being chosen for the sample. Before sampling, the researcher needs a sampling frame. All possible samples of a fixed size are equally likely. Each unit has an equal chance of being in a sample. Simple Random Sampling begins by having a list of all units. Utilizing tools such as a random number table or a pseudo-random number generator can create samples without any bias. Stratified Random Sampling is performed by dividing the population into distinct, non-overlapping strata and then choosing samples within those strata. Cluster Sampling is performed by grouping the samples into clusters, then sampling within those clusters. Two-Stage Sampling is similar to cluster sampling, but applies randomization from within those clusters. Systematic Sampling labels the units within the population (or sample) with a number, but begins with one number and then chooses from a multiple of a number. This would be important to make your data within your experiment vital.

Experiments are used to determine causality, through comparison of two or more conditions (known as treatments) from responses. What the researcher controls in the experiment are the conditions, and what is measured is the response. Experiments are designed to eliminate confounding variables, because the effects of such variables are impossible to decipher, and a conclusion cannot be drawn. A good, randomized experiment is superior to an observational study in terms of drawing conclusions. Why? Experimental studies allow the researcher to be in control, while the treatments in observational studies are already part of the units under study. The procedure must also have the ability to be replicated, or repeated.

The experiment should be designed so that the different between treatment groups is large enough so the variation within each treatment group is not considered vital. Researchers must design experiments to minimize in-treatment variation so it is inconsequential compared with the variation between treatment groups. There are two types of designs: the Completely Randomized Design and the Randomized Paired Comparison Design. The Randomized Paired Design chooses one unit within each to pair to receive the treatment, and withheld from another. These two designs will aid in experiments that involve precision and accuracy in their results, which is naturally in all experiments.

The importance of statistics is very subjective, meaning that it varies from one individual to another. To some, it may allow authorities to alter current policies for the betterment of the community. To others, it allows people to manipulate data for their advantage, making their argument and reasoning concerning an issue much stronger. Still, some may say it can be a compliment, showing that society has finally achieved something. These are all legitimate, but the main thing is to truly learn of these ways in order to know how they are able to do such things.