# Statistics: Independent Variables and Noise Coursework

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Updated: Jun 30th, 2020

## Differences Between Multiple Independent Variables and Multiple Levels of Independent Variables

Variables are the aspects measured or manipulated by the researcher in a given study. They enable researchers to come up with the right strategy needed to organize the expected observations and findings effectively. Marking out the variables in research enhances the understanding of the test that is being carried out (Patricia, 2012). Also, the researcher can determine the key outcomes expected in the study they are conducting.

Multiple independent variables (MIVs) are varied. Also, they can be easily manipulated by a researcher to create different scenarios. However, they are not dependent on the alterations made on other variables in the study. Also, they are regarded as the presumed cause or antecedent of phenomena. In non-experimental cases (where influence is not present), MIVs are erratic. As such, they have some level of effect on multiple dependents (Orme & Orme, 2009). According to Orme and Orme (2009), MIVs are also referred to as status variables. The term is applied in instances where a researcher is unable to control or manipulate them.

Multiple levels of independent variables, on the other hand, are slightly different. They are the total number of experimental situations in a study. For example, if a researcher is making a comparison between five different varieties of diet, the multiple independent variables will have five levels (Orme & Orme, 2009). Multiple independent variables are better compared to multiple levels. The reason behind this is the manipulation factor that is present during experimentation processes.

## Blocking and Reduction of ‘Noise’

Blocking is the process of putting together experimental units in clusters. The clusters and experimental units are related to one another (Beins & McCarthy, 2012). The process reduces the known variability in the study. Also, it operates on the core principle of the belief that an advanced order interaction confounds an inconsistency that cannot be overcome. The aim is to get rid of the inconsistency’s influence on the end product.

Blocking reduces ‘noise’ through various strategies. For example, it enables the researcher to deal with the ‘nuisance’ factors in a study. It is noted that irritant or ‘nuisance’ aspects have some effect on the response (Walker, 2010). However, the process is of no significance to the individual experimenting. As a result, the researcher is expected to reduce the resulting variability at the end of the study.

Blocking has several disadvantages. For example, it is not effective in a large number of treatments. The reason is that the units of the experiment within a block must be homogeneous. Also, it is noted that the technical controls only a single extraneous source of variability (Walker, 2010). As such, other sources of noise are left out. Additional sources increase the error term. As a result, detecting treatment differences becomes a challenge to the researcher.

### A Factor and How It Benefits Design

A factor is a controlled, independent variable (Jackson, 2012). According to Jackson (2012), a factor has two or more levels. The individual experimenting sets the levels. The reason is that each design requires a unique level of the factor. It is noted that factors benefit design in various ways. For example, they highlight the relationship between single and group items that form the unified models (Walker, 2010). As a result, the researcher can make the right assumptions about factor interrelationships during the study.

Factors also help in determining the measurement structure present in the study design. The evaluation can be carried out through loading. It identifies the relationship between observed and unobserved variables in the design. Also, factors allow for measurement error in less restrictive situations. They also make it possible for the researcher to carry out the extraction of maximum variance in design (Beins & McCarthy, 2012). Also, they enable the researcher to predict the outcome of the desired design.

## Main Effects and Interaction Effects

### Main Effects

The main effect is the result of a single independent variable on a dependent one (Jackson, 2012). The phrase is mainly used when describing factorial designs and regression. According to Jackson (2012), the effect helps the researcher to differentiate between main and interaction effects. In a factorial design, a key result test is used to examine the expected supposition. Such suppositions include, among others, HO and null hypothesis. It is noted that a core outcome test is non-specific. It does not support localization of specific mean and pair-wise contrasting. Generally, the main effects are upshots of a factor.

### Interaction Effects

Orme and Orme (2009) provide a working definition of an interaction effect. It is viewed as the process through which two autonomous variables interrelate. It is the situation where the outcome of one independent variable differs from that of the other due to their varying levels (Orme & Orme, 2009). The effect does not necessarily mean that the course of a result differs at certain levels of an erratic situation. An interaction occurs when the degree of an outcome is greater at one point compared to on the other. Two variables interrelate in combinations that would not produce the expected results based on the main effects.

### How a Covariate Reduces Noise

A covariate is a variable predicting the results of an experiment (Walker, 2010). It can be of undeviating interest or confounding erratic. It is also described as a secondary variable. The reason is because of its capability to influence the relationship between the dependent and independent erratic of major interest. A covariate reduces noise by using more than one variable in experiments. An erratic of a similar kind is measured in various contexts during the test. The process allows for adjustments and removal of less significant variables responsible for noise production.

A trade-off is a situation where the researcher leaves out one feature of something in an experiment to gain the desired result (Beins & McCarthy, 2012). If one aspect increases extensively, the other must be reduced. In a trade-off, decisions are made with complete awareness of both the positive and negative outcomes of the choice.

### Examples of Trade-Offs in Experiments

During the construction of a spaceship, experts can first fit the machine with three standing aids. Even though the aids reduce the weight of the ship, they are considered to be unsafe. The reason is that they do not provide enough support. As a result, the experts may decide to fit the ship with five aids. Tests prove them to be safe. However, they increase the weight of the ship. To deal with the problem, the engineers may resolve to fit the machine with four aids, engaging in a trade-off.

Another example entails the design of electronic music systems. Negative feedback is used in amplifiers to eliminate gaining effect. The aim is to accomplish other desired aspects, such as stability and noise immunity. In economics, trade-offs are employed in terms of opportunity costs. A plan is employed to acquire certain products instead of others. The foregone items could have been acquired using the same resources. Opportunity cost is also evident when an individual attends a football game instead of watching it at home. It is the resources spent on attending the game instead of staying at home and watching the match on television.

## References

Beines, B., & McCarthy, M. (2012). Research methods and statistics. Boston: Pearson.

Jackson, S. (2012). Research methods and statistics: A critical thinking approach (4th ed.). Belmont, CA: Wadsworth Cengage Learning.

Orme, J., & Orme, T. (2009). Multiple regression with discrete dependent variables. Oxford: Oxford University Press.

Patricia, T. (2012). Dependent and independent variables: Unabridged guide. Dayboro: Emereo Pub.

Walker, I. (2010). Research methods and statistics. Houndmills, Hampshire: Palgrave Macmillan.

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