The assignment is to write a 2000 word essay on one of the following topics. Include diagrams in your answer (not cut and pasted from the lecture slides). 1)Analysis of Variance (ANOVA) is a very...

Running head: Variance (ANOVA)    
Variance (ANOVA) 13
VARIANCE (ANOVA)

Table of Contents
Introduction    3
An introduction to variance    3
Significance of ANOVA variance in psychology    4
Use of ANOVA to determine occurrence of deviation by chance    5
Complex forms of ANOVA    10
Conclusion    10
Reference list    12
Introduction
The current essay focuses on identification of the significance of ANOVA (variance) in psychological studies and is effective in identifying the cause of deviation insignificant. It also discusses the complex forms of ANOVA as well as the type of data for which it is appropriate. A critical analysis has been done in discussing the method involved in the partitions of the total variance in case it has occurred due to chance using ANOVA. Moreover, its clinical significance in psychological experiments has been justified with relevant evidence.
An introduction to variance
Variance refers to the expectation of the squared deviation of a random variable derived from its mean. Heath (2014) supported this by stating that variance can be defined as a random variable X that is the expected value of the squared deviation from the mean of X. It is denoted by Var(X) = E [(X- μ)2]. However, Lakens (2013) argued that in case of generation of random variables, the processes that are involved include continuous, mixed, discrete or continuous. Thus, variance also refers to the covariance of a random variable with itself which is denoted as Var(X) = Cov(X, X). On the other hand, it has also been noted that variance can also be stated as the second cumulant of a probability distribution that tends to provide the X.
In this case, the variance is denoted as Var(X) = E[X2] - E[X]2 (Warne, 2014). Variance is generally non-negative in nature because the squares are either zero or positive which is represented as Var(X) = 0. In addition to this, the variance of a constant random variable is always zero (0). As opined by Roberts and Russo (2014), the variance is invariant if the location of the parameters has been changed. As stated by Field (2013), the Analysis of Variance (ANOVA) is a statistical analysis of the difference between group means and their associated procedures.
Significance of ANOVA variance in psychology
Although the presence of different statistical testing methods, the T-test and z-scores, they are limited to testing using two groups only. However, in case of ANOVA or the Analysis of Variance, it can be used to analyze designs that are within groups. It also facilitates the critical analysis of results of between and within group tests. As opined by Arnold and McDermott (2013), a t-test is used in Psychological experiments since it facilitates the distribution in case the null hypothesis is true. As argued by Warne (2014), in case the p-value is less than 0.05, it fails to relate it to the null hypothesis. On the contrary, ANOVA facilitates the detection of mean within more than two groups. Odacı and Çıkrıkçı (2014) supported this by stating that since ANOVA facilitates the testing of more than one treatment, it contributes to finding the relevance of more than one treatment in the treatment of a psychological disorder.
Figure 1: Significance of ANOVA
(Source: Warne, 2014)
It also contributes to psychological studies since it facilitates the understanding of the importance of each of the psychological treatments in case of the concerned group. This contributes to an evidence-based practice in treating psychological disorders and also identifying the various causes of a psychological issue (Danielson et al. 2016). Moreover, it also facilitates justifying the reasons of a specific psychological aspect based on the value of variance and its relevance in practice. ANOVA specifically contributes to planning and designing a healthcare intervention in a relation of a psychological issue since it guides on the manner in which a treatment works and also its validity (Robinson, Fleming & Higgs, 2014). Additionally, it also guides on the budget involved in the psychological issue adopted as observed in case of intensive Early Behavioural Intervention (EIBI) in case of autistic children. In this case, it also helps in identifying that the intervention lasts for an hour with effective results but are costly.
Moreover, it helps a researcher to analyse the difference between the conditions and whether the effect has occurred due to chance. As opined by Cramer et al. (2014), ANOVA also helps in analysing the cause of occurrence of variation in case of a therapeutic intervention. This is relevant in case of...