Discussion Question 1 – CLO 5, CLO 7
Provide detailed assessment for the following and support your responses with some numerical examples:
- What is the F probability distribution? In what way does it differ from a t probability distribution?
- In an ANOVA, what is between group difference and what is within group difference?
- What is covariance and how does it differ from correlation?
please give 100 words response with reference
What is the F probability distribution; in what way does it differ from a t probability distribution?
The probability distribution F-probability is a distributed procedure that plots the difference between the values of two or more sets of data (Vasileva, 2020). It uses the freedom of the denominator and the numerator to explore the variability of the data.
The T-distribution is a statistical procedure that is used to investigate the differences in means between small samples and large samples with n-1 degree of freedom.
Between group difference and what is within group difference
In ANOVA, the dissimilarity between groups is the total of the squared differences between each group and the grand mean of all groups. The within group difference in an ANOVA, on the other hand, is the squared difference between each observation and the group mean aggregated across all groups. The F-statistic value is the ratio of within-group and between-group differences, which is used to assess if the group means differ considerably.
Covariance and how does it differ from correlation
The term “covariance” describes how two variables are linked in a systematic way. Correlation, on the other hand, assesses how a change in one variable effects the change in the other. The concept of covariance refers to the direction of a linear relation between two sets of factors (Lippich et al., 2019). Correlation is a function that measures the strength of a linear relationship.
Lippich, M., Sánchez, A. G., Colavincenzo, M., Sefusatti, E., Monaco, P., Blot, L., … & Yepes, G. (2019). Comparing approximate methods for mock catalogues and covariance matrices–I. Correlation function. Monthly Notices of the Royal Astronomical Society, 482(2), 1786-1806.
Vasileva, M. T. (2020). Some Notes on the Omega Distribution and the Pliant Probability Distribution Family. Algorithms, 13(12), 324.