Statistics Assignment: ANOVA, Chi-Square, and Significance

This assignment delves into three key statistical concepts: ANOVA (Analysis of Variance), Chi-Square tests, and practical significance. The assignment explains ANOVA as a method to determine the significance of experimental results, differentiating between one-way, two-way, and N-way ANOVA based on the number of independent variables. It further discusses the Chi-Square test, focusing on its use in analyzing relationships between categorical variables and the difference between Chi-Square goodness-of-fit and test for independence. Finally, the assignment explains practical significance as the real-world relevance of statistical findings, emphasizing the importance of effect size and considering factors like time and cost. The assignment provides a concise explanation of each concept, making it a helpful resource for students studying statistical analysis.

Answer each question using essay format (sentences and paragraphs, not point form). For each
question, answers are limited to a maximum of 150-200 words
1. What is ANOVA?
ANS:
ANOVA is known to be a statistical technique which is mainly required to find out whether the
experimental results are significant or not. Basically in simple words ANOVA stands for analysis of the
variance. The main purpose of using ANOVA is to find out whether it is needed to reject the null
hypothesis in the analysis or to accept the alternative analysis in the analysis.
Basically on the research design the use of ANOVA mainly depends. Thus, the usage of ANOVA is
been divided into three ways namely one way ANOVA, two way ANOVA and the last N way ANOVA.
The main objective of one way ANOVA is that using F-distribution two means from two
independent groups are been compared. For two way ANOVA there are two independents and is an
extension of the previous one. It is mainly used when there is one measurement which can be a
qualitative variable and two nominal variables. Use of more than two independent variables is termed
to be as N way ANOVA.
2. What is chi square?
ANS:
Chi square is a kind of statistical hypothesis test which is generally use to test the relationships between
the categorical variables of the dataset. Using the null hypothesis of the Chi-Square test it can be said
that there should be no existing relationship over the variables which are mainly categorical and are in
the population as because they are independent. If there is no relationship in the population then tells
the difference observed between the output count and the expected count which is basically a single
number and is the Chi square statistics.
There exist mainly 2 types of chi-square tests and both of them were used for different purpose
and are mainly chi-square goodness of fit test and chi-square test for independence where if a sample
matched with the population then it determined to be chi-square goodness of fit test and on the other
hand when two variables which are in a contingency table are compared to see if they are related then it
is chi-square test for independence.

3. What is practical significance?
ANS:
The relationship between the variables of the real world application are known as practical significance.
In short it basically tells the magnitude of the difference, which is known as the effect size. It basically
relates if the result obtained from the statistical hypothesis test is useful or not. It can be said that when
the difference is more than the result is practically more significant in the real life.
The significance between two or more variables shows the probability of the relationship. It
consider the mean and variance of the analysis. It can also be stated that for some cases there may be
some dependency between two significances. It explains the relevance of the study which are taken
under consideration. It mainly focuses on the usefulness of the result which has been obtained from the
real world. Few factors which are the main cause of affecting the practical significance are time, factors,
condition, cost and many more.