Differences Between Percentages For Two Groups

Name: Instructor: Institution: Date: Week 7 Assignment Question 1 Differences test are important in establishing if there are statistically established differences or deviations between two or more groups. A test with regards to differences between percentages for two groups is basically testing a null hypothesis; no difference exists between the two group’s percentages. According to Burns (2017), to perform the test of significance of differences between two percentages, the first step requires a comparison of the two percentages i.e 100% versus 88%. Similarly, a difference test of averages of two groups involves testing a null hypothesis between the means of the groups. For instance, is there a difference in the average work performed by male engineers versus female engineers? Sample size and standard deviation are the major factors that affect the standard error. In the standard error method, population size (n) is part of the denominator, thus the standard error reduces as the sample size increases. Therefore, having a large sample size leads to a more precision of the results, (Dietrich, 2017). On the other hand, standard deviation investigates the totality of disparity in the entire population. In the calculation of the standard error, standard deviation is a numerator in the formula. As a result, the standard error increases as the standard deviation increase. Question 2 Bivariate regression and multiple regressions are valuable statistical analysis techniques, which are significant during the analysis of quantitative market reports before making decisions. A major difference between the two is that bivariate regression analysis involves using two variables to determine potency of their relationship. The variables are commonly known as X and Y, with an explanatory variable (independent) and an outcome variable (dependent), (Burns, 2017). On the other hand, multiple regression is basically a prediction technique used to describe the association of a single continuous dependent variable to two or more autonomous variables.  In this case, the autonomous variables can be categorical or continuous. Nevertheless, the major similarity is that both bivariate regression and multiple regressions explain the relationship between independent and dependent variables by fitting a line on a scatter plot. Bivariate regression uses a scatter diagram to establish a line of best fit through plotted values of the independent variable adjacent to dependent variable (x against y). However, Plonsky (2017) indicates that multiple linear regressions establish a line through a multi-dimensional area of data points. As a result, the complex nature of a multiple regression graph can be attributed to the numerous data points that originate from the multiple variables. Question 3 Analysis of Variance originated from the total variance law and was first used by Sir Ronald Fisher in the twentieth century. Therefore, Analysis of Variance is a set of statistical techniques used to determine the presence or absence of significant differences between two or more means. In ANOVA, all variances are classified into various classes primarily considering their source of variations (Burns, 2017). Hence, from a basic point of view, ANOVA presents a statistical test of establishing if two or various population means are equivalent. From the definition, it is clear that ANOVA is used w...