Anova Written Report [PDF]

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Philippine Women’s University JOSE ABAD SANTOS MEMORIAL SCHOOL

Written Report ANOVA (One- way and Two-way)

Group 6 Balacy, Beatriz Delarmente, Mikaela Domingo, Allyana Chaye Fidelino, Larissa Milliscent Karundeng, Jovelent Crissanta

T. Joyce Calingasan

22 October 2018

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Philippine Women’s University JOSE ABAD SANTOS MEMORIAL SCHOOL

ANOVA Definition ● ANOVA are a combination of the word Analysis Of Variances. The one way ANOVA are used to determine whether there’s a statistically significant differences between the means of two or more unrelated independent group. Purpose

● The test allows comparison of more than two groups at the same time to determine whether a relationship exists between them. The test analyzes multiple groups to determine the types between and within samples. Types of ANOVA ● ONE WAY ANOVA - Definition > The one way ANOVA only involves 1 factor or independent variables. The null hypothesis of these are when the two means are equal while if it is not then it has a significant differences with each others. - Purpose > Determine if the means of these independent unrelated groups have a significant differences with the of F-distribution. - Sample Studies/ Research Question >Are there differences in GPA by grade level (freshmen vs. sophomores vs. juniors)? >You have a group of individuals randomly split into smaller groups and completing different tasks. For example, you might be studying the effects of tea on weight loss and form three groups: green tea, black tea, and no tea. - Number of groups required > The one-way anova requires three or more groups and can be used in two study designs. > In the first design, a group of individuals is recruited and will be then divided into three or more groups which will undergo different treatments to see the different outcomes. On the second design, the individuals will be split into three or more groups depending on an independent variable. The independent variables is often called an attribute independent variable as the individuals are grouped by the similarities in attributes. Each group will then undergo the same testing and experience the same condition. ● TWO WAY ANOVA (Factorial Analysis) - Definition > Two-way ANOVA used to determine the effect of two nominal predictor variables on a continuous outcome variable and tests for differences in the effects of independent variables on a dependent variable. A two-way ANOVA tests the effect of two independent variables on a dependent variable. A two-way ANOVA test analyzes the effect of the independent variables on the expected outcome along with their relationship to the outcome itself. Random factors would

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Philippine Women’s University JOSE ABAD SANTOS MEMORIAL SCHOOL

be considered to have no statistical influence on a data set, while systematic factors would be considered to have statistical significance. - Purpose: > A factorial ANOVA compares means across two or more independent variables. The primary purpose of a two-way ANOVA is to understand if there is an interaction between the two independent variables on the dependent variable. The interaction term in a two-way ANOVA informs you whether the effect of one of your independent variables on the dependent variable is the same for all values of your other independent variable (and vice versa) - Sample studies/research question > A researcher was interested in whether an individual's interest in politics was influenced by their level of education and gender. They recruited a random sample of participants to their study and asked them about their interest in politics, which they scored from 0 to 100, with higher scores indicating a greater interest in politics. The researcher then divided the participants by gender (Male/Female) and then again by level of education (School/College/University). Therefore, the dependent variable was "interest in politics", and the two independent variables were "gender" and "education". - Number of groups required >The one-way anova requires three or more groups and can be used in two study designs. Data level and Assumptions - The level of measurement of the variables and assumptions of the test play an important role in ANOVA. In ANOVA, the dependent variable must be a continuous (interval or ratio) level of measurement. The independent variables in ANOVA must be categorical (nominal or ordinal) variables. Like the t-test, ANOVA is also a parametric test and has some assumptions. ● normal distribution of data ● m independent simple random samples ● m constant variance Variance Ratio - An analysis of variance constructs tests to determine the significance of the classification effects. A typical goal in an analysis of variance is to compare means of the response variable for various combinations of the classification variables. An analysis of variance may be written as a linear model. The two-way analysis of variance is an extension to the one-way analysis of variance. There are two independent variables. Two-way ANOVA determines how a response is affected by two factors. The two independent variables in a two-way ANOVA are called factors. The idea is that there are two variables, factors, which affect the dependent variable. Each factor will have two or more levels within it, and the degrees of freedom for each factor is one less than the number of levels. In the 2 way ANOVA interactions between row and column. These are differences between rows that are not the same at each column, equivalent to variation between columns that is not the same at each row. For each component in the 2 way ANOVA table consists of sum-of-squares,

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Philippine Women’s University JOSE ABAD SANTOS MEMORIAL SCHOOL

degrees of freedom, mean square, and the F ratio. Each F ratio is the ratio of the mean-square value for that source of variation to the residual mean square (with repeated-measures ANOVA, the denominator of one F ratio is the mean square for matching rather than residual mean square). Source of Variation

Sums of Squares (SS)

Degrees of Freedom (df)

Between Treatments

k-1

Error (or Residual)

N-k

Total

N-1

Mean Squares (MS)

F

● X = individual observation, ●

= sample mean of the jth treatment (or group),

● = overall sample mean, ● k = the number of treatments or independent comparison groups, and ● N = total number of observations or total sample size.

BIBLIOGRAPHY One-way ANOVA - Violations to the assumptions of this test and how to report the results | Laerd Statistics. (2018). Retrieved from https://statistics.laerd.com/statistical-guides/one-wayanova-statistical-guide-3.php

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Philippine Women’s University JOSE ABAD SANTOS MEMORIAL SCHOOL

Staff, I. (2018). Analysis Of Variance ANOVA. Retrieved from https://www.investopedia.com/terms/a/anova.asp#ixzz5UZtZbFM4 Hypothesis Testing - Analysis of Variance (ANOVA). (2018). Retrieved from http://sphweb.bumc.bu.edu/otlt/MPH-Modules/BS/BS704_HypothesisTestingANOVA/BS704_HypothesisTesting-Anova_print.html Two-way ANOVA in SPSS Statistics - Step-by-step procedure including testing of assumptions | Laerd Statistics. (2018). Retrieved from https://statistics.laerd.com/spss-tutorials/two-wayanova-using-spss-statistics.php ANOVA Test: Definition, Types, Examples. (2018). Retrieved from https://www.statisticshowto.datasciencecentral.com/probability-and-statistics/hypothesistesting/anova/ ANOVA. (2018). Retrieved from https://www.kean.edu/~fosborne/bstat/08ANOVA.html

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