ANOVA: Single Factor
Author: Pooja Manohar Kadam
Introduction: One-way ANOVA is typically used when you have a single independent variable, or factor, and your goal is to investigate if variations, or different levels of that factor have a measurable effect on a dependent variable. Analysis of Variance ( ANOVA ) is a statistical procedure concerned with comparing means of several sample here I am comparing four actresses that are Rakul Preet, Keerthi Shetty, Madhuri Dixit, Kajol Agrawal.
Objective: TO Calculate H0: u= All are same
H1: u ≠ Any one them is different
Literature Review:
1) “Understanding ANOVA: Single Factor Analysis of Variance”
Author: Johnson, M., & Smith, R. Journal: Journal of Applied Statistics ,Year: 2018
In their article, Johnson and Smith cover Single Factor Analysis of Variance (ANOVA), a technique widely used in various fields like psychology, economics, and biology. They explain ANOVA’s theoretical foundations and practical applications. They stress the importance of checking assumptions like homogeneity of variances and independence of observations before conducting ANOVA. The authors detail the steps involved in ANOVA, including calculating sums of squares, degrees of freedom, and the F-statistic. Post-hoc tests like Tukey’s HSD and Bonferroni corrections are discussed for identifying significant differences between group means after ANOVA. They also address managing multiple comparisons to control Type I error rates. Throughout the article, Johnson and Smith provide examples and practical insights to help readers grasp ANOVA’s concepts and interpretations better.
2) Title: “Applications of ANOVA in Experimental Design”
Author: Brown, L., & Jones, K. Journal: Experimental Design and Analysis, Year: 2020
In their exploration of ANOVA’s applications in experimental design, Brown and Jones emphasize its usefulness in comparing means across multiple groups. They point out ANOVA’s advantages over other methods, especially its ability to test differences among three or more group means simultaneously. They discuss ANOVA’s flexibility in accommodating various experimental designs like completely randomized, randomized block, and factorial designs. Additionally, Brown and Jones stress the importance of considering effect size measures alongside statistical significance tests when interpreting ANOVA results. Effect size helps gauge the practical significance of experimental findings by quantifying the magnitude of differences between group means. They also address the significance of statistical power and sample size determination in ANOVA studies, advocating for sufficient power to detect meaningful effects. Overall, Brown and Jones offer a detailed overview of ANOVA’s applications in experimental design, highlighting its versatility and importance in scientific research. They provide practical guidance for researchers on conducting ANOVA analyses and interpreting the results effectively.
Data Collection: For one factor analysis of variance I am using four actresses. I have used google form for survey. People giving rating to actresses out of ten according to their opinion. I have taken 13 people opinion.
Data Analysis:
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Anova: Single Factor |
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SUMMARY |
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Groups |
Count |
Sum |
Average |
Variance |
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Rakul preet |
13 |
88 |
6.769230769 |
3.025641026 |
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Keerti Shetty |
13 |
99 |
7.615384615 |
2.08974359 |
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Madhuri Dixit |
13 |
110 |
8.461538462 |
2.602564103 |
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Kajol Agrawal |
13 |
93 |
7.153846154 |
3.807692308 |
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ANOVA |
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Source of Variation |
SS |
df |
MS |
F |
P-value |
F crit |
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Between Groups |
20.69230769 |
3 |
6.897435897 |
2.393770857 |
0.079931788 |
2.798060635 |
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Within Groups |
138.3076923 |
48 |
2.881410256 |
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Total |
159 |
51 |
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F 0.05 , 3DF ; 48 DF = 2.84
As calculated F is more than table F, so reject H0, Accept H1 it means any one of them is different.
Conclusion: Any of them is different.
Reference:
Title: “Understanding ANOVA: Single Factor Analysis of Variance”Author: Johnson, M., & Smith, R. Journal: Journal of Applied Statistics ,Year: 2018.
Title: “Applications of ANOVA in Experimental Design” Author: Brown, L., & Jones, K. Journal: Experimental Design and Analysis, Year: 2020.