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FINDING THE PERFECT TEST FOR YOUR DATA
DECEMBER 2021
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TABLE OF CONTENTS
ANOVA
- Definition
- Writing of Hypothesis - Two types of ANOVA Regression
- Definition
- Writing of Hypothesis
- Two types of Regression Bonus Topic
Editor's Page
ANOVA Measures the strength of this 'signal' between groups amidst the 'noise' within each group and whether this 'signal strength' is strong enough to indicate a significant difference.
ANOVA General Linear Model (GLM) : Data = Model + Error The result of an ANOVA can be described as a "model."
ANOVA Two types of ANOVA : - One way ANOVA (one discrete variable) - Two way ANOVA (two discrete variable)
one way ANOVA hypothesis NULL HYPOTHESIS
Ho : There is NO SIGNIFICANT DIFFERENCE in X across the categories of Y.
ALTERNATIVE HYPOTHESIS Ho : There is A SIGNIFICANT DIFFERENCE in X across the categories of Y.
two way ANOVA hypothesis MAIN EFFECT HYPOTHESIS Ho-main1 : There is NO SIGNIFICANT DIFFERENCE in Y across the categories of X1 Ha -main1 : There is A SIGNIFICANT DIFFERENCE in Y across the categories of X1. Ho-main2 : There is NO SIGNIFICANT DIFFERENCE in Y across the categories of X2. Ha-main2: There is A SIGNIFICANT DIFFERENCE in Y across the categories of X2.
two way ANOVA hypothesis INTERACTION HYPOTHESIS Ho - Interaction : there is NO INTERACTION between the categories of X1 and X2 on Y. Ha - Interaction : There is AN INTERACTION between the categories of X1 and X2 on Y.
one way ANOVA steps
STEP 1 : Is the p-value significant? If the p-value is greater than 0.05 = do not proceed to step 2.
STEP 2 :
What is the effect size? (also called "eta squared") effect size will tell us the % variation in the values explained by the discrete variable.
one way ANOVA steps
How to write it: The F statistics, F(df) = (statistics), is significant at p-value <0.05. Thus we reject the null hypothesis. There is more evidence towards a significant difference in sprint among the categories of smoking. This model accounts for (effect size) of the variance in sprint.
one way ANOVA steps
STEP 1 :
Is the p-value for interaction effect is significant? if yes, we do not interpret main effect p - value
STEP 2 :
What is the effect size? (use partial etasquared for effect size) partial eta squared takes into account the presence of multiple discrete variables.
one way ANOVA steps
How to write it: The F statistics, F(df) = (statistics), is significant at p-value <0.05. Thus we reject the null hypothesis. There is more evidence towards an interaction effect between athlete status and smoking habits on sprint speed. The interaction effect explains (partial eta squared) of the variance in Sprint. Meanwhile, the main effects of Athlete and Smoking explain (partial eta squared) and (partial eta squared) of the variance in Sprint, respectively.
REGRESSION It answers the question "is variable X a significant predictor of variable Y?" It is a DIRECTIONAL analysis, we should not mix up the variables
REGRESSION General Linear Model (GLM) : Data = Model + Error Data = [mx + b] + error The result of regression can be described as "model"
Linear Regression Hypothesis NULL HYPOTHESIS
Ho : X is NOT A SIGNIFICANT PREDICTOR of Y
ALTERNATIVE HYPOTHESIS Ha : X is A SIGNIFICANT PREDICTOR of Y
Multiple Regression Hypothesis NULL HYPOTHESIS
Ho : Xn is NOT A SIGNIFICANT PREDICTOR of Y
ALTERNATIVE HYPOTHESIS Ha : Xn is A SIGNIFICANT PREDICTOR of Y
Linear Regression steps STEP 1 : Is the p-value significant? If the p-value is greater than 0.05 = do not proceed to step 2.
STEP 2 : Present the regression line with the coefficients. Regression line is presented in the format "Y=mx + b"
Linear Regression steps STEP 3 : Interpret Goodness of Fit ANOVA Insignificant : There is no significant difference in the dependent variable with or without the predictor (model is not good fit) Significant : There is a significant difference in the dependent variable with or without the predictor (model is good fit)
Linear Regression steps STEP 4 : Effect size. Tell us how big of a difference the predictor makes. R : Pearson's R correlation coefficient between the two continuous variables. R Square : % variance explained in the dependent variable by the predictor for the sample.
Linear Regression steps How to write it : A regression analysis showed that English scores is a significant predictor to Reading scores, with significant at a p-value < 0.05. Specifically, the regression model predicts a 0.372 increase in Reading scores per 1 point increase in English Scores. This regression model was found to be a good fit to the data with the Goodness of Fit ANOVA, significant at p-value < 0.05. Furthermore, the model predicted (R square) of the variance in Reading Scores.
Multiple Regression steps STEP 1 : Which p-value of predictor is significant? If all not significant do not proceed to step 2. interpret all significant predictor.
STEP 2 :
Present the regression line with the coefficients estimates. Present the standardized coefficient estimates.
Multiple Regression steps STEP 3 : Interpret Goodness of Fit ANOVA same as Simple Linear Regression
STEP 4 : Use adjusted R squared as there are more than 2 predictors.
Multiple Regression steps How to write : A multiple regression analysis showed that only English and Math are significant predictors to Reading, with pvalues <0.05. The regression model predicts a .253 and .419 increase in Reading per 1 point increase in English and Math, respectively. Looking at the standardized coefficients, the relationship between Math and Reading is around 1.8x stronger than that of English and Reading. This regression model was found to be a good fit to the data with the Goodness of Fit ANOVA, significant at pvalue < 0.05. Furthermore, the model predicted 31% of the variance in Reading.
Hierarchical Regression Why run this test? - You want to see the effects of multiple predictors on one variable - You want to see the step - wise prediction on the dependent variable as more and more predictors added - You want to see the change in effect size as more and predictors are added
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Editor's Page Get to know more about the Editor - in - Chief of STATSMAG
I am a 2nd year college student who is pursuing Bs - Psychology as my pre - med course. Someday I want to be a Pediatrician because of my love for kids. My friends call me the 'mother' of the group because I always care for them and help them if there is a chance. My friends also call me workaholic because I never know when to stop doing academics and org works. I can't deny that I'm a workaholic because it is really true. Despite being a workaholic, I still find time to rest and to catch up with my personal life. My love for Kpop makes me sane and makes me happy. Watching Kpop contents or just listening to their music makes me relax. The groups that I do love are EXO, WayV and NCT. So the next time you see me or ask me what makes me happy, I'll only answer you "Kpop" or "Kpop merchs".
MARTHA ANGELA S. AMON Editor-in-Chief
STATSMAG
Editor's Note If you're already at this page, I congratulate you for finishing my magazine. I hope you enjoyed my magazine! I hope you also learned a lot from it. I may not be a professional when it comes to Statistics but I do really hope that somehow this magazine helped you even in the smallest way. Thank you for your endless support for me and my magazine! I learned a lot from making this magazine and I dedicated my time in finishing this so Thank you so much! I hope to see you again in my next magazine!! Have a nice day and stay safe always!!