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2248 Q5 1WAI
| Term | Definition |
|---|---|
| How to conduct a relevant ANOVA test in STATA ? | Tests whether the means of a dependent variable differ across categories of a single independent(grouping) variable |
| step 1 - load your data | step 2 - understand your variables (dependent variable numeric, independent variable categorical) |
| example - score (dependent), group (categorical w three levels) | step 3 - run One way ANOVA - "anova score group" this tests whether the mean of score differs across levels of grp step 4 - interpret output - btwn groups, within groups (residual) and prob>F |
| the ANOVA output from stata | shows the results of a one way ANOVA testing whether BMI significantly differs across categories of the variable F=32.39 and p<0.00001 means there is highly significant difference in BMI btwn at least one pair of smeal grps |
| you can reject the null hypothesis that all grp means are equal | since the ANOVA is significant you should conduct post hoc tests like tukey's HSD to find which smeal group differs in BMI |
| How to run an ANOVA output in STATA ? | Use the anova command Scenario: you have a numeric dependent variable (BMI) and categorical independent variable (eg diet grp or treatment) command form - anova dependent_var group_var anova bmi diet_group |
| this tests | whether the mean BMI differs significantly across different diet_group categories |
| what is between group variance ? | refers to the variability in the data that is due to the difference between the group means |
| in other words | it answers the question: "how much do the group averages differ from the overall average" |
| in context of ANOVA test. you're comparing the variance | between groups (explain variation) |
| what is within group variance ? | (also called residual variance or error variance) measures the variation of individual observations with each group around their group mean |
| in simple terms | "how spread out the values within each group" |
| in the context of ANOVA - within grp | within grp variance focuses on how individual data points differ from there own group's mean |
| What is Bartlett's equal variance test ? | (also called Bartlett's test of homogeneity of variances) is a statistical test used to check whether multiple grps have the same variance - an important assumption in ANOVA and other parametric tests |
| what it does | test the null hypothesis that all group variances are equal |
| if the p value is low (typically <0.05) -> | reject the null hypothesis - at least one group has a significantly different variance |
| if the p value is high | there's no evidence of unequal variances |
| what command should be run in this anova ouput? | to support and validate the ANOVA results shown in the output you provided (anova bmi smeal) the next logical command you should run is a variance test |
| variance test | check whether the assumption of equal variances across group is met |
| how do we determine whether the model is significant ? | you look at the F statistic and its p value in the ANOVA ouput |
| interpretation steps | 1. Check the p value (Prob>F) for the model: if p<0.05 - the model is statistically significant this means at least one grp means differs significantly from the others |
| 2. The f statistic (f=32.29) | this is the ratio of between group variance to within group variance a higher F value typically supports the conclusion that the group mean differ |
| What is a partial one way ANOVA | usually refers to one way ANOVA where you assess the unique effect of one factor while controlling others - ie shows the partial effect of one categorical variable |
| in software like stata, when you run: | anova y x1 x2 |
| youre fitting a model where: | X1 and X2 are factors (categorical variables)) the output shows the partial SS (sum of squares) for each variable |
| these partial SS values tell you | "what is the effect of x1 on y, after accounting for x2" |
| to calculate the F ratio for each ANOVA output | use the formula F = mean square model over mean square residual |
| what is reflected by the residual SS | The residual sum of squares reflects the unexplained variation in the dependent variable - that is, the portion of the total variation not accounted for by the model |
| what is reflected by the model SS | known as the explained ss or between grp ss - reflects the variation in the dependent variable that is explained by the model (ie differences between grp means) |
| what does the output indicate ? | the outputs labeled A and B are ANOVA tables and they compare the same model (Model SS=102.60, df=4) under two different data conditions or scenarios as seen by their different residual SS and total SS values |
| (A) output - residual SS is relatively small, moderate evidence that the model explains significant variation, more favourable for model signifiicance | (B) output - residual ss is much larger, a lot of variation left unexplained, weaker evidence for model significance, the same model explains less proportion of total variation. |
| what is error variance in the analysis of variance ? | refers to the variance of residuals or the unexplained variation in the dependent variable within groups |
| what is between groups variance in ANOVA | the btwn groups variance measures the variability due to the differences between the group means - in other words how much the groups differ from each other relative to the overall mean |
| what is within groups variance in ANOVA | within group variance (also known as error variance, residual variance or mean square within) measures the variability of individual observations around their own group means |
| what is the most appropriate stata command to test the homogeneity of variance for the one way ANOVA model ? | estat bartlett 1. run your one way ANOVA Anova dependent_var group_var 2. then test for equal variances estat bartlett |
| what does it mean the assumption is met ? | means the underlying assumptions required for the ANOVA test to be valid are satisfied |
| these assumptionse | ensure that the results of ANOVA are reliable and interpretable. the key assumptions for ANOVA include: independence of observations, normality and homogenity of variance (homoscedasticity) |
| the assumption of homogeneity of variance pertains to what ? | also known as homoscedasticity pertains to the idea that the variances of the groups being compared in an ANOVA model should be approximately equal |
| when conducting an ANOVA | your'e assuming that the spread of scores within each group is similar across all the groups you are comparing. |
| Ensures that each grp is contributing equally to the analysis | and that any observed differences in means are not simply due to the diffferences in variability between groups |
| What is levene's test for equality of variance ? | statistical test used to assess whether the variances of different grps are equal. |
| particularly useful in situations | where the assumption of homogeneity of variance (equal variances) is important for analyses like ANOVA. |
| violating this assumption | can lead to inaccurate conclusions, so levenes test help determine if this assumption is met |
| what does it mean the p value is non significant? | there is no sufficient evidence to reject the null hypothesis at the chosen level of significance (0.05) |
| in other words | the data does not provide strong enough evidence to conclude that there is a statistically significant effect or outcome |
| in the context of ANOVA, what is the assumption of normality ? | the assumption of normality refers to the requirment that residuals (ie the differences between observed values and group means) are normally distributed with each group being coimpared |
| what is a shapiro wilk test in this data ? | the SWT is a statistical test used to check whether a dataset is normally distributed. |
| this means it helps you determine if your data follows a bell shaped curve (normal distribution) | which is a key assumption for many statistical tests like the t test and ANOVA |
| null hypothesis H0 | the data is normally distributed |
| alternate hypothesis H1 | the data is not normally distributed |
Created by:
brendonpizarro1