# Understanding Anova and Correlation in Research Studies

Classified in Mathematics

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## Ch 12 Anova

Goal/purpose: Evaluate mean difference between 2 or more treatments

• Factor: The IV that designates the groups being compared
• Levels: Individual conditions or values that make up a factor
• Factorial design: A study that combines two or more factors

### The Logic:

• Between treatment variance
• Variability results from general differences between the treatment conditions
• Variance between treatments measures differences among sample means
• Within treatments variance
• Variability within each sample
• Individual scores are not the same within each sample

Notations:
k= # of treatment condition
T= sum of squares for each treatment
G= grand total of all scores in study
N= total number of scores
kn= when all samples are same size
n1,n2= # of scores in each treatment

Post hocs: Are completed if we have a significant result from an Anova/if I rejected the null
Anova avoids type 1 error for experimental alpha
Two types of post hoc tests= Tukeys & Scheffe test

Anova hypothesis steps

• Step 1: Null and alternative
• Step 2: Fcrit using df(bt), df (wg) & alpha
• Step 3: Fill out summary table
• Step 4: Rej or FTR. f(df)= #.##, p (>,<).05

Ch 14 Correlation= Measures & describes the relationship between two variables (linear)
Characteristics are all independent - direction: (neg or positive, the sign) - form: (linear is most common) - strength or consistency (varies from 0 to 1)

### Limits:

Outliers: Extremely deviant individual in sample characterized by a much larger (or smaller) score than all others in the sample, produce disproportionately large impact on the correlation coefficient

• Correlation describes a relationship but does not demonstrate causation
• Correlation is not a proportion

Pearson correlation= Measures the degree & direction of the linear relationship between 2 variables

Restricted range of scores- r value (size) - severely restricted range - never generalize a correlation beyond
Coefficient of determination= squared correlation (r2) may be interpreted as proportion of shared variability

Alternative correlations:
Spearman= Used with data from an ordinal scales (ranks), both variables are measured on an ordinal scale, used if measurements scale is interval or ratio when relationship is consistently directional but may not be linear
Point biseral
Measures relationship between 2 variables - one variable has only ex: male/female - called a dichotomous or binomial variable
Effect size for independence sample t test in ch 10 can be measured by r2 - r statistic measures the correlation size - t statistic test significance of mean difference
Phi
- Both variables are re-coded to value 0&1 - The regular Pearson formulas is used to calculate r - r2 (coefficient or determination) measures effect size (proportion of variability in one score predicted by the other)