EDF+6938+Final+Exam+Dec+2011

**Blueprint for Exam 2 **
 * 2EDF 6938 **

1. One-Way Between Subjects ANOVA A method for determining group mean differences when there are 3 or more.  a. Assumptions
 * Normality (robust) - no consequence for violating **
 * Independence of errors - if violated use a different test like within subjects **
 * Homogeneity of variance - if violated use a different test like Welch's V Test **

 b. Source Table  i. Calculate degrees of freedom


 * dfB **: Number of groups -1 (aka: k-1)


 * dfW **: Sample size – Number of groups (aka: N-k)


 * dfT **: N-1 (sample size – 1)

<span style="font-family: 'Arial','sans-serif'; font-size: 16px;"> ii. Given the sum of squares calculate mean square and F

See slide 13 in the ANOVA presentation from Week 8.

Mean Square: Between - MSb = SSb/k-1 Within - MSw = SSw/n-k

F: MSb/MSw

<span style="font-family: 'Arial','sans-serif'; font-size: 16px;"> c. Conduct Test <span style="font-family: 'Arial','sans-serif'; font-size: 16px;"> i. Set up hypotheses


 * <span style="color: #e36c0a; font-family: 'Arial','sans-serif'; font-size: 16px;">H0: mu 1 = mu 2 = mu 3 **


 * <span style="color: #e36c0a; font-family: 'Arial','sans-serif'; font-size: 16px;">H1: mu i ≠ mu j **

<span style="font-family: 'Arial','sans-serif'; font-size: 16px;"> ii. Find critical value


 * <span style="color: #e36c0a; font-family: 'Arial','sans-serif'; font-size: 16px;">*use F table in text book **

<span style="font-family: 'Arial','sans-serif'; font-size: 16px;"> iii. Write observed test statistic using degrees of freedom

= F - Mean Between Groups / Mean Within Groups =

<span style="font-family: 'Arial','sans-serif'; font-size: 16px;"> iv. Decision and conclusion Example conclusion: There is not enough evidence to conclude a difference exists between any of the foods.

<span style="font-family: 'Arial','sans-serif'; font-size: 16px;"> v. Set up appropriate contrasts <span style="font-family: 'Arial','sans-serif'; font-size: 16px;"> vi. Apply Bonferroni adjustment = Purpose = to keep the experiment wise error rate to a specified level - divide the acceptable level (.05) by the number of comparisons. The alpha level is lowered for each additional comparison to keep reduce risk of rejecting null when it should be rejected.=

Familywise = (per contrast) + (per contrast) + (per contrast). This adjustment is called the bonferrioni adjustment.

2. Follow-up Procedures <span style="font-family: 'Arial','sans-serif'; font-size: 16px;"> a. Family-wise error rate vs per comparison error rate

**Familywise Error rate** (alpha fw )--probability that one or more contrasts for a single factor will be falsely declared significant in an experiment. [From elluminate: the likelihood of a Type I error for a group of hypothesis within a family.]

Error rate per contrast (alphapc) - the probability that a particular contrast will be falsely declared. [From elluminate: the error rate per hypothesis.]

<span style="font-family: 'Arial','sans-serif'; font-size: 16px;"> b. What it means to control the family-wise error rate

One way to control for inflated error is to adjust the alpha PC Use Bonferroni adjustment. Controls family-wise by adjusting the family-wise error by the number of comparisons you want to make.

<span style="font-family: 'Arial','sans-serif'; font-size: 16px;"> c. Planned vs post-hoc


 * Planned Contrasts: ** Contrasts that the experimenter decided to test prior to examination of the data


 * Post Hoc Contrast: ** Contrasts that the experimenter decided to test only after having observed some or all of the data

<span style="font-family: 'Arial','sans-serif'; font-size: 16px;"> d. Procedures <span style="font-family: 'Arial','sans-serif'; font-size: 16px;"> i. Set up hypotheses <span style="font-family: 'Arial','sans-serif'; font-size: 16px;"> ii. Bonferroni Adjustment

Bonferroni adjustment controls family-wise by adjusting the family-wise error by the number of comparisons you want to make.

<span style="font-family: 'Arial','sans-serif'; font-size: 16px;">3. One-Way Within Subjects ANOVA


 * Allows for the comparison of 3 or more groups when the independence assumption is violated.
 * Used when the probability of an observation occurring in one group is conditional on observations in one or more of the other groups.

<span style="font-family: 'Arial','sans-serif'; font-size: 16px;"> a. Assumptions <span style="display: block; font-family: Arial,sans-serif; font-size: 16px; text-align: left;">b. Source Table <span style="font-family: 'Arial','sans-serif'; font-size: 16px;"> i. Calculate degrees of freedom
 * **Normality** - Dependent variable is normally distributed at each level of the independent variable.
 * **Robust** - If normality does not hold, one-way between-subjects ANOVA is robust to violations of normality.
 * **Sphericity** - Holds when all measures have the same variance and all correlations between any pair of measures are equal. Similar to homogeniety of variance in between-groups. Never assume sphericity; use a correction instead.

s = number per treatment level || SS AS || (a - 1) (s - 1) || N = Total number of observations ||
 * ~ Source ||~ DF ||
 * Treatment || a - 1 ||
 * Subjects || s - 1
 * Error
 * Total || N - 1

<span style="font-family: 'Arial','sans-serif'; font-size: 16px;"> ii. Given the sum of squares calculate mean square and F

<span style="color: #201bda; font-family: Arial,sans-serif; font-size: 16px;">MSw = SSw/N-k

<span style="font-family: 'Arial','sans-serif'; font-size: 16px;"> c. Conduct Test <span style="font-family: 'Arial','sans-serif'; font-size: 16px;"> i. Set up hypotheses

<span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 120%;">H0: mu1 = mu2 = ... = ma <span style="color: #800080; font-family: Arial,Helvetica,sans-serif; font-size: 120%;">H1: muj ≠ muj1

<span style="font-family: 'Arial','sans-serif'; font-size: 16px;"> ii. Find critical value <span style="font-family: 'Arial','sans-serif'; font-size: 16px;"> iii. Write observed test statistic using degrees of freedom <span style="font-family: 'Arial','sans-serif'; font-size: 16px;"> iv. Decision and conclusion Example Conclusion: The results suggest that the number of weeks of spa participation is statisically significant. An association between spa participation and weight loss holds for the population of dogs.

<span style="font-family: 'Arial','sans-serif'; font-size: 16px;">4. Analysis of Covariance (ANCOVA)
 * <span style="color: #e36c0a; font-family: 'Arial','sans-serif'; font-size: 16px;">ANCOVA attempts to remove predictable individual differences, uses a covariate (which is a continuous variable) **

<span style="font-family: 'arial','sans-serif'; font-size: 16px;"> a. Assumptions <span style="color: #e36c0a; font-family: 'Comic Sans MS',cursive;">**I didn't find these in the presentation - instead I found them online...** <span style="color: #e36c0a; font-family: 'Arial','sans-serif'; font-size: 16px;">Independence <span style="color: #e36c0a; font-family: 'Arial','sans-serif'; font-size: 16px;">Homogeneity of variance //<span style="color: #fbd4b4; font-family: 'Arial','sans-serif'; font-size: 16px;">Linearity // //<span style="color: #fbd4b4; font-family: 'Arial','sans-serif'; font-size: 16px;">Homogeneity of regression // <span style="color: #e36c0a; font-family: 'Arial','sans-serif'; font-size: 16px;">Normality <span style="color: #e36c0a; font-family: 'Arial','sans-serif'; font-size: 16px;">Relationship between the dv and the covariate is the same in every group


 * <span style="font-family: 'arial','sans-serif'; font-size: 16px;"> b. Role of the covariate - **<span style="color: #e36c0a; font-family: 'Arial','sans-serif'; font-size: 16px;">Covariate increases power and allows for the adjustment of non-equivalent groups.


 * c. <span style="font-family: 'arial','sans-serif'; font-size: 16px;">Conduct Test **
 * <span style="font-family: 'Arial','sans-serif'; font-size: 16px;"> i. Set up hypotheses **

<span style="color: #e36c0a; font-family: 'Arial','sans-serif'; font-size: 16px;">H0: mu 1 = mu 2 = mu 3

<span style="color: #e36c0a; font-family: 'Arial','sans-serif'; font-size: 16px;">H1: mu i ≠ mu j


 * <span style="font-family: 'Arial','sans-serif'; font-size: 16px;"> ii. Write observed test statistics using degrees of freedom **

<span style="color: #e36c0a; font-family: 'Arial','sans-serif'; font-size: 16px;">F(2, 14) = 5.246, p=.02


 * <span style="font-family: 'Arial','sans-serif'; font-size: 16px;"> iii. Decision and conclusion **

<span style="color: #e36c0a; font-family: 'Arial','sans-serif'; font-size: 16px;">There is a statistically different test score between the three groups with different teaching strategies, F(2,14)-5.246, p=.02. The means for the post test scores adjusted for any pre-test differences are 17.383 for strategy 1, 25.90 for strategy 2, and 19.998 for strategy 3. **

5. Split-Plot

a. Assumptions >> ¡ Normality >> ¡ Homogeneity >> ¡ Independence >>  Within-subjects >> ¡ Normality >> ¡ Sphericity >> ¡ Within-subjects Independence > > <span style="font-family: 'Arial','sans-serif'; font-size: 16px;">b. Conduct Test <span style="font-family: 'Arial','sans-serif'; font-size: 16px;"> i. Set up hypotheses <span style="font-family: 'Arial','sans-serif'; font-size: 16px;"> 1. Within Subjects <span style="color: #2924e5; font-family: Arial,sans-serif; font-size: 16px;">H0: mu1 = mu2 = mu3 = mu4
 * 1) ## Between-subjects

<span style="font-family: 'Arial','sans-serif'; font-size: 16px;"> 2. Between Subjects <span style="color: #101cc6; font-family: Arial,sans-serif; font-size: 16px;">Ho: mu1 = mu2

<span style="font-family: 'Arial','sans-serif'; font-size: 16px;"> ii. Write observed test statistics using degrees of freedom <span style="font-family: 'Arial','sans-serif'; font-size: 16px;"> iii. Decision and conclusion Example There is not a significant effect on the growth of infants due to exposure to the sound of a heartbeat. There is not a significant effect on the growth of infants due to number of days exposed to the sound of a heartbeat. However, there is a significant effect due to the interaction of the number of days and whether or not the treatment was the sound of the heartbeat or not.

6. Sphericity

a. Definition
 * 1) **<span style="color: #e36c0a; font-family: 'Arial','sans-serif'; font-size: 16px;">Sphericity holds when all measures have the same variance and all correlations between any pair of measures are equal. **

b. When it is used
 * <span style="color: #e36c0a; font-family: 'Arial','sans-serif'; font-size: 16px;">One-way within subjects ANOVA & split-plot ****<span style="color: #e36c0a; font-family: 'Arial','sans-serif'; font-size: 16px;">Use the Greenhouse-Geisser Adjustment. This adjusts the degrees of freedom, critical & p-values. **

**<span style="font-family: 'Arial','sans-serif';">Practice Problems: ** **<span style="font-family: 'Arial','sans-serif';">1. **