# Review for Exam 1

Prof Randi Garcia
February 28, 2018

### Announcements

• HW 4, due today
• Exam 1 passed out today
• Due March 7, at 5pm

### Agenda

• Practice recognizing designs
• Exam review

### Design Questions

1. How many structural factors are there? What might you call them?
2. How many levels does each factor have? What are they?
3. How are the factors related? (i.e., crossing, blocking)
4. What is the response variable? What's its level of measurement?
5. What are the experimental units?
6. What's the name of this design?

The Canada goose is a magnificent bird, but it can be a nuisance in urban areas in large numbers. One method of population control is to addle eggs in nests, but this method can hard adult females. Would removal of the eggs at the usual hatch date prevent harm? It is suspected that females nesting together at different sites are similar to each other. We randomly select 5 different sites, and we then randomly assign 5 nests per site to the addle with no removal condition, and 5 nests per site to the addle plus removal condition. The females at the nests are banded such that survival age can be measured later.

### Paper Helicopters

Paper helicopters can be cut from one half of an 8.5 by 11 sheet of paper. We can conduct an experiment by dropping helicopters from a fixed height and clocking the time it takes to drop. We can vary wing length: 4.25 in, 4.0 in, 3.75 in, and 3.5 in, as well as body width: 3.25 in, 3.75 in, 4.0 in, and 4.25 in. We'll make 32 planes and randomly assign them to the 16 combinations.

### Parks and Recreation

Deputy director of the Pawnee Parks and Rec department, Leslie Knope, needs to know how resistant different vegetative types are to trampling so that the number of visitors can be controlled in sensitive areas. Twenty lanes of a park are established, each .5 m wide and 1.5 m long. These twenty lanes are randomly assigned to five treatments: 0, 25, 75, 200, or 500 walking passes. Each pass consists of a 70-kg individual wearing boots, walking in a natural gait. One year after trampling, the average height of the vegetation along the lanes are measured.

### ANOVA Source Table for BF[1]

• Using algebraic Notation

${y}_{ij}=\mu+{\alpha}_{i}+{e}_{ij}$

${H}_{0}:{\alpha}_{1}={\alpha}_{2}=...={\alpha}_{a}$

Source SS df MS F
Treatment $$n\sum_{i=1}^{a}(\bar{y}_{i.}-\bar{y}_{..})^{2}$$ $$a-1$$ $$\frac{{SS}_{Treatments}}{{df}_{Treatments}}$$ $$\frac{{MS}_{Treatments}}{{MS}_{E}}$$
Error $$\sum_{i=1}^{a}\sum_{j=1}^{n}({y}_{ij}-\bar{y}_{i.})^{2}$$ $$N-a$$ $$\frac{{SS}_{E}}{{df}_{E}}$$

### Inside-outside Factors

• One factor is inside another if each group of the first (inside) fits completely inside some group of the second (outside) factor.
• Estimated effect for a factor = Average for the factor - sum of estimated effects for all outside factors.
• The sum of estimated effects for all outside factors is called the partial fit.
• Thus, the general rule is:

$Effect = Average - Partial Fit$

### Inside-outside Factors

student animal cute scary
2 cat 5 1
5 cat 5 5
1 dog 5 1
3 dog 4 2
• Draw the factor diagram as a hierarchy of inside and outside factors.
• Use the inside-outside rule to calculate effects for this example we we did for the leafhoppers.

### Six Fisher Assumptions

• C. Constant effects
• S. Same standard deviations
• I. Independent residuals
• N. Normally distributed residuals
• Z. Zero mean residuals

### Measurement Scale

• nominal: alcohol drinking (yes/no) of college students
• ordinal: “small,” “medium,” and “large” size drinks at a movie theater.
• interval: scores on a “self-esteem” scale of middle- and upper-level managers
• ratio: students’ individual times to complete cognitive task (e.g., 2:15, 2: 21, 2:33, etc.)

### Design Principals

1. Random Assignment
2. Blocking
3. Factorial Crossing

### Four Basic Designs

1. Randomized Basic Factorial Design BF[1]
2. One-Way Complete Block Design CB[1]
3. Two-Way Basic Factorial Design, BF[2]
4. Split Plot/Repeated Measures Design, SP/RM[1,1]

### Leafhoppers

An experiment was conducted to compare the effects of four sugar diets on the survival of leafhoppers. The four diets were glucose and fructose (6-carbon atoms), sucrose (12-carbon), and a control (2% agar). The experimenter prepared two dishes with each diet, divided the leafhoppers into eight groups of equal size, and then randomly assigned them to dishes. Then she counted the number of days until half the insects had died.

### Leafhoppers

Randomized Basic Factorial Design BF[1]

### Gender Bias in STEM

In a randomized double-blind study (n = 127), science faculty from research-intensive universities rated the application materials of a student who was randomly assigned either a male or female name for a laboratory manager position. Faculty participants rated the male applicant as significantly more competent and hireable than the (identical) female applicant. These participants also selected a higher starting salary and offered more career mentoring to the male applicant. See materials here

### Gender Bias in STEM

Randomized Basic Factorial Design BF[1]

### Acid Rain

“Clean” precipitation has a pH in the 5.0 to 5.5 range, but observed precipitation pH in northern New Hampshire is often in the 3.0 to 4.0 range. Is this acid rain hurting trees? 240 six-week-old yellow birch seedlings were randomly assigned to one of 5 groups. Each group received an acid rain mist at the following pH levels: 4.7, 4.0, 3.3, 3.0, and 2.3. After 17 weeks, the seedling were weight, and their total plant (dry) weight was recorded.

### Acid Rain

Randomized Basic Factorial Design BF[1]

### Inappropriate Insects

Modern zoos try to reproduce natural habitats in their exhibits as much as possible. They try to use appropriate plants, but these plants can be infested with inappropriate insects. Cycads (plants that look vaguely like palms) can be infected with mealybugs, and the zoo wishes to test three treatments: 1) water, 2) horticultural oil, and 3) fungal spores in water. Five infested cycads are taken to to the testing area. Three branches are randomly selected from each tree, and 3 cm by 3 cm patches are marked on each branch. The number of mealybugs on the patch is counted. The three treatments then get randomly assigned to the three branches for each tree. After three days the mealybugs are counted again. The change in number of mealybugs is computed ($$before-after$$).

### Inappropriate Insects

One-Way Complete Block Design CB[1]

Most people believe that country air is better to breather than city air, but how would you test it? You might start by choosing a response that narrows down what you mean by “better.” One feature of healthy lungs is tracheobronchial clearance—how fast they get rid of nasty stuff. To test this idea, investigators found 7 sets of mono-zygotic twins where one was living in the country and one in the city. Each person inhaled an aerosol of radioactive Teflon particles. Then the level of radioactivity was measured once right after inhaling, and again an hour later. The percent of the original radioactivity remaining was calculated.

One-Way Complete Block Design CB[1]

Objectification theory (Fredrickson & Roberts, 1997) posits that American culture socializes women to adopt observers' perspectives on their physical selves. This self-objectification is hypothesized to (a) produce body shame, which in turn leads to restrained eating, and (b) consume attentional resources, which is manifested in diminished mental performance. An experiment manipulated self-objectification by having participants try on a swimsuit or a sweater. Further, it tested 21 women and 20 men, in each conditiobn, and found that these effects on body shame and restrained eating replicated for women only. Additionally, self-objectification diminished math performance for women only.