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181

test statistics

used to evaluate whether the data is reasonably expected under the Ho

182

P-value

probability of getting the data, or something more unusual, given Ho is true

183

reject Ho if

p-value ≤ alpha
less than OR equal to
0.049, 0.05

184

Steps in hypothesis testing

1. State Ho and Ha
2. Calculate test statistic
3. Determine critical value or P-value
4. Compare test statistic to critical value
5. Evaluate Ho using sig. level (and interpret)

185

Type I error

Reject Ho, given Ho true

186

Type II error

Do not reject Ho, given Ho is false

187

If we reduce alpha

P[Type I] decreases, P[Type II] increases

188

Experimental design steps

1.Develop clear statement of research question
2.List possible outcomes
3.Develop experimental plan
4.Check for design problems

189

How to minimize bias

control group, randomization, blinding

190

How to minimize sampling error

replication- lare n lowers noise
balance- lowers noise
blocking

191

to avoid pseudoreplication

check df- obviously if its huge something is wrong

192

Tukey-Kramer

for 3 means: three Y bars, three Ho's; Q distribution; 3 row table w/ group i, group y, difference in means, SE, test statistic, critical q, outcome (reject/do not)

193

Q-distribution

symmetrical, uses larger critical values to restrict Type I error; more difficult to reject null

194

Tukey-Kramer test statistic

q = Y_i(bar) - Y_j(bar) / SE
SE = √ MSerror(1/n1 + 1/n2)

195

Tukey-Kramer testing

test statistic, q-value
critical value, q_α,k,N-k
k = # groups
N = total # observations

196

Tukey-Kramer assumptions

random samples
data normally distributed in each group
equal variances in all groups

197

2 Factor ANOVA

2 Factors = 3 Ho's: difference in 1 factor, difference in 2nd factor, difference in interaction

198

If interaction is significant

do not conclude that factor is not

199

Interaction plots

y-axis: response variable
x-axis: one of 2 main factors
legend for: other of 2 main factors (different symbols or colors)
2 lines

200

interpreting interaction plot, interaction

lines parallel: no significance in interaction

201

interpreting interaction plot, b (data not on x-axis)

take average along each line and compare the 2 on the y-axis, if they are not close then they are significant

202

interpreting interaction plot, a (data on x-axis)

x-axis: take average between the 2 dots (for each level of a), compare on y-axis, if they are not close they are significant

203

control groups in an observational/experimental study will

reduce bias
will not affect sampling error

204

correlation ≠

causation

205

correlation

"r"- comparing 2 numerical variables, [-1,1], no units, always linear
quantify strength and direction of LINEAR relationship (+/-)

206

how to calculate correlation

r = signal/noise
signal= deviation in x and y together for every point (multiply each deviation before summing)

207

correlation Ho

no correlation between interbreeding and number of pup surviving their first winter (ρ = 0)

208

determining correlation

test statistic: r/SE_r
SE_r = √ (1-r^2) / (n-2)
df = n-2
critical: tα,(2),df
compare statistic w/ critical

209

df

n - number of parameters you estimate
correlation- you estimate 2
mann whitney- 0 parameters

210

stating correlation results

be careful not to interpret-- no causation!