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Flashcards in BIO 330 Deck (379)
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211

understanding r

easy to understand because of lack of units, however, can trick you into thinking comparable across studies- across studies need to limit ranges

212

Attenuation bias

if x or y are measured with error, r will be lower; with increasing error, r is underestimated; avoided by taking means of subsamples

213

correlation and significance

statistically sig. relationships can be weak, moderate, strong
sig.– probability, if Ho is true
correlation– direction, strength of linear relationship

214

weak, moderate, strong correlation

r = ±0.2 – weak
r = ±0.5 – moderate
r = ±0.8 – strong

215

correlation assumptions

bivariate normality- x and y are normal
relationship is linear

216

dealing with assumption violations (correlation)

histograms
transformations in one or both variables
remove outlier

217

outlier removal

–need justification (i.e. data error)
–carefully consider if variation is natural
–conduct analyses w/ and w/o outlier to assess effect of removal

218

natural variation, outliers

is your n big enough to detect if that is natural variation in the data

219

if outlier removal has no effect

may as well leave it in!

220

non-parametric Correlation

Spearman's rank correlation; strength and direction of linear association btw ranks of 2 variables; useful for outlier data

221

Spearman's rank correlation assumptions

random sampling
linear relationship between ranks

222

Spearman's rank correlation

r_s: same structure as Pearson's correlation but based on ranks
r_s = [Σ(Ri-Rbar)(Si-Sbar)] / [ Σ(Ri-Rbar)^2Σ(Si-Sbar)^2 ]

223

conducting Spearmans

rank x and y values separately; each data point will have 2 ranks; sum ranks for each variable; n = # data pts.; divide each rank sum by n to get Rbar and Sbar; calculate r_s (statistic); calculate critical r_s(0.05,df)

224

if 2 points have same rank (Spearman)

average of that rank and skip rank before/after; w/o any ties, the 2 values on the bottom of r_s equation will be the same

225

Spearman hypothesis

ρ_s = 0, correlation = 0

226

Spearman df

df = n because no estimations are being made in ranking

227

linear regression

–relationship between x and y described by a line
–line can predict y from
–line indicates rate of change of y with x
Y = a + bX

228

correlation vs. regression

regression assumes x,y relationship can be described by a line that predicts y from x
corr.- is there a relationship
reg.- can we predict y from x

229

perfect correlation

r = 1, all points are exactly on the line– regression line fitted to that 'line' could be the exact same line for a non-perfect correlation

230

rounding mean results

DO NOT; 4.5 puppies is a valid answer

231

best line of fit

minimizes SS = least squares regression; smaller sum of square deviations

232

used for evaluating fit of the line to the data

residuals

233

residuals

difference between actual Y value and predicted values for Y (the line); measure scatter above/below the line

234

calculating linear regression

calculate slope using b = formula; find a– a = Ybar - bXbar; plug in to Ybar = a + bXbar; rewrite as Y = a + bX; rewrite using words

235

Yhat

predicted value- if you are trying to predict a y value after equation has been solved

236

why do we solve linear regression with Xbar, Ybar

line of fit always goes through Xbar, Ybar

237

how good is line of fit

MSresiduals = Σ(Yi - Yhat)^2 / n-2
which is SSresidual / n-2
quantifies fit of line- smaller is better

238

Prediction confidence, linear regression

precision of predicted mean Y for a given X
precision of predicted single Y for a given X

239

Precision of predicted mean Y for a given X, linear regression

narrowest near mean of X, and flare outward from there; confidence band– most confident in prediction about the mean

240

precision of predicted single Y for a given X, linear regression

much wider because predicting a single Y from X is more uncertain than predicting the mean Y for that X