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32 Cards in this Set
- Front
- Back
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Comparing sample mean to population mean:
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H_0: X ̅= μ (null hypothesis)
H_1: X ̅≠ μ (non-directional research hypothesis) H_1: X ̅< μ (directional research hypothesis) H_1: X ̅> μ (directional research hypothesis) |
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Comparing two means (independent samples)
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H_0: μ_1= μ_2
H_1: X ̅_1≠ X ̅_2 H_1: X ̅_1< X ̅_2 H_1: X ̅_1> X ̅_2 |
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Comparing two means (dependent samples)
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H_0: μ_(post-test)= μ_(pre-test)
H_1: X ̅_(post-test)≠ X ̅_(pre-test) H_1: X ̅_(post-test)< X ̅_(pre-test) H_1: X ̅_(post-test)> X ̅_(pre-test) |
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Comparing more than two means (ANOVA)
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H_0: μ_1= μ_2= μ_3
H_1: X ̅_1≠ X ̅_2≠ X ̅_3 |
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Chi-square test for goodness-of-fit (one sample)
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H_0: P_1= P_2= P_3
H_1: P_1≠ P_2≠ P_3 |
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Chi-square test for independence (two sample)
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H_0: Variable A and variable B are independent
H_1: Variable A and variable B are not independent |
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Mean of a sample
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X ̅= (∑Xbar)/n
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Standard Deviation
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s= √((∑〖(X-Xbar)〗^2 )/(n-1))
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Variance of a sample
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s^2=(∑〖(X-X ̅)〗^2 )/(n-1)
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Standard error of the mean (for Z test)
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SEM= σ/√n
σ = standard deviation of the population |
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Short-cut for Chi-square for 2x2 contingency table:
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Yes No Total
Yes a b a+b No c d c+d Total a+c b+d n χ^2= 〖n(ad-bc)〗^2/((a+c)(b+d)(a+b)(c+d)) |
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Creating a histogram
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Find the range
create class intervals create frequency table histogram |
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Kurtosis
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Leptokurtic is pointy
Platykurtic is flat |
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What is under the curve
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o 1 SD from the mean is 34.13%
o Between 1 and 2 SD is 13.59% o Between 2 and 3 is 2.15% o After 3 SD is .13% |
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Z-Score
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z-score is the number of standard deviations from the mean
z= (X-Xbar)/s |
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Z test
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examines the difference between one sample and a population
Z= (Xbar-μ)/SEM SEM=σ/√n |
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Correlation
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ranges between -1 and 1
rxy= the correlation coefficient between x and y n= size of the sample x= individuals score on the x variable y = individuals score on the y variable |
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Geographic Distribution
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Mean center
Median Center Central Feature |
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Mean center
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the average x and y coordinate for all features in the study area
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Median center
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location having the shortest total distance to all features in the study area
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central feature
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feature having the shortest distance from all other features
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Linear regression formula
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y' = bx+a
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multivariate regression
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for every independent variable:
- separate coefficient - separate p-value - separate standard error |
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Global clustering
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determines weather a pattern is clustered
produces a single statistic with confidence intervals - NNI, Moran's I |
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Local Clustering
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determines where clusters are located
produces a map of clusters (hotspots) Kernal density, local Moran's I |
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NNI
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Nearest Neighbor Index
- compares the mean distance to the CSR hypothesis - NNI is determined as the ratio between observed mean distance and expected mean distance for CSR |
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NNI expected mean distane
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de=0.5/√(n-A)
n= number of features A= study area |
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NNI standard error
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SE = o.26136/√((n^2)-A)
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Global clustering for aggregated data
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Moran's I
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Moran's I
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Are differences between neighboring features smaller, greater of the same as the differences between the features and the mean
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Local Moran's I
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Clusters
HH - cluster of high values LL - cluster of low values |
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Gi* Interpretation
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Local clustering of aggregated data
Positive z score >1.96 = clustering of high values Negative z score <-1.96 = clustering of low values |
