Report the Result Flashcards
Sharpiro-Wilk- test
testing for normality
p > πΆ
- accept H0: normally distributed
- The observed data on Cheetah speed do not significantly deviate from Normal distribution (Sharpiro-Wilk-test, W=0.985, p>0,05)
- F-test to test for equal variance
p < πΆ
- reject H0: not normally distributed
- The observed data on lion speed significantly deviate from Norma distribution (Shapiro-WIlk_test, W=0,93, p<0,001)
- Wilcoxon rank sum test
Fischers F-test
testing for equal varainces
p > πΆ: Accept H0 equal variance
- The variance of the ozone concentrations mesured in gardenA and B are not significantlly different (F-test, F19,19= 1,09, p> 0,05)
- t-test
p < πΆ: reject H0: no equal varaince
- The variance of the weight of mallards in Germnay and NYC are significantlly different (F-test, F29,29= 0,188, p< 0,05)
- Welch-test
One Samle T-Test
does the mean differ from a specific value (equal means)
p> πΆ/2: accept H0 equal means
* The mean ozone concentration of garden A is not significanttyl different to the accepted air quality standard (t-test, t= 5, df= 19, p>0,05)
p β€ πΆ/2: reject H0 non equal means
* The mean ozone concentration of garden B differeres significantly from the accpeted standard for air qualitiy (t-test, t=5,4, df=19, p< 0,001*)
Two samle T-test
testing for eqaul means in 2 data sets/ compare
p > πΆ: accept H0
- The mean ozone concentrations measured in garden B (3.11 pphm) and garden D (3.11 pphm) do not differ significantly (t-test, t=-5.3, df = 38, p > 0.05)
p < πΆ: reject H0
* The mean ozone concentrations measured in garden A (3.11 pphm) and garden B (4.98 pphm) differ significantly (t-test, t=-5.3, df = 38, p β€ 0.001***)
Welsch-test
unequal variance t-test for comparing means
p > πΆ: accept H0
* The men ozone concentartion measured in garden C and D do not significantlly differ (Welcht-test, t= 0,47, p>005)
p < πΆ: reject H0
- The mean ozone concentartion measured in garden G and D significantlly differ (Welcht-test, t= 0,47, p<0,001*)
Wilcoxonβs rank-sum-test
non-parametric test for comparing means with not normally distributed errors
p > πΆ: accept H0
* The mean speed of CheetahsA do not significantlly differ from CheetahsB (ilcoxon rank-sum test, W=100, p>0,05)
p < πΆ: reject H0
* The mean speed of cheetah (76.4 km/h) is significantly larger than the mean speed of lion (26.4 km/h; Wilcoxon rank-sum test, W=100, p < 0.001***).
Chi-squared test
How likely are the observed frequencys if H0 was true (if the two variables were independent)
π2 = β (O-E)^2 /E (observed and expected)
- compare π2 to critical value. If π2 is bigger -> reject H0.
- There is a highly significant assosiaction between hair and eye color for this group of people (Chi-saquare test, π2= 35,4, df=1, p> 0,0001*)
Contingency tables
Fishers exact test
if one or more of the expected frequencies of the contingousy table are less than 5
- Ants do not prefer a specific tree species (Fishers exact test, p> 0,05)
Pearson correlation coefficient
Correlation between two variables significantlly differ from zero
r = 1 Strong positive correlation
r= 0 No correlation
r = -1 Strong negative correlation
- There is a significant positive correlation between species richness of spiders and carabids in the plots (right-tailed Pearson correlation test, t=5.86, df=22, p<0.001***, correlation r=0.78).
Spearmans rank correlation coefficient
linear releationship between two variables if data is not normally distributed
rho = 1 Strong positive correlation
rho = 0 No correlation
rho = -1 Strong negative correlation
- There is a significant positive correlation between species richness of spiders and carabids in the plots (right-tailed Spearman rank correlation test, S=507.82, p<0.001***, correlation rho=0.78).
Linear regeression
- The linear regression model identified a significantly positive effect of girth (at breast height) on the volume of black cherry trees (F- test, F1,29=419.4, p<0.001***, R2=0.94).
Anova F-test
Including Girth as predictor in the linear model has significantly reduced the un- explained variance in the data compared to the null model (F-test, F1,29=419.4, p<0.001***).
One-way ANOVA
categorical predictor variable (factor) with 3 or more levels
(Check assumptions: just 3 plots this time
Normality of errors, Costancy of variance, no influencial outliers)
- We carried out an ANOVA to test whether the garden location had a significant effect on the measured ozone concentration. The mean ozone concentrations significantly differ between the three garden markets (F-test, F2,57=4.197, p<0.05*). Assumptions were checked by residual diagnostic plots. The estimated means are shown in Table 1
ANCOVA
Polinomial Regressions plot curve shapes
linear
parabola (- β, +β)
cubic
quartic
TWO WAY ANOVA
GLM Logistic regression (binomial)
We estimated a GLM with binomial error distribution to test the effect of island area and island isolation from mainland on the occurrence probability of the Galapagos Royal Frigate bird (likelihood-ratio test, deviance 39.63, df=2, p<0.001).
We found that bird incidence significantly decreases with island isolation and significantly increases with island area.
Errors
Type 1 Error: H0 rejected but H0 is true (probability πΌ
Type 2 Error: H0 is accepted, but it is false (probability Ξ²)
