Nurse Wages

Note:
  • Make sure to include the \(\mu\) part on the left-hand-side of yoru models.
  1. The hypotheses for the parallel lines test are:
    • HA \(\mu_{WAGE|EXPER,MALE} = \alpha+\beta EXPER+\delta_{1}MALE+\gamma_{1}EXPER:MALE\).
    • H0 \(\mu_{WAGE|EXPER,MALE} = \alpha+\beta EXPER+\delta_{1}MALE\).
  2. The hypotheses for the coincident lines test are:
    • HA \(\mu_{WAGE|EXPER,MALE} = \alpha+\beta EXPER+\delta_{1}MALE\).
    • H0 \(\mu_{WAGE|EXPER,MALE} = \alpha+\beta EXPER\).
  3. The hypotheses for the relationship test are:
    • HA \(\mu_{WAGE|EXPER,MALE} = \alpha+\beta EXPER\).
    • H0 \(\mu_{WAGE|EXPER,MALE} = \alpha\).

 

Turtle Nesting Ecology

Note:
  • Make sure to include the \(\mu\) part on the left-hand-side of yoru models.
  • The parallel lines test indicates that ALL of the lines are statistically parallel.
  • The coincident lines test indicates that SOME of the lines are not coincident.
  • When plotting the lines without any data then the y-axis label should include “mean.”
  1. The models for parallel lines test are as follows:
    • HA: \(\mu_{CSIZE|CCL,\cdots} = \alpha+\beta CCL+\)\(\delta_{1}IO+\delta_{2}RS+\delta_{3}+\delta_{4}WA+\) \(\gamma_{1}CCL:IO+\gamma_{2}CCL:RS+\gamma_{3}CCL:CO+\gamma_{4}CCL:WA\).
    • H0: \(\mu_{CSIZE|CCL,\cdots} = \alpha+\beta CCL+\)\(\delta_{1}IO+\delta_{2}RS+\delta_{3}+\delta_{4}WA\).
  2. The models for coincident lines test are as follows:
    • HA: \(\mu_{CSIZE|CCL,\cdots} = \alpha+\beta CCL+\)\(\delta_{1}IO+\delta_{2}RS+\delta_{3}+\delta_{4}WA\).
    • H0: \(\mu_{CSIZE|CCL,\cdots} = \alpha+\beta CCL\).
  3. The lines appear to be parallel across all regions (p=0.1192). Thus, the relationship between clutch size and curved carapace length does NOT differ among the regions.
  4. The intercepts appear to differ among some of the regions (p<0.00005). Thus, the mean clutch size at the same curved carapace length, no matter what that carapace length is, differs among some regions.
  5. There does appear to be a significant relationship between clutch size and curved carapace length (p<0.00005).

R Code and Results

ht <- read.csv("https://raw.githubusercontent.com/droglenc/NCData/master/HawksbillTurtles.csv")
ht$Region <- factor(ht$Region,
                    levels=c("Arabian Gulf","Indian Ocean","Red Sea",
                             "Caribbean","West Atlantic"))
ivr.ht <- lm(Clutch.Size~CCL+Region+CCL:Region,data=ht)
anova(ivr.ht)
Analysis of Variance Table

Response: Clutch.Size
            Df Sum Sq Mean Sq  F value    Pr(>F)
CCL          1 246757  246757 526.8775 < 2.2e-16
Region       4  22045    5511  11.7675 5.266e-09
CCL:Region   4   3461     865   1.8472    0.1192
Residuals  368 172349     468                   
ggplot(data=ht,mapping=aes(x=CCL,y=Clutch.Size,color=Region)) +  
  labs(x="Curved Carapace Length (cm)",y="Clutch Size") +  
  theme_NCStats() +  
  geom_smooth(method="lm",se=FALSE)
`geom_smooth()` using formula 'y ~ x'
Warning: Removed 140 rows containing non-finite values (stat_smooth).

 

Water Quality Near a Gold Mine

Analysis of Variance Table

Response: phosp
              Df  Sum Sq Mean Sq F value    Pr(>F)
distance       1  8863.5  8863.5 48.0590 1.763e-09
type           2  3135.0  1567.5  8.4992 0.0005016
distance:type  2     5.0     2.5  0.0137 0.9864185
Residuals     69 12725.7   184.4
  1. The models for parallel lines test are as follows:
    • HA: \(\mu_{P|DIST,\cdots} = \alpha+\beta DIST+\)\(\delta_{1}DP+\delta_{2}SP+\) \(\gamma_{1}DIST:DP+\gamma_{2}DIST:SP\).
    • H0</sub: \(\mu_{P|DIST,\cdots} = \alpha+\beta DIST+\)\(\delta_{1}DP+\delta_{2}SP\).
  2. The models for coincident lines test are as follows:
    • HA: \(\mu_{P|DIST,\cdots} = \alpha+\beta DIST+\)\(\delta_{1}DP+\delta_{2}SP\).
    • H0: \(\mu_{P|DIST,\cdots} = \alpha+\beta DIST\).
  3. The lines appear to be parallel across all three types of phosphorous (p=0.9864). Thus, the relationship between phosphorous level and distance from the gold mine does NOT differ among phosphorous types.
  4. The intercepts appear to differ among some of the phosphorous types (p=0.0005). Thus, the mean phosphorous level at the same distance from the gold mine, no matter what that distance is, differs among phosphorous types
  5. There does appear to be a significant relationship between phosphorous level and distance from the gold mine (p<0.00005).

R Code and Results

gm <- read.csv("http://derekogle.com/NCMTH207/modules/ce/data/GoldMine.csv")
gm$type <- factor(gm$type,levels=c("total","dissolved","soluble"))
ivr.gm <- lm(phosp~distance+type+distance:type,data=gm)
anova(ivr.gm)
Analysis of Variance Table

Response: phosp
              Df  Sum Sq Mean Sq F value    Pr(>F)
distance       1  8863.5  8863.5 48.0590 1.763e-09
type           2  3135.0  1567.5  8.4992 0.0005016
distance:type  2     5.0     2.5  0.0137 0.9864185
Residuals     69 12725.7   184.4                  
ggplot(data=gm,mapping=aes(x=distance,y=phosp,color=type)) +  
  labs(x="Distance from Gold Mine (km)",y="Phosphrous Level (ppm)") +  
  theme_NCStats() +  
  geom_smooth(method="lm",se=FALSE)
`geom_smooth()` using formula 'y ~ x'