What is the statistical hypothesis?

Null Hypothesis: H0: All the means are equal. There is no significant difference between the sample means of distance felt of the paper clip between different body parts

Alternative Hypothesis: Ha: Not all the means are equal, and the test is right-tailed. There is a significant difference between the sample means of distance felt of the paper clip between different body parts

Design and conduct your experiment. Explain any flaws in the execution of the experiment.

In order to get the most consistent results, as a team we decided to use the Target brand paper clips. The materials needed to conduct the experiment are one paper clip and one participant. For the results to be even more consistent we used one person to the test the 5 different body parts on. In order to have had better results we could have all had our participant’s ages are around the same. We were not able to do this due to everyone’s different living situation.

Materials Needed: 3 people Target brand paperclip Ruler (mm)

Instructions:

  1. Open up the paperclip and fold it into a half circle making sure the two ends of the paperclip are aligned.

  2. Make sure the people you are testing the experiment on have their elbow, underside of the arm, underside of the index finger, and elbow exposed.

  3. Blindfold the participant being tested in order for them to not know how ends of the paperclip they are actually feeling.

  4. Start with the paperclip wide and poke the participant on each part of the body asking them if they feel like they are being poked in one or two different places. Close the paperclip little by little until the participant responds saying they feel like they are only being poked in one place. Once you make sure then is when they started feeling the 2 ends of the paperclip being poked in the same spot, write down the measurement using mm as your unit. Repeat until data is collected for all 4 body parts.

  5. Repeat steps 3 and 4 for the other 2 participants.

How did you analyze the data and show graphical display? (ie, graphs, descriptions, test of assumptions like normality, independent two sample ttest, dependent paired ttest, Mann Whitney, ANOVA, Chisquare test of Association, Kruskall-Wallis etc.)

We decided to use the ANOVA test in order to analyze our data. This is because the data we collected has more than 2 samples, is quantitative, and examines the difference between means. The tests are also independent of each other which is why we decided on the one way ANOVA test instead of randomized block ANOVA test. We also had to do an assumptions of normality test to make sure that the distributions of independent samples were normal.

Data (by person)

sara.ali
## # A tibble: 3 × 5
##    ...1 `Arm Underside` `Top of Hand` `Index Finger Underside` Elbow
##   <dbl>           <dbl>         <dbl>                    <dbl> <dbl>
## 1     1              63            10                       25    55
## 2     2              75            25                       23    36
## 3     3             100            50                       10    79
sana.taleb
## # A tibble: 3 × 5
##    ...1 `Arm Underside` `Top of Hand` `Index Finger Underside` Elbow
##   <dbl>           <dbl>         <dbl>                    <dbl> <dbl>
## 1     1              81            27                        4    67
## 2     2             102            42                       18    54
## 3     3              80            45                       17    65
george.tsirkas
## # A tibble: 3 × 5
##    ...1 `Arm Underside` `Top of Hand` `Index Finger Underside` Elbow
##   <dbl>           <dbl>         <dbl>                    <dbl> <dbl>
## 1     1              68            36                        5    24
## 2     2              62            28                        5    20
## 3     3              58            25                        5    18
ayah.farran
## # A tibble: 3 × 5
##    ...1 `Arm Underside` `Top of Hand` `Index Finger Underside` Elbow
##   <dbl>           <dbl>         <dbl>                    <dbl> <dbl>
## 1     1              62            25                        5    20
## 2     2              56            24                        3    17
## 3     3              67            30                        7    29
donnie.lee
## # A tibble: 3 × 5
##    ...1 `Arm Underside` `Top of Hand` `Index Finger Underside` Elbow
##   <dbl>           <dbl>         <dbl>                    <dbl> <dbl>
## 1     1              20            15                        2    20
## 2     2              25            17                       10    28
## 3     3              30            11                       18    26

Cummalitive Data

projectb <- read_excel("/Users/saraali/Downloads/projectb.xlsx")
view(projectb)
distance <- projectb$distance
bodypart <- projectb$bodypart
ggplot(projectb, aes(y=distance, x=bodypart)) + 
    geom_bar(position="dodge", stat="identity")

projectb
## # A tibble: 60 × 2
##    distance bodypart
##       <dbl> <chr>   
##  1       81 arm     
##  2      102 arm     
##  3       80 arm     
##  4       63 arm     
##  5       75 arm     
##  6      100 arm     
##  7       68 arm     
##  8       62 arm     
##  9       58 arm     
## 10       27 hand    
## # … with 50 more rows
summary(projectb)
##     distance        bodypart        
##  Min.   :  2.00   Length:60         
##  1st Qu.: 17.00   Class :character  
##  Median : 25.00   Mode  :character  
##  Mean   : 34.57                     
##  3rd Qu.: 55.25                     
##  Max.   :102.00

Test for normality

The data is normal because most of the data points fall on a straight line. The anderson-darling test also shows that the p-value is much smaller than 0.05 so the data is normally distributed.

qqnorm(projectb$distance, pch=1, frame=FALSE)
qqline(projectb$distance, col="steelblue", lwd=2)

ad.test(projectb$distance)
## 
##  Anderson-Darling normality test
## 
## data:  projectb$distance
## A = 2.1688, p-value = 1.422e-05

Test for equal variance

Bartlett’s test shows that we have unequal variance because the p-value is less than 0.05 which means we will have to conduct an ANOVA test with pooled variances

bartlett.test(projectb$distance~projectb$bodypart)
## 
##  Bartlett test of homogeneity of variances
## 
## data:  projectb$distance by projectb$bodypart
## Bartlett's K-squared = 19.098, df = 3, p-value = 0.000261

Anova test with normality and unequal variance

The p-value is smaller than 0.05 so we can reject the null hypothesis and conclude that there is a significant difference between the sample means.

oneway.test(projectb$distance~projectb$bodypart)
## 
##  One-way analysis of means (not assuming equal variances)
## 
## data:  projectb$distance and projectb$bodypart
## F = 27.784, num df = 3.000, denom df = 28.691, p-value = 1.245e-08

Analysis w/ graph support

The tukeyHSD test shows that p-value for most of the pairs are far below 0.05, this means there is a significnat difference between the sensory ability of those bodyparts. We reject the null hypothesis since there is sufficient evidence that there is a significant difference between sensory ability of bodyparts.

res.aov <- aov(projectb$distance~projectb$bodypart)
TukeyHSD(res.aov)
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = projectb$distance ~ projectb$bodypart)
## 
## $`projectb$bodypart`
##                    diff          lwr        upr     p adj
## elbow-arm    -26.066667 -42.94859867  -9.184735 0.0007886
## finger-arm   -52.800000 -69.68193200 -35.918068 0.0000000
## hand-arm     -35.933333 -52.81526534 -19.051401 0.0000035
## finger-elbow -26.733333 -43.61526534  -9.851401 0.0005596
## hand-elbow    -9.866667 -26.74859867   7.015265 0.4166181
## hand-finger   16.866667  -0.01526534  33.748599 0.0502898
ggplot(projectb, aes(x=distance, y=bodypart)) +
  geom_point()

Outliers (special causes)

There are multiple outliners for the arm data. A possible cause for this could be which area of the arm was tested since the arm is a larger part of the body compared to the other body parts being tested and could be hard to standardize where exactly on the arm the paper clip is tested. The difference in age and body size could also play a role in the outliers, the larger someone is the more spaced out the nerve endings are. Gender can also a part since women tend to be more sensitive to touch than men because a women’s skin is typically thinner than a man’s skin. The arm is less sensitive to touch and many of the participants reported not being able to feel it as distinctly as other body parts.

ggplot(projectb, aes(x=distance, y=bodypart)) + 
    geom_boxplot(fill="slateblue", alpha=0.2)