A few researchers set out to determine the optimal length of chopsticks for children and adults. They came up with a measure of how effective a pair of chopsticks performed, called the "Food Pinching Performance." The "Food Pinching Performance" was determined by counting the number of peanuts picked and placed in a cup (PPPC).
Link to Abstract and Paper
the abstract below was adapted from the link
Chopsticks are one of the most simple and popular hand tools ever invented by humans, but have not previously been investigated by ergonomists. Two laboratory studies were conducted in this research, using a randomised complete block design, to evaluate the effects of the length of the chopsticks on the food-serving performance of adults and children. Thirty-one male junior college students and 21 primary school pupils served as subjects for the experiment to test chopsticks lengths of 180, 210, 240, 270, 300, and 330 mm. The results showed that the food-pinching performance was significantly affected by the length of the chopsticks, and that chopsticks of about 240 and 180 mm long were optimal for adults and pupils, respectively. Based on these findings, the researchers suggested that families with children should provide both 240 and 180 mm long chopsticks. In addition, restaurants could provide 210 mm long chopsticks, considering the trade-offs between ergonomics and cost.
Download the data set for the adults, then answer the following questions based on the abstract and the data set.
If you double click on this cell, you will see the text change so that all of the formatting is removed. This allows you to edit this block of text. This block of text is written using Markdown, which is a way to format text using headers, links, italics, and many other options. You will learn more about Markdown later in the Nanodegree Program. Hit shift + enter or shift + return to show the formatted text.
The dependent variable in the experiment is the Food Pinching Efficiency as it is dependent on the Chopstick Length in order to have a value.
The dependent variable Food Pinching Efficiency is operationally defined by the number of peanuts picked and placed in a cup (PPPC).
One great advantage of ipython notebooks is that you can document your data analysis using code, add comments to the code, or even add blocks of text using Markdown. These notebooks allow you to collaborate with others and share your work. For now, let's see some code for doing statistics.
In [3]:
import pandas as pd
# pandas is a software library for data manipulation and analysis
# We commonly use shorter nicknames for certain packages. Pandas is often abbreviated to pd.
# hit shift + enter to run this cell or block of code
In [4]:
path = r'~/udacity-data-analyst-nanodegree/P0/data.csv'
# Change the path to the location where the chopstick-effectiveness.csv file is located on your computer.
# If you get an error when running this block of code, be sure the chopstick-effectiveness.csv is located at the path on your computer.
dataFrame = pd.read_csv(path)
dataFrame
Out[4]:
Let's do a basic statistical calculation on the data using code! Run the block of code below to calculate the average "Food Pinching Efficiency" for all 31 participants and all chopstick lengths.
In [5]:
dataFrame['Food.Pinching.Efficiency'].mean()
Out[5]:
This number is helpful, but the number doesn't let us know which of the chopstick lengths performed best for the thirty-one male junior college students. Let's break down the data by chopstick length. The next block of code will generate the average "Food Pinching Effeciency" for each chopstick length. Run the block of code below.
In [6]:
meansByChopstickLength = dataFrame.groupby('Chopstick.Length')['Food.Pinching.Efficiency'].mean().reset_index()
meansByChopstickLength
# reset_index() changes Chopstick.Length from an index to column. Instead of the index being the length of the chopsticks, the index is the row numbers 0, 1, 2, 3, 4, 5.
Out[6]:
In [6]:
# Causes plots to display within the notebook rather than in a new window
%pylab inline
import matplotlib.pyplot as plt
plt.scatter(x=meansByChopstickLength['Chopstick.Length'], y=meansByChopstickLength['Food.Pinching.Efficiency'])
# title="")
plt.xlabel("Length in mm")
plt.ylabel("Efficiency in PPPC")
plt.title("Average Food Pinching Efficiency by Chopstick Length")
plt.show()
Based on the data and the plot, we can conclude that the chopstick of length 240mm performed the best for the group of thirty-one male junior college students.
The chopstick of this length has the best mean value of PPPC (26.322903) when compared to all other lengths.
Although not perfect, we can see an inversal correlation between the length of the chopsticks and it's efficiency. If we divide the plot into four equal quadrants, this relationship is easily visible.
Based on the data analyzed, I do agree with the claim.
It is clear from analyzing at the mean efficiency of each chopstick length and from analyzing the plot that the chopsticks of about 240mm is optimal for adults.
The mean efficiency for the chopsticks of 240mm length is the greatest out of all of the other chopstick sizes (26.322903).
In [69]:
import math
efficiencyMeans = dataFrame.groupby('Chopstick.Length')['Food.Pinching.Efficiency'].mean().reset_index()['Food.Pinching.Efficiency']
def getMeanFromArrayOfData(data):
return sum(data) / len(data)
def getDataMinusMean(data, mean):
return [value - mean for value in data]
def elevateValuesToPower(data, power):
return [value ** power for value in data]
mean = getMeanFromArrayOfData(efficiencyMeans)
standardDeviation = math.sqrt(sum(elevateValuesToPower(getDataMinusMean(efficiencyMeans, mean), 2)) / len(efficiencyMeans))
maximumMean = efficiencyMeans[2]
standardError = standardDeviation / math.sqrt(len(efficiencyMeans))
cohensD = (maximumMean - mean) / standardError
cohensD
Out[69]:
Also, from Conhen's Distance, we can see that there is a significant difference between the maximum efficiency mean and the average efficiency (4.257 standard errors). This is a statistically significant difference, which concludes that the 240mm chopstick length is the optimal value.