by: kristen lawlor and katie walsh. egyptians – used reddish-brown stains derived from henna to...
TRANSCRIPT
Nail Polish Experiment
By: Kristen Lawlor and Katie Walsh
The History of Nail Polish
• Egyptians– Used reddish-brown stains derived
from henna to color nails and fingertips
– Signified social order
• Chinese– Used colored lacquer: gum arabic,
egg whites, gelatin, beeswax– Colors chosen by royalty
• 1920s and 1930s– French make-up artist, Michelle
Menard, invented the modern, glossy nail polish
• Similar to car paint
– Revlon= first modern nail polish brand
Durability of Nail Polish
Categorical
• Brand• Color• Variation of Color• Style• General Style• Extra/Regular
Quantitative
• Cost• Number of Swipes• Nail Area
• Test how durable each nail polish was• Test theory to see if more expensive brands or styles are worth the extra cost
• Put same clear coat on each nail painted to eliminate nail texture error• 1 Coat of nail polish• Stratified and Systematic Sampling
• Different variety of age, lined up in groups of color and took every 4th from line• Used cotton balls and nail polish remover to take nail polish off
• Till nail polish completely removed
2%
7%2%
2%2%
2%
49%
9%
13%
2% 11%
Colors
BlueBrownGlitterGrayGreenOrangePinkPurpleRedSilverWhite
Brands
Colors
Histograms and Bar Charts
2
4
6
8
10
12
_of_Swipes
0 2 4 6 8 10 12 14 16
Collection 1 Histogram
2
4
6
8
10
12
14
16
18
Brand
Boun
dles
s C
olor
Chi
Cla
ire's
Del
ia's
Jord
ana
Just
Shi
neL.
A. G
irls
Lore
alLy
cra
May
bellin
em
olly
'n m
eN
.Y.C
.O
PIPu
re Ic
eR
evlo
nSa
lly H
anse
n Ulta
count
Collection 1 Bar Chart
2
4
6
8
10
12
14
16
General_Style
Glitt
er
Long
Wea
ring
Max
imum
Gro
wth
Nai
l Ena
mel
Nai
l Har
dene
r
Nai
l Lac
quer
Salo
n
count
Collection 1 Bar Chart
Linear Regression T-TestNumber of Swipes vs. Cost
0
2
4
6
8
10
12
14
16
Cost
0 1 2 3 4 5 6 7 8
_of_Sw ipes = -0.262Cost + 7.1; r2 = 0.029
-4
04
8
0 1 2 3 4 5 6 7 8
Cost
Collection 1 Scatter Plot
All costs received from store: A Beautiful Secret
•Negative•Linear•Weak•Scattered Residual Plot•Correlation (r)=0.170•Variance (r2)=0.029•17% of the change in number of swipes is due to the change in cost.•Overall, for our population of nail polish, as the cost increases the number of swipes decreases. Thus, the costlier the nail polish is, the less amount of nail polish remover is actually used. However, our data is not sufficient enough to show a strong enough relationship between the two variables.
Linear Regression T-TestNumber of Swipes vs. Cost
CONDITIONS
ASSUMPTIONS1. SRS2. Linear Data3. Independence4. Normal Residuals5. Equal Variance
CHECKS1. Sample is
randomized, but not by an SRS
2. Data is linear, but weak
3. Assumed 4. Normal Probability
Plot of Residuals5. In Residual plot,
change in spread but a very weak change
Linear Regression T-TestNumber of Swipes vs. Cost
We reject Ho because the p-value is less than alpha = 0.05.We have sufficient evidence that the change in number of swipes is equal to the change in cost on the linear regression graph. Thus as the number of swipes changes the cost also changes.
Ho: β= 0 Ha: β 0 ≠
-3.343
-3.343 92.5784 0.00122 *
Linear Regression T-TestNumber of Swipes vs. Nail Length (Area)
0
2
4
6
8
10
12
14
16
Nail_Length
0.0 0.5 1.0 1.5 2.0 2.5 3.0
_of_Sw ipes = 1.33Nail_Length + 4.2; r2 = 0.086
-4
0
48
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Nail_Length
Collection 1 Scatter Plot •Positive•Linear•Moderately Strong•Scattered Residual Plot•Correlation (r)= 0.293•Variance (r2)=0.0.086•29% of the change in the number of swipes is due to the change in nail length•Overall, for our population of nail polish, as the nail length (amount of nail polished used) increases, the amount of swipes of nail polish remover will also increase. Thus as more nail polish is used on one nail, the more swipes will needed to be used to get the nail polish off.
Calculated MeansAverage Number of Swipes for each General Style
GlitterLong Wearing
Maximum GrowthNail Enamel
Nail HardenerNail Lacquer
Salon
9.57.55.25.555565.857145.083335.85714
Calculated MeansAverage Number of Swipes for each General Style
• Overall, glitter had the most extreme average mean compared to all other styles
• Ironically, nail hardeners had lowest mean but large range
• According to our means: glitter averaged most durable
Glitter
Long Wearing
Maximum Grow th
Nail Enamel
Nail Hardener
Nail Lacquer
Salon
_of_Swipes
0 2 4 6 8 10 12 14 16
Collection 1 Box Plot
2-Sample T-TestCONDITIONS
ASSUMPTIONS1. 2 Independent
SRS
2. Pop1 ≥10*n1
Pop2 ≥10*n2
3. 2 Normal pop or
n1 and n2 ≥ 30
CHECKS1. Assumed 2. 510 ≤ 40 (doesn’t
check but we go on…)
3. n1 and n2 ≤ 30 (doesn’t check but we go on…)
2-Sample T-Test
Ho: 1 = 2 Ha: 1 2
= 2.246
P(t 2.246 df= 3.30016) = 0.051
We fail to reject Ho because our p-value is greater than alpha = 0.05.We have sufficient evidence that the number of swipes of all nails is equal to the number of swipes for the glitter.
>
Chi Squared Test for Independence
ASSUMPTIONS1. Categorical Data2. SRS3. All expected cell
counts are ≥ 5
CHECKS1. Yes, variation of color
and number of swipes are in categories
2. Data is randomized but not from an SRS
3. 8 out of 12 of cell counts are ≤ 5
Chi Squared Test for IndependenceHo: There is no association between the color and amount of swipesHa: There is an association between the color and amount of swipes
= 17.15
P(χ2>17.15/df=6)= 0.0087
We reject Ho because the p-value is less than α=0.05.There is an association between the color variance and the amount of swipes.
Overall Opinions
• Cost of nail polish does not affect the durability
• There is an association between the color variance (light/dark) and the number of swipes of nail polish remover it took to get it off.
• The glitter nail polish didn’t take longer to come off than the regular nail polish.
• In the future, if repeating this project, would suggest taking a larger sample size.
• Overall our tests proved our initial thoughts wrong.
Application to the Population• The population at large could use our
information, or similar information with larger data in nail salons in order to see which nail products to purchase according to their business strategy. – Some nail salons would preferably have
cheaper nail polish that comes off quicker– Others might want customer satisfaction
and get the best nail products.
Possible Errors
• Pressure of cotton ball while removing nail polish• Amount of remover on cotton ball• Size of nail proved to be positive slope
– Could effect entire results– Areas so close, not huge affect
• Some bias on randomization• Not having every brand and color of nail polish• Sally Hansen Nail Polish Remover