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 PolishCategorical

• 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_Swipes0 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

PI

Pure

Ice

Rev

lon

Sally

Han

sen 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

02

4

6

810

12

14

16

Cost0 1 2 3 4 5 6 7 8

_of_Sw ipes = -0.262Cost + 7.1; r2 = 0.029

-4048

0 1 2 3 4 5 6 7 8Cost

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 SRS2. Data is linear, but

weak3. 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)

02

4

6

810

12

14

16

Nail_Length0.0 0.5 1.0 1.5 2.0 2.5 3.0

_of_Sw ipes = 1.33Nail_Length + 4.2; r2 = 0.086

-4048

0.0 0.5 1.0 1.5 2.0 2.5 3.0Nail_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_Swipes0 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*n23. 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-TestHo: 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.

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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