One-Way ANOVA AnalysisEffects of Mentos on Different Types of Soda

Matt Estock

Jacky Li

Huseyin Zorba

January 4, 2011

Executive SummaryThe effects which Mentos have on soda are commonly known. However the statistical

significance of the difference in the reaction dependent on the type of soda is not as clearly defined. Through this experiment the null hypothesis that all sodas will have the same reactivity to Mentos was tested. Four different types of sodas were used as the different treatments and the volume of soda left after the eruption was measured. The smaller the amount left over the larger the reaction to the presence of Mentos.

The sample size of six that was used for the experiment was sufficient enough to produce a 0.9155 confidence level. This was significant because if fewer samples were used, the same amount of confidence would not have been achieved and the results would have been questioned far more. Since the degree of this experimentation was not life threatening like those of medical research, there was no need for a very high confidence level and a confidence level of ~ .90 was sufficient enough for this experiment.

After determining the right sample size and performing the experiment, with the help of Minitab it was concluded that all of the types of soda tested do not react the same when Mentos were added. After the ANOVA analysis was completed, it was clear that the experiment’s null hypothesis H0: µcoke = µDietCoke = µSprite = µFanta should be rejected because of the fairly large F-stat value of 53.97 when compared with the F-test value of 2.38.

In order to validate the ANOVA assumptions so that the ANOVA analysis yielded legitimate results, the residuals from the collected data were analyzed. When analyzing the Residual Plots, all graphs seem to support the assumptions that the residuals were normally distributed, statistically independent, with a constant mean of zero and a constant variance. However the histogram contradicts the assumption that the residuals were normally distributed due to the presence of a bimodal distribution. With this contradiction the legitimacy of the results from the ANOVA analysis can be brought into question.

Aside from the One-way ANOVA analysis, the data was also analyzed using the Tukey and Fisher methods. The Tukey test revealed that all of the types were statistically similar except Fanta. This method showed Fanta in a group separate from the other three types. The Fisher method recognized this separation as well but also included Diet Coke in its own separate grouping. Although both methods had different grouping results, both methods pair-wise comparison produced results that supported the rejection of this experiment’s null hypothesis of H0: µcoke = µDietCoke = µSprite = µFanta.

IntroductionThis experimental procedure was set up to determine the effects which Mentos had on

different types of soda. From past research and experimentation it was commonly known that Mentos would have a great reaction with Diet Coke. This sparked an interest to see whether or not Mentos would have a similar reaction with other variety of sodas. It was determined that the most accurate way to determine the reactivity that Mentos would have on the soda would be to measure the amount of liquid left in a 2 liter bottle after a reaction had taken place. Past experimentations had observed the height at which the soda eruption had reached. However, to get accurate quantitative data, measuring volume left in the bottle would be more appropriate.

The null hypothesis (H0) that all sodas would have roughly the same amount of liquid volume left after the eruption was tested. This made the alternate hypothesis (HA), that different soda types would have a different reaction to Mentos. The type of soda would be the variable which would be manipulated at four different levels (types of soda) and the response would be the amount of liquid volume left in the 2 liter after the chemical reaction. The four levels (types of soda) were chosen to be Coke, Diet Coke, Sprite, and Fanta.

Experimental ProtocolThe goal of this experiment was to see the effect that Mentos had on different variety of

soda types. Before the experiment was conducted, research was conducted online and online videos were also watched. Based on the online data, it was concluded to use three (3) tablets of Mentos for every two (2) liters of soda. To conduct a complete one way analysis of variance on the volumetric effect of Mentos on the sodas, different soda types were chosen. Since it was required to observe at least three (3) levels of experimental systems, the number of levels was chosen to be four (4) among the group members. The chosen sodas and the Mentos can be seen in their pre-experiment phase below:

The experiment was conducted for the corresponding type based on the following procedure:

1. Place the 2-Liter bottled soda upright on a horizontal table. Open the caps of the bottles.2. Drop 3 tablets of Mentos as quickly as possible into the bottle.3. Position yourself 2 meters away from the table and observe the reaction.4. Pour the remaining liquid into the measure cup for every type.

5. Measure the remaining amount of liquid in the 2-Liter soda bottle.6. Tabulate the remaining volume in “milliliters” for the corresponding soda.7. Analyze the results in Minitab and MS Excel.

All of the group members were involved in the process of conducting the experiment so that they could efficiently observe, analyze and discuss the outcome.

On the other hand, the other potential effects, such as different temperature of the soda, different outside temperature and the varying amount of the liquid in the 2-Liter bottle, were minimized to clearly see the effects Mentos had on different sodas.

After watching the videos online, the team members were familiar with the safety hazards during the time of the experiment. All of the observers were kept at least 2 meters away from the table where the experiment was conducted and did not get closer until the reaction was over.

Analysis of Data The table which was created in Excel showed the experimental findings along with the

associated means and standard deviations corresponding to the specified soda samples. The table showed the six samples of each of the four types of soda tested. Just by quickly looking at the data, it can be determined that all four types of soda did not react similarly with the Mentos. It was clear to see that Fanta has a significant amount of soda left after the reaction. It was also clear that Diet Coke had the least amount of soda left. These were first glance assumptions but to truly tell if these conclusions were statistically valid we need to analyze the data in Minitab.

A one way ANOVA was completed which showed that with the four treatments that were tested, there was a statistical difference between some of the types of soda when compared to others. With an F-Test value of 2.38 and an F-Stat value of 53.97 it was easy to conclude that there was a statistical difference when comparing the different types of soda. Since the F-Stat value was greater than the F-test value of 2.38, it could be concluded with a high degree of confidence that H0 would be rejected. Having a P-Value of 0.000 also solidifies the fact that the null hypothesis should be rejected.

One-way ANOVA: Coke, Diet Coke, Sprite, Fanta

Source DF SS MS F PFactor 3 865208 288403 53.97 0.000Error 20 106875 5344Total 23 972083

S = 73.10 R-Sq = 89.01% R-Sq(adj) = 87.36%

4 treatments = 3 DFF test = F .10,3,20 = 2.38Reject Ho that all the sodas would erupt the same amount of liquid volume.

Validation of ANOVA Assumptions

For the Analysis of Variance procedure to yield legitimate results, a set of 4 underlying assumptions must be valid:

1) Residuals must be normally distributed2) Residuals must be independent3) Residuals must have a constant mean of 04) Residuals must have a constant variance of σ2

Looking at the residual analysis for the experiment produced by Minitab, the normal probability plot shows that the residuals are normally distributed because the residuals approximate a straight line. However, the histogram shows a bimodal distribution, which indicates that certain data points of measurement show up frequently and in equal amounts and that the normality of the residuals may be questionable. This also brings into question whether

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Residual Plots for Coke, Diet Coke, Sprite, Fanta

the ANOVA procedure yielded legitimate results. Looking at the scatterplot above where the residuals were plotted against the order of collection, it can be concluded that the residuals are statistically independent due to the lack of any visible patterns.

With the Versus Fits graph there are no patterns indicating a trend or systematic departure from 0 in the average of the residuals. The residuals seem to be evenly distributed above and below 0. This validates the assumption that the residuals must have a constant mean of 0. The Versus Fits graph also shows that there are no evident patterns indicating an unusual spread in the residuals, which validates the assumption that residuals must have a constant variance.

Discussion of the Sample SizeAll of the group members were familiar with the saying of “the greater the sample size

the better the results”. Therefore, the power of the test was decided to be around 0.90. To determine a sufficient sample size a power curve analysis for One-way ANOVA was completed using Minitab. For that, a pilot study was conducted which included four (4) different types of sodas and the procedures for the experiment were followed. As a result of the pilot study, the standard deviation was found to be 201.3 milliliters. The number of levels was four (4) as a result of four different types observed. By using the output of the power curve, the sample size was determined to be six (6) for the power of 0.90. The outcome of the power curve can be seen below

After conducting the experiment (i.e. the volume collected from six samples taken from each type as a result of observing the effects that Mentos had on the four different levels (types) of sodas), the data was tabulated in the Minitab and the power of the actual experiment resulted to be 0.9155.

Discussion of Findings One-way ANOVA: Coke, Diet Coke, Sprite, Fanta Source DF SS MS F PFactor 3 865208 288403 53.97 0.000Error 20 106875 5344Total 23 972083

S = 73.10 R-Sq = 89.01% R-Sq(adj) = 87.36%

Individual 95% CIs For Mean Based on Pooled StDev

Level N Mean StDev -+---------+---------+---------+--------Coke 6 779.2 67.9 (---*---)Diet Coke 6 679.2 87.2 (--*---)Sprite 6 783.3 37.6 (---*---)Fanta 6 1175.0 88.0 (--*---) -+---------+---------+---------+-------- 640 800 960 1120

Pooled StDev = 73.1

Plotted Results for Each Tested Soda

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Looking at the One-way ANOVA output, the F Value was shown to be 53.97 and the F Test = F0.10,3,20 was calculated to be 2.38. Given that the F Value> F0.10,3,20, the null hypothesis H0 : µcoke = µDietCoke = µSprite = µFanta was rejected. This meant that the experiment’s initial assumption and hypothesis that carbonated sodas would react similarly to Mentos was invalid.

The Individual 95% CI’s for Mean Based on pooled standard deviation and the plotted results from the experiment also showed clearly that Fanta was an outlier. Looking at the ranges

for each soda, it was clear that Fanta’s range was different from the rest. Its range was the only one above the thousand mL range, whereas Coke, Diet Coke, and Sprite had ranges that fell between the 500 and 900 mL range. Both Tukey’s Pair-wise Comparison and Fisher’s LSD Method indicate that Fanta’s remaining volume after reacting with Mentos significantly differs from the volumes found in Coke, Diet Coke, and Sprite.

Minitab Output:

Grouping Information Using Tukey Method N Mean GroupingFanta 6 1175.00 ASprite 6 783.33 BCoke 6 779.17 BDiet Coke 6 679.17 B

Means that do not share a letter are significantly different.

Tukey 95% Simultaneous Confidence IntervalsAll Pairwise ComparisonsIndividual confidence level = 98.89%Coke subtracted from:

Lower Center Upper --------+---------+---------+---------+-Diet Coke -218.18 -100.00 18.18 (--*---)Sprite -114.01 4.17 122.35 (--*--)Fanta 277.65 395.83 514.01 (--*---) --------+---------+---------+---------+- -350 0 350 700Diet Coke subtracted from:

aLower Center Upper --------+---------+---------+---------+-Sprite -14.01 104.17 222.35 (--*--)Fanta 377.65 495.83 614.01 (--*---) --------+---------+---------+---------+- -350 0 350 700Sprite subtracted from:

Lower Center Upper --------+---------+---------+---------+-Fanta 273.49 391.67 509.85 (--*---) --------+---------+---------+---------+- -350 0 350 700

Tα = q 0.05,3,20√MSEn = 3.58 * √ 53444

= 130.85

Based on the notion that if | yi. – yj.| >Tα, the ones highlighted in green does not have significant difference.

Grouping Information Using Fisher Method N Mean GroupingFanta 6 1175.00 ASprite 6 783.33 BCoke 6 779.17 BDiet Coke 6 679.17 CMeans that do not share a letter are significantly different.

Fisher 95% Individual Confidence IntervalsAll Pairwise ComparisonsSimultaneous confidence level = 80.83%Coke subtracted from:

Lower Center Upper ---------+---------+---------+---------+Diet Coke -188.04 -100.00 -11.96 (--*--)Sprite -83.87 4.17 92.20 (--*--)Fanta 307.80 395.83 483.87 (--*--) ---------+---------+---------+---------+ -300 0 300 600Diet Coke subtracted from:

Lower Center Upper ---------+---------+---------+---------+Sprite 16.13 104.17 192.20 (-*--)Fanta 407.80 495.83 583.87 (--*-) ---------+---------+---------+---------+ -300 0 300 600Sprite subtracted from:

Lower Center Upper ---------+---------+---------+---------+Fanta 303.63 391.67 479.70 (--*--) ---------+---------+---------+---------+ -300 0 300 600

LSD = t 0.025,20√ 2∗MSEn

= 2.086 * √ 2∗53444

= 107.83

Based on the notion that if | yi. – yj.| > LSD, all have significant difference except for ones that are highlighted in Green.

From the ANOVA output, what was interesting was how little Fanta reacted with the Mentos compared with how close Coke, Diet Coke, and Sprite were with their results. Aside from Fanta being an outlier, the groupings displayed in Tukey’s Method and Fisher’s Method were also quite interesting. As found in the Minitab output displayed above, with Tukey’s Method, all tested sodas were grouped together with the exception of Fanta. However looking at Fisher’s Method, with the exception of Fanta being in its own group, Diet Coke was also in a group of its own. The reason behind why this was interesting was because the pair-wise comparison tests from both produced similar results that exhibited Fanta as an outlier.

Discussion for Future ExperimentationIf the experiment was to be performed again, a different approach might have been to

standardize the Mentos dropping procedure, perform the experiment in a controlled room temperature, place bottles of soda on a flat surface rather than on snow, and let the soda set for

the same amount of time after opening the cap. Although it is uncertain whether or not these variables may affect the results gathered, performing the experiment again with this new approach may help minimize the variability in the experiment’s testing procedure. With this approach there would be less external factors to worry about, and more focus can be placed on the type of soda being tested.

Conclusion From past research and experimentation it was commonly known that Mentos would

have a great reaction with Diet Coke. This experiment shows that Mentos also reacts well with Coke and Sprite. However, from this experiment, results also show that Mentos reacts poorly with Fanta rejecting the idea behind how all sodas would react similarly with Mentos (H0).