ABV,IPU,Type 3.40%,5,Weissbier 7.20%,5,Sour Ale 5.70%,6,Pumpkin Ale 6.90%,6,Winter Warmer 10.50%,6.5,Pale Ale 5.30%,7,Witbier 5.30%,7,Ale 4.50%,8,Berliner Weisse (Peach) 4.50%,8,Summer Lager 5.80%,8,White Ale 7.00%,8,Sahti 8.00%,8,Kriek 4.60%,9,Hefeweizen 5.40%,9,Witbier 5.80%,9,Wheat Ale 3.70%,9.5,Light Ale 4.90%,10,Gose 5.00%,10,Cream Ale 5.00%,10,Chili Beer 5.00%,10,Chili Beer 5.20%,10,Belgian Pale Ale 5.20%,10,Fruit Lager 5.20%,10,Wheat Ale 5.50%,10,Witbier 5.50%,10,White Ale 6.00%,10,Raspberry Espresso Stout 4.20%,11,Shandy 5.30%,11,White Ale 5.50%,11,Belgian Ale 5.80%,11,Bock 7.20%,11,Imperial Stout 4.30%,12,Hefeweizen 4.50%,12,Chili Beer 4.50%,12,Golden Ale 4.70%,12,Hefeweizen 4.80%,12,Amber 5.00%,12,Lager 5.20%,12,Wheat Ale 5.50%,12,Witbier 4.20%,13,Raspberry Lager 4.40%,13,Bock 4.90%,13,Witbier 5.00%,13,Witbier 5.00%,13,Wheat Ale 5.30%,13,Brown Ale 5.50%,13,Elderberry Weiss 5.70%,13.9,Stout 4.20%,14,Wheat Ale 4.40%,14,Wheat Ale 5.60%,14,Wheat Ale 5.80%,14,Oatmeal Stout 5.80%,14,Kentucky Common 4.80%,14.3,Pilsner 4.50%,15,Golden Ale 4.80%,15,Lager 5.00%,15,Pumpkin Ale 5.30%,15,Wheat Ale 5.50%,15,Chile Stout 6.00%,15,Amber Ale 6.00%,15,Gose 10.30%,15,Witbier 5.25%,15.5,Amber 4.30%,16,Belgian Pale Ale 4.70%,16,Porter 4.70%,16,Porter 4.80%,16,Kolsch 5.30%,16,Mrzen 5.40%,16,Lager 5.80%,16,Amber Ale 3.80%,17,Coffee Stout 5.30%,17,Fruit Lager 10.00%,17,Tripel 5.10%,17.6,Wheat Ale 4.20%,18,Wheat Ale 4.50%,18,Saison 4.90%,18,Black Lager 5.00%,18,Summer Ale 5.00%,18,Milk Stout 5.10%,18,Porter 5.30%,18,Amber Ale 5.50%,18,Pale Ale 5.50%,18,Wheat Ale 5.50%,18,Unfiltered Lager 5.50%,18,Fruit Lager 5.70%,18,Porter 10.00%,18,Quadrupel 5.70%,18.2,Witbier 5.20%,18.5,Amber Ale 9.50%,18.5,Imperial Chocolate Stout 4.50%,19,Blonde Ale 4.50%,19,Brown Ale 6.00%,19,Porter 7.80%,19,Scotch Style Ale 9.00%,19,Tripel 9.70%,19,Quadrupel 5.50%,19.5,Amber Lager 5.20%,19.7,English Porter 4.00%,20,Porter 4.20%,20,Pilsner 4.50%,20,Ginger Ale 4.70%,20,Blonde Ale 4.70%,20,Pumpkin Porter 4.90%,20,Irish Red 5.00%,20,Roggenbier 5.00%,20,Belgian Pale Ale 5.00%,20,Kolsch 5.00%,20,Witbier 5.00%,20,Kolsch 5.00%,20,Gluten Free Red Ale 5.10%,20,Kolsch 5.10%,20,Amber Ale 5.10%,20,Pale Ale 5.20%,20,Nitro English Porter 5.20%,20,Witbier 5.25%,20,Golden Ale 6.70%,20,Scottish Ale 7.10%,20,Kottsbusser 11.50%,20,Wheatwine 4.20%,21,Pale Ale 5.50%,21,Pale Wheat 5.60%,21,Belgian Black Ale 6.20%,21,Porter 7.90%,21,Belgian Red Ale 10.20%,21,Quadrupel 5.10%,21.4,Saison 5.80%,21.5,Dunkel 5.00%,22,Pilsner 5.00%,22,Witbier 5.40%,22,Red Ale 5.60%,22,Witbier 5.60%,22,Bock 4.60%,23,Milk Stout 5.30%,23,Pilsner 6.00%,23,Stout 6.00%,23,Stout 6.00%,23,Oatmeal 6.20%,23,Baltic Porter 6.50%,23,Saison 8.00%,23,Dubbel 8.00%,23,Braggot 5.10%,24,Amber 5.60%,24,Sour Ale 5.70%,24,Dunkel 6.20%,24,Bock 6.20%,24,Bock 6.60%,24,Mrzen 10.00%,24,Imperial Oktoberfest 5.00%,25,Dark Lager 5.10%,25,Brown Ale 5.20%,25,Pale Ale 5.20%,25,Dunkel 5.50%,25,Black Ale 5.50%,25,Wheat Ale 6.00%,25,Oatmeal Stout 6.00%,25,Milk Stout 6.00%,25,Nitro Milk Stout 6.30%,25,Scottish Ale 6.40%,25,Porter 6.50%,25,Dubbel 6.70%,25,Copper Ale 7.60%,25,Doppelbock 7.70%,25,Pumpkin Ale 7.80%,25,Belgian Ale 8.00%,25,Bock 8.00%,25,Belgian Style Brown Ale 8.00%,25,Golden Strong Ale 8.20%,25,Double Bock 8.20%,25,Winter Warmer 10.00%,25,Belgian Style Golden Ale 4.50%,26,Ale 4.70%,26,Pale Ale 5.10%,26,Brown Ale 5.40%,26,Belgian Stout 5.80%,26,Red Ale 6.00%,26,Brown Ale 6.00%,26,Brown Ale 6.80%,26,Dunkel 8.90%,26,Doppelbock 10.70%,26.9,Quadrupel 5.20%,27,Scottish Ale 5.30%,27,American ESB 5.40%,27,Porter 5.50%,27,Oatmeal Stout 6.20%,27,Amber Lager 4.40%,28,Brown Ale 4.70%,28,Lager 4.90%,28,Stout 5.00%,28,Summer Lager 5.25%,28,Pale Ale 5.50%,28,Brown Ale 5.60%,28,Brown Ale 5.70%,28,Oatmeal Stout 5.70%,28,Pale Ale 5.80%,28,Amber 6.60%,28,Blonde Ale 7.70%,28,Stout 7.80%,28,Saison 11.00%,28,Belgian Strong Dark Ale 11.00%,28,Quadrupel 5.00%,28.1,Pilsner 5.15%,29,Brown Ale 5.30%,29,Milk Stout 5.40%,29,Milk Stout 6.00%,29,Winter Warmer 6.30%,29, 4.30%,30,Ale 4.70%,30,Bitter 4.70%,30,Bitter 4.90%,30,Amber Lager 4.90%,30,Hefeweizen 5.00%,30,Brown Ale 5.00%,30,Milk Stout 5.00%,30,Pale Ale 5.00%,30,English Pale Ale 5.20%,30,Lager 5.20%,30,Porter 5.20%,30,Milk Stout 5.30%,30,Red Ale 5.50%,30,Red Ale 5.60%,30,Belgian Pale Ale 5.60%,30,"Doughnut, Bacon, Maple Ale" 5.80%,30,Gold Lager 5.90%,30,ESB 5.90%,30,ESB 5.90%,30,Brown Ale 6.00%,30,Porter 6.00%,30,Milk Stout 6.00%,30,Coffee Stout 6.50%,30,Scotch Style Ale 6.90%,30,Stout 7.40%,30,Winter Ale 7.50%,30,Belgian Pale Ale 7.80%,30,Smoked Ale 8.00%,30,Imperial Stout 8.00%,30,Dubbel 9.50%,30,Scottish Ale 10.00%,30,Strong Ale 5.00%,32,White IPA 5.60%,32,Amber Ale 9.00%,32,Imperial Porter 10.80%,32,Belgian Strong Dark Ale 5.30%,33,Stout 5.30%,33,Red Ale 6.00%,33,Stout 8.00%,33,Tripel 8.20%,33,Doppelbock 8.50%,33,Belgian Ale 9.00%,33,Belgian Strong Pale Ale 4.30%,34,Stout 7.80%,34,Doppelbock 3.90%,35,English Bitter 4.20%,35,Cucumber Hibiscus Ale 5.00%,35,Wheat Ale 5.20%,35,Oatmeal Stout 5.30%,35,Pilsner 5.40%,35,Pale Ale 5.50%,35,Pale Ale 5.50%,35,Stout 5.50%,35,Pale Ale 5.90%,35,Oatmeal Porter 6.00%,35,Porter 6.00%,35,ESB 6.00%,35,Pilsner 6.00%,35,Black Lager 6.00%,35,Coffee Stout 6.20%,35,Porter 6.20%,35,Black Saison 6.80%,35,Porter 7.50%,35,Brown Ale 7.80%,35,Smoked Baltic Porter 9.00%,35,Saison 10.20%,35,Imperial Kentucky Common 4.95%,36,Oatmeal Stout 5.00%,36,American Pale Ale 5.20%,36,English Pale Ale 5.60%,36,Pale Ale 5.80%,36,Pale Ale 6.00%,36,Winter Warmer 7.40%,36,Double Oatmeal Stout 7.60%,36,Old Ale 4.60%,37,Pilsner 4.70%,37,Porter 5.00%,37,Altbier 5.10%,37,Pale Ale 5.20%,37,Oatmeal Stout 8.70%,37,Old Ale 4.20%,37.1,California Common 4.90%,38,Pale Ale 5.10%,38,Amber Ale 5.50%,38,Pale Ale 5.50%,38,Brown Ale 5.50%,38,Rye Ale 5.60%,38,IPA 5.60%,38,Pale Ale 5.70%,38,Red Ale 6.10%,38,Porter 6.10%,38,Porter 8.50%,38,Saison 5.30%,39,Blond Ale 5.40%,39,Porter 5.90%,39,Porter 5.90%,39,Porter 6.00%,39,Porter 8.10%,39,Imperial Pilsner 4.60%,40,Czech Pilsner 4.80%,40,IPA 5.00%,40,Pale Ale 5.20%,40,Pale Ale 5.25%,40,Belgian White India Pale Ale 5.30%,40,Pale Ale 5.30%,40,Pilsner 5.50%,40,Pale Ale 5.70%,40,Pale Ale 5.70%,40,Pale Ale 5.70%,40,White IPA 5.80%,40,Pale Ale 6.00%,40,IPA 6.00%,40,Porter 6.40%,40,Winter Warmer 6.50%,40,Winter Ale 6.50%,40,Winter Ale 6.50%,40,Coffee Stout 6.50%,40,German Maibock 6.70%,40,Stout 7.20%,40,Imperial Brown Ale 10.70%,41,Quadrupel 4.70%,42,IPA 5.15%,42,Red Ale 5.90%,42,Amber Ale 5.90%,42,Double IPA 5.90%,42,IPA 8.00%,42,Imperial Porter 5.00%,43,India Pale Lager 4.80%,44,Extra Pale Ale 6.00%,44,IPA 4.40%,45,Amber Ale 5.00%,45,Extra Pale Ale 5.50%,45,Extra Pale Ale 5.70%,45,IPA 6.00%,45,Pale Ale 6.00%,45,India Pumpkin Ale 6.20%,45,Pale Ale 6.50%,45,Porter 6.50%,45,Porter 6.50%,45,Porter 6.50%,45,IPA 6.70%,45,Brown Ale 7.00%,45,Rye Stout 7.25%,45,Black IPA 7.25%,45,IPA 7.25%,45,White IPA 8.30%,45,Old Ale 8.50%,45,Russian Imperial Stout 8.50%,45,Russian Imperial Stout 8.80%,45,Imperial Stout 9.00%,45,Imperial Pumpkin Ale 10.20%,45,Russian Imperial Stout 10.20%,45,Russian Imperial Stout 6.20%,45.6,IPA 5.50%,46,Porter 5.90%,46,Pale Ale 6.00%,46,IPA 6.50%,46,Extra Pale Ale 6.10%,47,Pale Ale 6.90%,47,IPA 5.20%,48,Amber Ale 6.00%,48,Blonde Ale 6.70%,48,Porter 7.40%,48,White IPA 8.10%,48,Imperial Stout 5.50%,50,IPA 5.80%,50,Stout 6.00%,50,Black IPA 6.70%,50,IPA 6.70%,50,India Pale Lager 7.00%,50,Stout 7.20%,50,India Brown Ale 7.20%,50,Winter Warmer 8.50%,50,Imperial Stout 8.50%,50,Imperial Stout 8.50%,50,Scotch Style Ale 8.50%,50,Chili Beer 9.00%,50,Imperial Stout 9.60%,50,Imperial Porter 4.50%,51,Pale Ale 6.30%,51,Stout 6.30%,51,Stout 6.90%,51,IPA 6.20%,52,IPA 6.50%,52,IPA 6.50%,52,IPA 5.90%,53,Porter 6.50%,53,Porter 6.30%,54,IPA 7.50%,54,Extra Pale Ale 5.00%,55,Session IPA 5.30%,55,Pale Ale 5.80%,55,IPA 5.90%,55,IPA 6.50%,55,IPA 6.50%,55,IPA 6.50%,55,Oatmeal Pale Ale 6.60%,55,Rye IPA 6.90%,55,IPA 7.00%,55,IPA 7.60%,55,Baltic IPA 10.50%,55,Russian Imperial Stout 5.70%,56,Black IPA 7.20%,56,Winter Warmer 5.90%,57,Coffee Stout 6.30%,57,IPA 7.00%,57,Pale Ale 5.40%,59,IPA 5.90%,60,Lager 6.00%,60,IPA 6.00%,60,IPA 6.00%,60,IPA 6.00%,60,Red Ale/IPA 6.10%,60,Belgian IPA 6.20%,60,Pale Ale 6.20%,60,IPA 6.20%,60,Red IPA 6.50%,60,IPA 6.50%,60,IPA 6.60%,60,Red IPA 6.70%,60,Winter Warmer 7.00%,60,IPA 7.00%,60,Stout 7.00%,60,IPA 7.00%,60,Dubbel 7.10%,60,IPA 7.50%,60,IPA 8.30%,60,Choc. Oatmeal Coffee Stout 8.30%,60,Belgian IPA 8.70%,60,Imperial Red Ale 9.00%,60,Russian Imperial Stout 9.50%,60,Double Black IPA 10.00%,60,Barleywine 10.00%,60,Russian Imperial Stout 11.50%,60,Imperial Stout 7.00%,62,IPA 6.00%,63,IPA 6.60%,63,IPA 5.40%,64,IPA 6.10%,64,Porter 6.40%,64,Belgian Pale Red Ale 6.50%,64,Black Ale 7.30%,64,IPA 7.50%,64,Pale Ale 11.30%,64,Imperial Porter 7.00%,64.5,IPA 4.50%,65,Session IPA 5.00%,65,Pale Ale 6.00%,65,Double Hopped Red Ale 6.00%,65,IPA 6.00%,65,Sour IPA 6.20%,65,IPA 6.20%,65,IPA 6.20%,65,Pale Ale 6.20%,65,IPA 6.40%,65,Rye IPA 6.50%,65,Black Rye IPA 6.50%,65,IPA 6.50%,65,Pale Ale 6.50%,65,Black IPA 6.70%,65,IPA 6.80%,65,IPA 6.80%,65,IPA 6.80%,65,IPA 6.80%,65,IPA 7.00%,65,IPA 7.00%,65,IPA 7.20%,65,IPA 7.20%,65,IPA 7.20%,65,IPA 7.50%,65,Double Red Ale 7.60%,65,Double IPA 7.80%,65,IPA 8.00%,65,Imperial Stout 8.00%,65,Imperial Stout 6.10%,66,Black IPA 9.30%,66,IPA 6.70%,67,Black IPA 6.70%,67,IPA 6.80%,67,Amber 6.20%,68,IPA 16.00%,68,Belgian Strong Dark Ale 6.10%,69,Oatmeal Stout 6.50%,69,IPA 6.50%,69,IPA 6.50%,69,IPA 6.50%,69,IPA 7.60%,69,IPA 5.40%,70,Pale Ale 6.10%,70,IPA 6.20%,70,White IPA 6.30%,70,IPA 6.30%,70,IPA 6.50%,70,IPA 6.50%,70,IPA 6.50%,70,IPA 6.50%,70,IPA 6.50%,70,Pale Ale 6.55%,70,IPA 6.60%,70,Rye IPA 6.70%,70,IPA 6.70%,70,Belgian IPA 6.80%,70,Black IPA 6.90%,70,Maibock 7.00%,70,IPA 7.00%,70,IPA 7.00%,70,Red IPA 7.20%,70,IPA 7.20%,70,IPA 7.25%,70,IPA 7.25%,70,IPA 8.00%,70,Imperial Rye Stout 8.20%,70,Belgian Black IPA 8.50%,70,Imperial IPA 9.00%,70,Double Red Rye 9.20%,70,Double IPA 9.30%,70,Double IPA 9.80%,70,Double IPA 10.00%,70,Imperial IPA 13.00%,70,Old Ale 8.50%,71,IPA 10.00%,71,Imperial Red Ale 6.60%,72,IPA 8.00%,72,Red IPA 6.80%,73,IPA 7.50%,73,Winter Warmer 6.00%,75,IPA 6.50%,75,IPA 6.70%,75,IPA 6.80%,75,IPA 7.00%,75,IPA 7.00%,75,IPA 7.50%,75,IPA 7.50%,75,Pale Ale 8.00%,75,Double IPA 9.25%,75,Double IPA 9.50%,75,Imperial Stout 9.80%,75,Imperial Stout 7.10%,75.5,IPA 10.50%,75.5,Double IPA 7.10%,76,Red IPA 6.90%,77,Belgian IPA 6.90%,77,IPA 9.60%,77,Double IPA 7.00%,78,IPA 6.30%,80,IPA 6.80%,80,IPA 7.10%,80,IPA 8.30%,80,Black Rye IPA 8.60%,80,Imperial IPA 9.00%,80,Belgian Red Rye Double IPA 10.50%,80,Double IPA 10.50%,80,Double IPA 15.40%,80,Imperial Stout 6.20%,81,IPA 7.30%,82,IPA 9.30%,82,Belgian-style Imperial Stout 6.70%,84.5,Red IPA 6.50%,85,Black IPA 7.30%,85,India Brown Ale 7.50%,85,Imperial IPA 8.00%,85,IPA 8.40%,85,Black IPA 8.50%,85,Imperial IPA 8.60%,85,Double IPA 9.20%,85,Imperial Porter 10.50%,85,Imperial Stout 11.50%,85,Double IPA 6.50%,86,IPA 9.40%,86,Imperial IPA 7.50%,87,Porter 6.80%,87.2,IPA 8.30%,88,Double IPA 10.80%,88,Imperial IPA 7.00%,90,Indica Black Lager 7.30%,90,Double Black IPA 7.70%,90,Coconut IPA 8.25%,90,Imperial IPA 8.70%,90,Black Ale 9.00%,90,IPA 9.60%,90,Imperial IPA 9.60%,90,Barleywine 10.00%,90,Imperial IPA 11.50%,90,Barleywine 7.50%,92,Rye IPA 9.30%,92,IPA 8.50%,93,Double IPA 6.10%,94,IPA 7.30%,95,IPA 8.20%,95,IPA 8.60%,95.1,Imperial Red Ale 8.70%,97,Imperial IPA 9.80%,98,Double IPA 5.60%,100,IPA 8.00%,100,Double IPA 8.50%,100,Imperial Red Ale 8.60%,100,Double IPA 9.00%,100,Belgian-style Double IPA 9.50%,100,Imperial Black IPA 9.50%,100,Double IPA 9.40%,101,Imperial IPA 7.00%,102,IPA 8.00%,102,Double IPA 10.41%,102,Imperial IPA 10.50%,102,Imperial IPA 9.20%,104,Barleywine 9.50%,104,Double IPA 7.90%,117,Black IPA 12.00%,120,Double IPA 10.70%,127,Barleywine 8.50%,130,Double IPA 9.00%,130,Double IPA 6.80%,165,IPA 9.80%,170,Black IPA 10.20%,185,Imperial IPA 11.20%,100 (ish),Strong Ale 7.70%,100+,IPA 9.00%,100+,Imperial IPA 9.40%,100+,Double IPA 9.50%,100+,Imperial IPA 10.00%,100+,Double IPA 10.00%,100+,Imperial IPA 9.50%,150 calc?,Double IPA

Preform a PCA on the data and replot your new variables on your new axis. Switch your data to z-scores (using the eigenvalues for each Eigen vector) and replot. Which beer is the biggest outlier? Preform a Hoteling T-test on the mean of the Ales vs the mean IPAs. Is it a different result than a regular t-test?

USE R