Anova: Single Factor
SUMMARY Population
Groups Count Sum Average Variance
LA 8 1083 135.38 980.84 1954.1
SF 8 1211 151.38 3414.8
DC 8 1083 135.38 1771.1
NY 8 1585 198.13 1649.6
ANOVA dfB=number of groups -1
Source of Variation SS df MS F P-value F crit
Between Groups 21145 3 7048.5 3.607 0.0255 2.9467
Within Groups 54715 28 1954.1
dfW=( number of items in each group -1)*number of grou
Total 75860 31
dfT = the number of total items -1
75860
MSB and MSW are both estimates of the popla
If there is no difference between the groups, the
population variance
BUT: if there is a difference between the groups
MSW is the average of the 4 estimates of the p
Bad if we claim a difference when there is no di
Type 1 error
We want to mimimize Type 1 errors
Suppose we say that we want the chance (prob
1 in 20 chance than we claim there is a differen
If Fobt is greater than Fcrit, we conclude that th
differ from each other
Null hypothesis: all means are the same (there
Alternative hypothesis: at least one pair of mea
If Fobt is greater than Fcrit, we reject the null hy
of means differs from each other.
3.607
-1)*number of groups)
mates of the poplation variance
een the groups, then both MSB and MSW will be accurate estimates of the
between the groups, then MSB will be larger than MSW
estimates of the population variance
when there is no difference
nt the chance (probability) of a type 1 error to be 5%
m there is a difference when in fact there is no diffence
we conclude that there is at least one pair of means that
e the same (there are no differences)
st one pair of means differs
we reject the null hypothesis and conclude that at least one pair
LA SF DC NY
119 99 115 170
150 185 185 135 Step 1: Estimate the population
110 265 166 185 Step 2: estiamte the population
79 109 189 250 Step 3: is one estimate different
145 169 125 250 If there is a difference between t
140 99 64 170 between groups will be much lar
165 175 120 210 within groups
175 110 119 215 Total Sums of Squares- sum of
135 151 135 198
155.1 Within-group variability- squared
1301 3143 1605 223 within a group
25.6 896 896 403
2031 #### 120 896 Between-group variability- squar
5786 2122 1152 9013 between groups
101 194 904 9013
227 3143 8292 223
98.8 398 1229 3018
398 2031 1301 3593
Total Sum of squared deviations
75860
the population variance from each individual group
the population variance from the means
timate different than the other?
ence between the cities, the estimate from
will be much larger than the estimate from
quares- sum of the squared deviations from the grand mean
iability- squared devaitions due to differences
variability- squared deviations due to differences
Hotel Data
City Hotel Stars Price
LA NEW OTANI 3 119
LA HILTON 3 150
LA BEVERLY PLZA 3 110
LA HOL INN CONV 2 79
LA LE DUFY 2 145
LA BILTMORE 4 140
LA LE PARC 2 165
LA SHERATON GRD 3 175
SF HOL INN FIN 2 99
SF STOUFFER 5 185
SF MANDARIN 4 265
SF DIVA 2 109
SF GRAND HYATT 4 169
SF HOL INN GATE 2 99
SF NOB HILL LAM 2 175
SF INN AT OPERA 3 110
DC LOMBARDY 2 115
DC SHERATON 2 185
DC HILTON 3 166
DC GRAND HYATT 3 189
DC ONE WASH CIR 3 125
DC COMFORT INN 1 64
DC CAPITOL HILL 1 120
DC RAD PRK TERR 3 119
NY EASTGATE 1 170
NY HELMSLEY MID 2 135
NY HOL INN CRWN 2 185
NY THE MARK 3 250
NY PENINSULA 4 250
NY WARWICK 2 170
NY GRAND HYATT 3 210
NY THE REGENCY 4 215
Page 7
Anova: Single Factor
SUMMARY
Groups Count Sum Average Variance
LA 8 1083 135.375 980.839286
SF 8 1211 151.375 3414.83929
DC 8 1083 135.375 1771.125 1954.08929
NY 8 1585 198.125 1649.55357
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 21145.375 3 7048.45833 3.60702982 0.02548955 2.94668467
Within Groups 54714.5 28 1954.08929
Total 75859.875 31