1
00:00:06,440 --> 00:00:08,580
When we are comparing

2
00:00:08,580 --> 00:00:10,620
the difference in
means or when we are

3
00:00:10,620 --> 00:00:12,360
comparing the averages between

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00:00:12,360 --> 00:00:14,145
groups that are more than two,

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00:00:14,145 --> 00:00:18,000
we will use ANOVA or
analysis of variance.

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00:00:18,000 --> 00:00:20,505
We know that if there
are only two groups,

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00:00:20,505 --> 00:00:22,230
we can use the t-test,

8
00:00:22,230 --> 00:00:23,535
but when we are comparing

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00:00:23,535 --> 00:00:25,470
averages for more
than two groups,

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00:00:25,470 --> 00:00:27,960
we use analysis of variance.

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00:00:27,960 --> 00:00:30,884
Working with our teaching
evaluation dataset,

12
00:00:30,884 --> 00:00:32,940
we took the teaching
evaluation scores

13
00:00:32,940 --> 00:00:34,650
and then we wanted to see what

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00:00:34,650 --> 00:00:35,700
would happen if we took

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00:00:35,700 --> 00:00:38,535
the instructors and divide
them into three groups,

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00:00:38,535 --> 00:00:40,155
40 years and younger,

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00:00:40,155 --> 00:00:43,055
those between 40
and 57 years of age

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00:00:43,055 --> 00:00:45,905
and those that are
57 years or older.

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00:00:45,905 --> 00:00:48,020
We computed the average value for

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00:00:48,020 --> 00:00:50,675
teaching evaluation score
for the three groups.

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00:00:50,675 --> 00:00:52,610
We wanted to determine if

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00:00:52,610 --> 00:00:55,955
the three mean values were
statistically different.

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00:00:55,955 --> 00:00:58,850
To recap, we ran the analysis of

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00:00:58,850 --> 00:01:02,225
variance test, which
uses F-distribution.

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00:01:02,225 --> 00:01:05,780
The p-value is less than 0.05.

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00:01:05,780 --> 00:01:08,000
We reject the null hypothesis

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00:01:08,000 --> 00:01:09,755
that averages of the group are

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00:01:09,755 --> 00:01:11,450
equal and concluded that

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00:01:11,450 --> 00:01:14,360
the differences are
statistically significant.

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00:01:14,360 --> 00:01:17,645
Now, let us do this with
the regression model.

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00:01:17,645 --> 00:01:20,179
We will use the
statsmodel library

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00:01:20,179 --> 00:01:22,805
and also import the OLS function.

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00:01:22,805 --> 00:01:24,340
We will create or

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00:01:24,340 --> 00:01:26,770
initiate a linear model
of the beauty score,

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00:01:26,770 --> 00:01:28,675
which is our y-variable.

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00:01:28,675 --> 00:01:30,430
Please note that
when dealing with

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00:01:30,430 --> 00:01:32,005
a linear regression model,

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00:01:32,005 --> 00:01:35,245
the y-variable has to be
a continuous variable.

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00:01:35,245 --> 00:01:37,895
Otherwise results
will not be accurate.

40
00:01:37,895 --> 00:01:40,345
Now, create the linear model

41
00:01:40,345 --> 00:01:42,820
and fit it using
the fit function.

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00:01:42,820 --> 00:01:46,210
Use the ANOVA_IM
function to create

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00:01:46,210 --> 00:01:47,650
a table that prints out

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00:01:47,650 --> 00:01:49,760
the results of the
test statistics.

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00:01:49,760 --> 00:01:51,915
The results will look like this.

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00:01:51,915 --> 00:01:53,830
It will print out the
degree of freedom,

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00:01:53,830 --> 00:01:57,350
the sum of square F
statistic and the p-value.

48
00:01:57,350 --> 00:01:59,785
Like ANOVA from this api package,

49
00:01:59,785 --> 00:02:01,270
we get the same results,

50
00:02:01,270 --> 00:02:03,909
which is that we will
reject the null hypothesis,

51
00:02:03,909 --> 00:02:06,440
the averages of the
group are equal and

52
00:02:06,440 --> 00:02:07,850
conclude that the differences

53
00:02:07,850 --> 00:02:10,280
are statistically significant.

54
00:02:10,280 --> 00:02:12,920
You can also turn the
age group values into

55
00:02:12,920 --> 00:02:14,450
dummy values and run it like you

56
00:02:14,450 --> 00:02:16,400
run the regression for t-test.

57
00:02:16,400 --> 00:02:18,080
To do that, you will need to

58
00:02:18,080 --> 00:02:20,150
create dummy variables
for the age groups

59
00:02:20,150 --> 00:02:24,250
using the get_dummies
function in pandas.

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00:02:24,250 --> 00:02:27,080
It will look like this,
where one means they

61
00:02:27,080 --> 00:02:29,930
belong to that group and
zero means otherwise.

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00:02:29,930 --> 00:02:32,479
Just like a binary variable,

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00:02:32,479 --> 00:02:35,515
values can only
belong to one group.

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00:02:35,515 --> 00:02:38,510
Run the same as you did
for the t-test by fitting

65
00:02:38,510 --> 00:02:41,180
the variables into
an OLS function,

66
00:02:41,180 --> 00:02:44,165
predict, and print out
the model summary.

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00:02:44,165 --> 00:02:47,100
We will get results like this.

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00:02:49,700 --> 00:02:52,115
Taking a closer look,

69
00:02:52,115 --> 00:02:53,780
we can see the same results for

70
00:02:53,780 --> 00:02:56,910
the F statistic and the p-value.