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1. looks like
p
is less than 1/2.
2. I plugged x equals 1 over 1 plus
p
,
3. A good
p
-value is less than 10 to the minus 4.
4. Come on up here
p
up here up here nice nice
5. or alpha psi of
p
, let's say, because we're talking about
p
.
6. This says the variance of
p
hat sub 1 minus
p
hat sub 2 is equal to, and I’m running
7. And what it spits out is the
p
-value.
8. If you've seen more than 100
p
-values in your life,
9. STUDENT QUESTION: are those two equal only when
P
10. But what is the only
p
I can get?
11. it's multiplying this by 1 plus
p
.
12. We assume that
P
of m holds.
13. And for her, a
p
-value is just the number
14. the value of
p
they would put into these formulas.
15. coordinates x, y, z, of a point
P
,
16. So now I view my
p
-value as a random variable.
17. and take the
p
-th route of that.
18. So a
p
-value of a test is the smallest,
19. So that's
P
of A given B is equal to
P
of B given A?
20. what is the distribution of the
p
-value under the null?
21. Given two vectors and a power,
p
,
22. divided by
P
of A and B.
23.
p
-value--
24. plus
p
to the n minus 1, all over
p
.
25. So
p
can range between 0 and 1, that's for sure.
26. as long as
p
is bigger than 0.
27. you've been doing some
p
-hacking until you found
28. And that's what the
p
-value is.
29. so the
p
-value is the probability
30. And so this number is actually something called the
p
-value.
31. The definition of the
p
-value is a mouthful.
32. a-, a-pe. And finally, the
P
sound, ape. Go ape.
33. plus
p
over
p
.
34. We replace
p
by 0.5.
35. That's the number 7, S-T-E-
P
-S.
36. And the
p
-value's a number between 0 and 1, right?
37. OK, now S&
P
500 is around 1,800.
38. Second thing is about S&
P
500.
39. have a point,
P
, in space with coordinates x,
40. that psi is equal to 0, which is 1 minus
p
theta
41. if
p
is smaller.
42. And I know that the
p
-value is--
43. So under
p
, this guy--
44. So we've defined what the
p
-values were.
45. axes, and in these new coordinates,
P
will have
46. And we're going to call it
p
.
47. you talked about the implied frequency of the S&
P
500
48. So the
p
-value is nice.
49. and we get m 1 minus 1 over 1 plus
p
50. papers that actually refused to publish
p
-values now.
51. But if you tell me what the
p
-value is,
52. So I have
p
squared.
53. is if you look at the
p
-values.
54. That thing is the
p
-value.
55. we know this diverges. It's a
p
-series with
p
equals 1... diverges. Okay, well, you know,
56. volume. But, if
P
is in the plane,
57. we have x1 xn, their IID [INAUDIBLE]
p
.
58. Pictorially, you can actually represent the
p
-value.
59. is strictly equivalent to
p
is equal to 0.5,
60. It's 1 plus
p
minus 1 is
p
.
61. if your goal is to just threshold the
p
-value,
62. to
p
k minus 1, and then 1 minus the sum,
63. One over 1 plus
p
, because what's happening here
64. One plus
p
squared, because every year you
65. by 1 plus
p
, and I'll get 1 plus
p
minus 1 on the bottom.
66. So the
p
-value is nice.
67. makes my
p
-value automatically adjust to what
68. And I want to test if those
p
-values have
69. This test will never conclude that
p
is equal to 1--
70. Palindrome with a capital
P
. Only in New York, in Canada we
71.
P
. CHASE, MUCH MORE LIBERAL THAN
72. devaluing by 1 over 1 plus
p
.
73. hat sub 2 is equal to the mean of
p
hat1 plus or minus the mean of
p
hat, of
p
sub 2.
P
74. One over 1 plus
p
, because what's happening here
75. So the
p
-value is the tipping point in terms of alpha.
76. Sorry, that's
p
-value over 2.
77. How do you compute the
p
-value?
78. As we'll see, a slight difference in
p
79. We'll plug in x equals 1 over 1 plus
p
,
80. the right definition for the
p
-value.
81. is equivalent to taking
p
and taking the value of
p
that's
82. if you have this
p
-value which is less than 1%,
83. That's the definition of the
p
-value.
84. So when
p
is getting closer to 1/2,
85. equal to
P
of B given A times
P
of B divided by
P
of A. This
86. of people who are using
p
-values out there
87. said yes, that means that maybe you're
p
-value was 4.99,
88. we have here a
p
-series with a
p
value of 2. That
p
value of 2 is greater than 1; thus,
89. of m over 1 plus
p
to the i.
90. So that's the probability under
p
, which is unknown.
91. So people are tempted to see small
p
-values.
92. The
p
-value is the probability that you
93. What
p
-value does, you just feed it the data itself.
94. One plus
p
squared, because every year you
95. mentalistic idioms of propositional attitude-- x believes that
p
, x regrets that
p
, x hopes
96.
p
-value than you should have.
97. of Z over here I get a lower bound on
P
of y minus
P
of Z which is Z times the
98. that looks like under
p
.
99. Say that
p
stays fixed, the same over all time.
100. do I want to see a small
p
-value or a large
p
-value?
101. h0 is 0.5,
p
is 0.5, h1p is 0.43.
102. When I'm at 0, when
p
is equal to 0,
103. that the CDF of my data, that my
p
-value is uniform,
104. John Oliver talks about when he talks about
p
-hacking.
105. that
p
is larger than 1/2, just because xn bar
106. Your
p
-value under the null will have a distribution
107. we get m 1 plus
p
over
p
squared.
108. very very small
p
values. So our conclusion is going to be, "With such a small
p
-value
109. And I want to test if
p
is 1/2 versus
p
not equal to 1/2,
110. One over 1 plus
p
squared.
111. plus
p
squared.
112. Rooftop
p
-
113. if
p
is equal to 2, this is Euclidean distance, right?
114. Scientists want to see small
p
-values because small
p
-values
115. that
p
, this sort of thing.
116. minus
p
to the k-th power of
p
is less than or equal to 1/2.
117. so the
p
-values are typically compared--
118. Say that
p
stays fixed, the same over all time.
119. AUDIENCE: So the thing on the bottom is
P
of B?
120. So that's how I would compute
p
-values.
121.
P
of A given B is equal to
P
of B given A times
P
of A
122. And the bigger
p
gets, the less your payment is worth.
123. required to specify
p
to be equal to 0.5.
124. telling us whether
P
is in the plane or not.
125. value will be nonzero. If
P
is in the plane,
126. n, the number of years, and then
p
, the interest rate.
127. So my
p
-value is just this number
128. compute the
p
-value, and check if my
p
-value has
129. or minus p1 plus or minus
p
hat sub 2 is equal to the mean of
p
hat sub 1 plus or minus
p
130. "
P
" for pronoun, "
p
" for person. Okay? And the verb: to walk. "You walk." Okay? But,
131. conclude that
p
is equal to 1.
132. So we suppose
P
of n.
133. And we're going to call it
p
.
134. and when I do, even the great James
P
. Sullivan
135. So now we're done, because this shows
P
n plus 1.
136. That's the first pivot
P
-I-V-O-T. Pivot.
137. And this scale is the scale of
p
-values.
138. this payment will
P
until one sole candidate remains okay
139. It's the probability-- so the
p
-value-- let's look
140. coordinates of point
P
. And for that it is a very
141. said let's convert the IV antihypertensive medicine to
P
oh let's
142. We assume that
P
of m holds.
143. Why does the
p
-value have to be normal?
144. So if I'm testing whether
p
is larger
145. AUDIENCE: --where S right now is m over 1 plus
p
--
146. Later we'll plug in values for
p
,
147. One over 1 plus
p
squared.
148. Now, as I said, the
p
-value is a beauty
149. multiply what you got by 1 plus
p
, because that's
150. Just gives me a
p
on the bottom.
151. root of n xn bar minus
p
divided by--
152. Sorry, that's
p
-value over 2.
153. as being a maximum of
p
theta of psi is equal--
154. Then the
p
-value is the probability
155. that
p
is larger than 1/2, just because xn bar
156. Now, what is the definition of the
p
-value?
157. okay this item is a Funko
p
0
p
Game of
158. In fact, say
p
was 0.
159. my square root p1 minus
p
.
160. that, m times 1 plus
p
over
p
, because the limit as n
161. No, actually, that's
p
-value.
162. moving point. So, maybe our point is here,
P
.
163. That's my
p
-value.
164.
p
(1-
p
)/n, the sub 2s because it’s the second group, and I’m squaring that standard deviation
165. sample proportions in this calculation, the standard error of
p
hat sub 1 minus
p
hat
166. That's worth m over 1 plus
p
squared,
167. S&
P
500 index is higher than 880.
168. so that means you've seen
p
-values.
169. That's my
p
-value.
170. the same except for these
p
hats were missing, and Ps, just
p
alone was in its place. Again,
171. is actually the
p
-value itself up
172. So the
p
-value is a random number.
173. That's what the
p
-value is.
174. what the
p
-value is.
175. And what it spits out is the
p
-value.
176. So I'm going to take
p
for some variable in the experiment.
177. I need scarers like... like... James
P
. Sullivan.
178. between our two sample proportions, so
p
hat sub 1 times (1-
p
hat sub1) over n1 plus
p
179. I'm actually making my
p
-value strictly smaller
180. But then maybe you want a
p
-val--
181. but those dollars are worth 1 over 1 plus
p
182. population distribution, then we can say that the mu of
p
hat sub 1 minus
p
hat sub 2 is
183. but rather
p
less than 1/2, that's
p
-hacking.
184. is that they take the numbers for the
p
-values that
185. mu of
p
hat equals
p
, since the center of our sampling distribution is the same as the
186. over
p
to the number of years.
187. But the only
p
that's in theta 0 is actually
p
is equal to 0.5.
188. Because right now, for example, S&
P
500 index
189. PROFESSOR: That's the
p
-value, right?
190. That's what the
p
-value is.
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