In re: High-Tech Employee Antitrust Litigation

Filing 716

Omnibus Declaration of Christina J. Brown in Support of #715 Reply re Joint Motion to Exclude the Expert Testimony of Edward E. Leamer, Ph.D. , #714 Reply to Joint Motion to Strike the Improper Rebuttal Testimony in Dr. Leamer's Reply Expert Report or, in the Alternative, MOTION for Leave to Submit a Reply Report of Dr. Stiroh filed by Apple Inc.. (Attachments: #1 Exhibit A, #2 Exhibit B, #3 Exhibit C, #4 Exhibit D, #5 Exhibit E, #6 Exhibit F, #7 Exhibit G, #8 Exhibit H, #9 Exhibit I, #10 Exhibit J, #11 Exhibit K, #12 Exhibit L, #13 Exhibit M, #14 Exhibit N, #15 Exhibit O, #16 Exhibit P, #17 Exhibit Q)(Related document(s) #715 , #714 ) (Brown, Christina) (Filed on 2/27/2014) Modified text on 2/28/2014 (dhmS, COURT STAFF).

EXHIBIT J

OMNIBUS BROWN DECLARATION

H0 is called the null hypothesis: in this example, the null hypothesis states that
drug X is no improvement over standard treatment. HA, sometimes written as H1,
is called the alternative hypothesis: in this case, the alternative hypothesis is that
drug X is more effective than standard treatment. Note that the null and alternative hypotheses must be both mutually exclusive (no results could satisfy both
conditions) and exhaustive (all possible results will satisfy one of the two
conditions).
In this example, the alternative hypothesis is single-tailed: we state that the blood
pressure of the group treated with drug X must be lower than that of the standard
treatment group for the null hypothesis to be rejected. We could also state a twotailed alternative hypothesis if that were more appropriate to our research question. If we were interested in whether the blood pressure of patients treated with
drug A was different, either higher or lower, than that of patients receiving standard treatment, we would state this using a two-tailed alternative hypothesis:
H0: μ1 = μ2
HA: μ1 ≠ μ2
Normally the first two steps would be performed before the experiment is
designed or the data collected; the statistic to be used for hypothesis testing is also
sometimes specified at this time, or is implicit in the hypothesis and type of data
involved. We then collect the data and perform the statistical calculations, in this
case probably a t-test or ANOVA, and based on our results make one of two
decisions:
• Reject the null hypothesis and accept the alternative hypothesis, or
• Fail to reject the null hypothesis
The first case is sometimes called “finding significance” or “finding significant
results.” The process of statistical testing involves establishing a probability level
or p-value (a topic treated in greater detail below) beyond which we will consider
results from our sample strong enough to support rejection of the null hypothesis. In practice, the p-value is commonly set at 0.05. Why this particular value?
It’s an arbitrary cutoff point and dates back to the early twentieth century, when
statistics were computed by hand and the results compared to published tables
used to determine whether a result was significant or not. The use of p < 0.05 as
the standard for significant results has been challenged (see the upcoming sidebar,
“Controversies About Hypothesis Testing”) but still remains common practice for
published research. Alternative lower values are sometimes used, such as p < 0.01
or p < 0.001, but no one has been successful in legitimizing the use of a higher
cutoff, such as p < 0.10.
Note that failure to reject the null hypothesis does not mean that we have proven
it to be true, only that the experiment or study did not find sufficient evidence to
reject it.
Inferential statistics allows us to make probabilistic statements about the data, but
the possibility of error is inherent in the process. Statisticians have classified two
types of errors when making decisions in inferential statistics, and set levels for
error rates that are commonly considered acceptable. The two types of error are
displayed in Table 7-1.

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Chapter 7: Inferential Statistics