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Hypothesis Testing

Null Hypothesis The means of the populations

from which the samples were drawn are the

same. The samples come from the same population.

mG/R

Alternative Hypothesis The means of the

populations from which the samples were drawn are

different. The samples come from different

populations.

mG

mR

Our problem All we see are the data we have

sampled, not the populations.

Are the sampled data most consistent with the

null hypothesis single population idea?

mG/R

Or with the alternative hypothesis separate

populations idea,

mG

mR

Distribution of differences between the means of

two samples drawn from the same population

(m0,s1)

Frequency (Probability 1000)

Difference Between the Means of the Samples

What is the probability that the observed

samples could have been drawn from the same

population?

mG/R

P0.79

x

x

Distribution of differences between the means of

two samples drawn from the same population

(m0,s1)

214

189

183

Frequency (Probability 1000)

120

118

65

54

21

15

11

9

1

0

Difference Between the Means of the Samples

What is the probability that the observed

samples could have been drawn from the same

population?

mG/R

P0.18

Distribution of differences between the means of

two samples drawn from the same population

(m0,s1)

214

189

183

Frequency (Probability 1000)

120

118

65

54

21

15

11

9

1

0

Difference Between the Means of the Samples

What is the probability that the observed

samples could have been drawn from the same

population?

mG/R

P0.02

Distribution of differences between the means of

two samples drawn from the same population

(m0,s1)

214

189

183

Frequency (Probability 1000)

120

118

65

54

21

15

11

9

1

0

Difference Between the Means of the Samples

The Dilemma

How much risk to take when deciding whether the

null or alternative hypothesis is correct? Too

much risk and you may commit a Type I error

rejection of a true null hypothesis (accepting a

false alternative). Too little risk and you may

commit a Type II error failure to reject a

false null hypothesis (accepting a false

null). The accepted risk level is set at 0.05 or

a 1 out of 20 chance that you will accidentally

accept a false alternative. Statistical tables

are set to this level of risk.

More on Type I and II Errors

- Sometimes in medical studies we seek to lower the

chance of Type I errors (rejecting a true null

hypothesis) and we may set the level for

rejecting the null hypothesis lower such as p

0.01 or a 1 in 100 chance of committing Type I

error - Decreasing chance of Type I error will increase

the chance of Type II error - The only way to simultaneously reduce the risk of

Type I and Type II errors is to increase sample

size

(No Transcript)

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