Agr Educ 387 Data Analysis in Applied Sciences

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Agr Educ 387Data Analysis in Applied Sciences

• Dr. Jamie Cano, Instructor
• Ms. Kristy Brewer, TA

May 17, 2004
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Problem

• During the 1998 Tour de France, some cyclist
  were expelled for attempting to enhance their
  performance by blood doping with EPO. An
  investigator wants to determine whether this type
  of blood doping increases the endurance of
  athletes under controlled laboratory conditions.

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Two Independent Samples

• Observations in one sample arent paired on a
  one-to-one basis with observations in the other
  sample.

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Effect

• Any difference between two population means

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Possible Hypotheses

• Non directional
• Ho µ1 - µ2 0
• H1 µ1 - µ2 ? 0
• Directional, Lower tail critical
• Ho µ1 - µ2 ? 0
• H1 µ1 - µ2 lt 0
• Directional, Upper tail critical
• Ho µ1 - µ2 ? 0
• H1 µ1 - µ2 gt 0

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Specify Both the Null and Alternative Hypothesis

• After randomly assigning children to two groups,
  a school psychologist wishes to determine whether
  there is a difference in the mean reading
  comprehension scores between the group that
  receives a special bilingual reading program and
  the group that receives a traditional reading
  program.
• H0 ?1 - ?2 0 H1 ?1 - ?2 ? 0

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• On further reflection, the school psychologist
  decides that, because of the extra expense of the
  special bilingual reading program, she wishes to
  reject the null hypothesis only if there is
  evidence that reading comprehension scores are
  improved, on the average, by the special reading
  program.
• H0 ?1 - ?2 ? 0 H1 ?1 - ?2 ? 0

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Sampling Distribution of Sample Means
Differences ?1 -?2

• Differences between sample means based on all
  possible pairs of random samples -- of given
  sizes -- from two underlying populations.

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Standard Error of ?1 -?2

• A rough measure of the average amount by which
  any difference between sample means deviates from
  the difference between population means.

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t Ratio for Two Population Means(two independent
samples)

• t

(x1 x2) (µ1 - µ2)hyp
Sx1 x2
df n1 n2 - 2
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Confidence Interval for µ1 - µ2

• A range of values that, in the long run,
  includes the unknown difference between
  population means for a certain percent of the
  time.

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Pooled Variance Estimate sp2

• The most accurate estimate of the population
  variance (assumed to be the same for both
  populations) based on a combination of two sample
  variances.