Comparing Two Means Presented by Elsa R' Barron

1
Comparing Two MeansPresented by Elsa R. Barron

• Two sample problems
• Confidence Intervals for Two Means
• Significance Test for Two Means

2
Statistically Significant

• Compare two samples to see if difference is
  statistically significant.
• Example Two groups
• ? People assigned to Welfare
• ? Participants in Options Pgm
• Purpose of experiment Find out if Options Pgm
  helps women get off Welfare and earn more money.

3
Sampling Distribution

• Sampling distribution of the difference between
  two means (x1-x2) is the distribution that is
  of concern to analyze.
• ? Standardize this difference (x1-x2) get it
  into SD units
• ? Need mean and SD of
• distribution
• ? Use rules of means and
• variances

4
T-statistic Formula

• t (x1-x2) (u1-u2)
• s1 s2
• n1 n2
• T-statistic is basis for formulas to find
  Confidence Interval and do Significance Tests.

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Confidence Interval

• For single mean
• x t s Find value of t in
• n distribution table.
• ? For Two means
• (x1-x2) t s1 s2
• n1 n2
• Find value of t using t distribution with
  degrees of freedom for smaller of two samples.
  The smaller size always gives conservative result.

6
95 Confidence Level

• Plug in data in Confidence Interval formula
• (6595-7638) 1.96 247 289
• 1395 1362
• CI 1043 20
• 95 confident that true difference in earnings
  between two populations is in range of 1023-1063.
  CI gives a precise statement of the accuracy of
  the result.

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Significance Test

• To determine if there is a significant difference
  between two samples
• First step Null hypothesis
• Then Alternate hypothesis
• Then t-statistic formula
• Example Ultra Cell Foam and conventional foam

8
Significance LevelsConfidence Intervals

• Testing (SAT)
• ? To find out if sample
• (coaching class) is effective
• ? Computing CI gives
• different perspective on
• whether to take coaching
• class.

9
Normal Distributions

• So far, it has been assumed all populations were
  normally distributed, but even if they werent
  normal, t-test gives accurate scores since
  t-statistics for two means are robust
• ? no outliers
• ? neither population is
• strongly skewed

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Comparing variability, SDs

• Big drawback that two-sample t-tests do not have
• ? SDs sensitive to shape of
• population distribution
• ? if population not very close
• to normal, procedures can
• give wrong answers
• Best to leave comparisons of SDs to experts.