Independent Samples t-test

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Independent Samples t-test

• Mon, Apr 12th

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t Test for Independent Means

• Comparing two samples
• e.g., experimental and control group
• Scores are independent of each other
• Focus on differences betw 2 samples, so
  comparison distribution is
• Distribution of differences between means

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Hypotheses

• Ho or ?1 - ?2 0 (no group difference) or ?1
  ?2
• Ha ?1 - ?2 not 0 (2 tailed) or ?1 - ?2 gt or
  lt 0 (if 1-tailed)
• If null hypothesis is true, the 2 populations
  (where we get sample means) have equal means
• Compare T obs to T critical (w/Df N-2)
• If Tobs gt T crit ? Reject Null

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Pooled Variance

• T observed will use concept of pooled variance to
  estimate standard error
• Assume the 2 populations have the same variance,
  but sample variance will differ
• so pool the sample variances to estimate pop
  variance
• Then standard error used in denom of T obs
• Note Ill show you 2 approaches (you decide
  which to use based on what data is given to you)

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Finding Estimated Standard Error using SS (lab
approach)

• Pooled variance (S2p)
• S2p (SS1 SS2) / df1 df2
• Where, df1 N1-1 and df2 N2-1 and SS1 and SS2
  are given to you
• Then use this to estimate standard error (S
  xbar 1 xbar2) sqrt (S2p/N1) (S2p/N2)

Estimated Standard Error (using x notation)
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Estimated Standard Error using S2y (sample
variances book HW approach)

• Skip calculating pooled variance and just
  estimate standard error
• Sybar1 ybar2 sqrt ((N1-1)S2y1)
  ((N2-1)S2y2) (N1N2) 2
• Sqrt (N1 N2)/ N1N2

Estimated Standard Error(using y notation)
Note See p. 480 in book for betterrepresentation
of this formula!!
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T observed

• Once youve estimated standard error, this will
  be used in T obs
• T obs (xbar1 xbar2) (?1 - ?2) S xbar1
  xbar2

Always 0)
EstimatedStandardError(doesntmatter ifuse x
or ynotation!)
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Example using S2y info

• Group 1 watch TV news Group 2 radio news
  difference in knowledge?
• Ho ?1 - ?2 0 Ha ?1 - ?2 not 0
• ybar1 24, S21 4, N1 61
• ybar2 26, S22 6, N2 21
• Alpha .01, 2-tailed test, df tot N-2 80
• S ybar1-ybar2 sqrt((60)4) ((20)6)
• (61 21) - 2 2.12 sqrt (61 21) /
  61 21
• 2.12 .253 .536

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• T obs (24-26) 0
• .536 -3.73
• t criticals, alpha .01, df80, 2 tailed
• 2.639 and 2.639
• T observed gt T critical (3.73 gt 2.639)
• Reject null there is a difference in knowledge
  based on news source
• (check means to see which is best)radio news was
  related to higher knowledge.
• Note in lab 22 youll use other approach (find
  SS first, then standard error for T denom) this
  ex. is how HW will look

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SPSS example

• Analyze ? Compare Means ? Independent Samples t
• Pop up windowfor Test Variable choose the
  variable whose means you want to compare. For
  Grouping Variable choose the group variable
• After clicking into Grouping Variable, click on
  button Define Groups to tell SPSS how youve
  labeled the 2 groups

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(cont.)

• Pop up window, Use Specified Values and type in
  the code for Group 1, then Group 2, hit
  continue
• For example, can label these groups anything
  youd like when entering data. Are they coded 0
  and 1? 1 and 2?etc. Specify it here.
• Finally, hit OK
• See output example in lab for how to interpret

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GSS data example

• Ho ?male - ?female 0,
• Ha difference not 0
• DV siblings
• Male xbar 4.00, female xbar 3.98
• In output, 1st look at Levenes test of equality
  of variances (2 lines) Ho equal variances
• Equal variances assumed ? look at sig value
• Equal variances not assumed
• If sig value lt .05 ? reject Ho of equal
  variances and look at equal variance not
  assumed line
• If sig value gt .05 ? fail to reject Ho of equal
  variances and use equal variance assumed line

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(cont.)

• Here, fail to reject Ho, use equal variances
  assumed
• Next, using that line, look for sig 2-tailed
  value ? this is the main hypothesis test of mean
  differences
• If sig lt .05 ? reject Ho of no group
  differences
• Here, gt .05, so fail to reject Ho, conclude
  sibs doesnt differ between male/female