1-Sample%20t-test

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1-Sample t-test

• Mon, Apr 5th

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T-test purpose

• Z test requires that you know ? from pop
• Use a t-test when you dont know the population
  standard deviation.
• One sample t-test
• Compare a sample mean to a population with a
  known mean but an unknown variance
• Use Sy (sample std dev) to estimate ? (pop std
  dev)

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T formula

• T obtained (ybar - ?y)
• Sy/sqrt N
• Procedure
• Compute t obtained from sample data
• Determine cutoff point (not a z, but now a
  critical t) based on ?
• Reject the null hypothesis if your observed t
  value falls in critical region (t observed gt t
  critical)

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T distribution

• Cant use unit normal table to find critical
  value must use t table to find critical t
• Based on degrees of freedom (df) scores free
  to vary in t obtained
• Start w/sample size N, but lose 1 df due to
  having to estimate pop std dev
• Df N-1
• Find t critical based on df and alpha level you
  choose

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(cont.)

• To use the t table, decide what alpha level to
  use whether you have a 1- or 2-tailed test ?
  gives column
• Then find your row using df.
• For ? .05, 2 tailed, df40, t critical 2.021
• Means there is only a 5 chance of finding a
  tgt2.021 if null hyp is true, so we should reject
  Ho if t obtained gt 2.021

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Note on t-table

• When gt 30 df, critical values only given for 40,
  60, 120 df, etc.
• If your df are in between these groups, use the
  closest df
• If your df are exactly in the middle, be more
  conservative ? use the lower df
• Example You have 50 df, choose critical t value
  given for 40 df (not 60).
• Youll use a larger critical value, making a
  smaller critical region ? harder to find signif

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Another note

• Note that only positive values given in t table,
  so
• If 1-tailed test,
• Use t critical value for upper-tail test
  (1.813)
• Use t critical value for lower-tail test (you
  have to remember to switch the sign, - 1.813)
• If 2-tailed test,
• Use and signs to get 2 t critical values, one
  for each tail (1.813 and 1.813)

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Example

• Is EMT response time under the new system (ybar
  28 min) less than old system (? 30 min)? Sy
  3.78 and N10
• Ha new lt old (? lt 30)
• Ho no difference (? 30)
• Use .05 signif., 1-tailed test (see Ha)
• T obtained (28-30) / (3.78 / sqrt10) (28-30)
  / 1.20 - 1.67

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(cont.)

• Cutoff score for .05, 1-tail, 9 df 1.833
• Remember, were interested in lower tail (less
  response time), so critical t is 1.833
• T obtained is not in critical region (not gt
  -1.833 ), so fail to reject null
• No difference in response time now compared to
  old system

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1-sample t test in SPSS

• Use menus for
• Analyze ? Compare Means ? One sample t
• Gives pop-up menuneed 2 things
• select variable to be tested/compared to
  population mean
• Notice test value window at bottom. Enter the
  population/comparison mean here (use ? given to
  you)
• Hit OK, get output and find sample mean, observed
  t, df, sig value (AKA p value)
• Wont get t critical, but SPSS does the
  comparison for you(if sig value lt ?, reject null)