Estimation

1
Estimation

• Minium, Clarke Coladarci, Chapter 12

2
Hypothesis Testing vs Estimation

• Examples
• Estimating
• the average heartrate of Canadians
• the average score on a stats test
• the average number of songs on an iPod
• voting behaviour (estimating a proportion)
• lifespan of a Siamese fighting fish in captivity
• the correlation between shoe size and math scores
• NHST is more common than Estimation but
• this is changing (which is a good thing)
• estimation procedures can often be used in place
  of NHST
• in some cases NHST cant be done (is simply
  inappropriate) and estimation should be used

3
Point Estimates vs Interval Estimates

• A point estimate is a single value--a
  point--taken from a sample and used to estimate
  the corresponding parameter of a population
• , s, s2 and r estimate ???????????????pectively
• an interval estimate is a range of values--an
  interval--within which it can be stated with
  reasonable confidence the population parameter
  lies
• e.g., we might state that the average heartrate
  is 605 beats per minute with 95 confidence
• in this case the 95 confidence interval is 55 to
  65.
• what does it mean to say we have 95 confidence
  in an interval estimate?

4
Constructing an Interval Estimate of ?

• Recall that 68 of all sample means fall within
  ?x of ?x
• Consequently, for 68 of all sample means ?x is
  no more than ?x away
• So the interval will contain 68
  of the time
• This is the 68 confidence interval

?x 65 ?x 4
5
Constructing an Interval Estimate of ?

• 95 of all sample means fall within 1.96 ?x of
  ?x
• Consequently, for 95 of all sample means ?x is
  no more than ?x away
• So the interval will contain
  95 of the time
• This is the 95 confidence interval

6
Interval Width and Level of Confidence

• Rule for the 95 confidence interval (? known)
• Rule for the 99 confidence interval (? known)
• General rule for a confidence interval (? known)
• z? is the value of z that contains the middle
  area of the sampling distribution that
  corresponds to the level of confidence
• (1-?)(100) is the level of confidence

7
Interval Width and Sample Size

• The width of a confidence interval depends on the
  number of scores (n) in the sample
• The CI depends on and depends on n
• i.e.,

8
Interval Estimation and Hypothesis Testing
9
Interval Estimation and Hypothesis Testing
10
Advantages of Interval Estimation

• Once you know the 95 CI you automatically know
  the results of a two-tailed test on any H0 (?
  .05)
• An interval estimate exhibits the influence of
  sampling variation and sample size
  straightforwardly
• the width of an interval can tell you whether the
  precision of your measure is useful in any sense.
• CI is the only analysis possible in certain
  circumstances (e.g., when you have no basis for
  stating H0 ).
• Even though NHST is the dominant statistical
  approach in behaviourial sciences measuring CIs
  is more informative and (in conjunction with the
  measurement of effect sizes) is increasingly
  used.
• some believe well eventually drop NHST