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Chapter 6 Statistical Significance

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Statistical Significance. By: Vanessa Cortes. Darlene Villafranca ... Blue collar workers are will not buy significantly more product than white collar workers. ... – PowerPoint PPT presentation

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Title: Chapter 6 Statistical Significance


1
Chapter 6Statistical Significance
  • By Vanessa Cortes
  • Darlene Villafranca

2
Significant means reliable not important
  • In normal English, "significant" means important,
    while in Statistics "significant" means probably
    true (not due to chance).
  • A research finding may be true without being
    important.
  • When statisticians say a result is "highly
    significant" they mean it is very probably true.
  • They do not (necessarily) mean it is highly
    important.

3
Statistics vs. Parameters
  • Characterized aspects of data that constitute a
    sample Statistics
  • Characterized features of data that constitute a
    populationParameters
  • Researchers want to know if the sampling
    descriptive statistics accurately approximates
    population parameters

4
Three types of Significance
  • Statistical Significance
  • Practical Significance
  • Clinical Significance
  • All require calculations
  • All yield numerical results

5
Statistical Significance Inferential Statistics
  • Inferential Statistics are often the next step
    after you have collected summarized data
  • Inferential statistics are used to make
    inferences from smaller group of data to possibly
    larger one
  • Inferential statistics are used to infer
    something about the population based on the
    samples characteristics

6
Null Hypothesis
  • Null is always a statement of equality
  • Null can be true or false
  • No difference or truly is an inequality
  • Null applies ONLY to the population
  • The researcher never really knows the Null
    hypothesis and if there is or is not a difference
    between groups
  • WHY?

7
Hypothesis Testing
  • You cannot make both Type I and Type II Error on
    a given hypothesis
  • Once you reject, you could not have made a Type
    II error.
  • Once you fail to reject, you could not have made
    Type I error.
  • Hypotheses predicting zero differences or zero
    relationship

8
Accept or Reject the Null Hypothesis
9
Statistical Power
  • The power of a statistical test is the
    probability that the test will reject a false
    null hypothesis (that it will not make a Type II
    error). As power increases, the chances of a Type
    II error decrease, and vice versa. The
    probability of a Type II error is referred to as
    ß. Therefore power is equal to 1 - ß.

10
One-Tailed and Two-Tailed Significance Tests
  • One important concept in significance testing is
    whether you use a one-tailed or two-tailed test
    of significance. The answer is that it depends on
    your hypothesis. When your research hypothesis
    states the direction of the difference or
    relationship, then you use a one-tailed
    probability. For example, a one-tailed test would
    be used to test these null hypotheses Females
    will not score significantly higher than males on
    an IQ test. Blue collar workers are will not buy
    significantly more product than white collar
    workers. Superman is not significantly stronger
    than the average person. In each case, the null
    hypothesis (indirectly) predicts the direction of
    the difference.

11
Two-Tailed Significance Tests
  • A two-tailed test would be used to test these
    null hypotheses There will be no significant
    difference in IQ scores between males and
    females. There will be no significant difference
    in the amount of product purchased between blue
    collar and white collar workers. There is no
    significant difference in strength between
    Superman and the average person. The one-tailed
    probability is exactly half the value of the
    two-tailed probability.

12
Properties of Sampling Distributions
  • For all sampling distributions, the standard
    deviation of the sampling distribution gets
    smaller as sample size increases.
  • The mean of the statistics in a sampling
    distribution for unbiased estimators will equal
    the population parameter being estimated

13
Standard Error/Sampling Error
  • Standard deviation of the sampling
    distributionStandard error of the statistic or
    Standard error. (SE)

14
Inferentially
  • Statistical significance test is to divide the
    statistic by its standard error.
  • 3 synonymous names for the fundamental ratio
  • 1. t statistic
  • 2. critical ratio
  • 3. Wald statistic

15
Test Statistics
  • Test statisticsstandardized sampling
    distributions
  • Test statistics (TS) distributions can be used in
    place of P values .
  • The comparison of a given P calculated with a
    given PCRITICAL will always yield the same
    decision about the comparison of a given TS
    calculated with a given TSCRITICAL.

16
P calculated
  • P calculated is calculating the estimated
    probability
  • P values range from 0 to 1
  • or 0 to 100

17
Procedure Used to Test for Significance
  • Whenever we perform a significance test, it
    involves comparing a test value that we have
    calculated to some critical value for the
    statistic. It doesn't matter what type of
    statistic we are calculating (e.g., a
    t-statistic, a chi-square statistic, an
    F-statistic, etc.), the procedure to test for
    significance is the same.
  • 1. Decide on the critical alpha level you will
    use (i.e., the error rate you are willing to
    accept).
  • 2. Conduct the research.
  • 3. Calculate the statistic.
  • 4. Compare the statistic to a critical value
    obtained from a table.

18
If your statistic is higher than the critical
value from the table
  • Your finding is significant.
  • You reject the null hypothesis.
  • The probability is small that the difference or
    relationship happened by chance, and p is less
    than the critical alpha level (p lt alpha ).

19
If your statistic is lower than the critical
value from the table
  • Your finding is not significant.
  • You fail to reject the null hypothesis.
  • The probability is high that the difference or
    relationship happened by chance, and p is greater
    than the critical alpha level (p gt alpha ).
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