2/10/11. infer properties of the population from what is observed in the sample an inference is a...
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2/10/11
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Infer properties of the population from what is observed in the sample
An inference is a generalization, as inferences go beyond the data
Assumption: the sample is representative of the population Random or probability sample
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A point estimate looks at one value and is an unbiased estimate of the population meanNot accurate!
An interval estimate or confidence interval can estimate with a specified degree of confidence that the population mean is within a certain range of values
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Probability of obtaining any of the possible values in a statistic
Enable researcher to infer with a determined level of confidence, the population parameters from the sample statistics
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Used with continuous data A statement that the shape of the sampling
distribution of the mean will approximate a normal curve if the sample is sufficiently large
If random samples of a fixed n are drawn from any population, as n increases the distribution of the sample mean approaches a normal distribution
Approximation of a normal distribution is n ≥ 30 Sample sizes less than 30 use t distributions to
identify curve
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A range of values or scores from sample data that probably include the true value (population parameter)
Necessary to tell the amount of error present or the accuracy of the estimate
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A statistical decision on whether the finding in a study reflect chance or real effects, at a given level of probabilityThe larger the sample size (n), the more
likely we are to reject H0
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1. State alternative hypothesis (HA) – claims results are real or significant (independent variable influenced dependent variable)
2. State null hypothesis (H0) –claims that any difference in data was due to chance (independent variable had no effect upon dependent variable)
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3. Set decision level (α)common level in medicine = 0.05 results are not significant if p > 0.05
4. Calculate probability of H0 being true
the smaller decision level α, less likely we are to reject H0
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5. Decision rule: p (H0 is true) ≤ α; reject H0 (Accept HA)
p (H0 is true) > α; retain H0
Important: Cannot PROVE H0, can ONLY reject or retain
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There is always a risk of making an error when inferences are made
To test a null hypothesis requires both:A test of significance, andA selected probability level that indicates
how much risk you are willing to take that the decision you make is wrong
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Type I- we reject the H0 when it is really true and claim HA is supported when it is actually falseSmaller α, less chance of making a Type I
error Type II- we retain the H0 when it is really
false and conclude the alternate hypothesis was not supported (β error)Larger n, less chance of making Type II
error
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Tests of significance are almost always two-tailed which allows for the possibility that a difference may occur in either direction
A one-tailed test assumes that if a difference occurs, it will favor one direction
More likely to reject H0 if use a one tail test (directional HA) than a two-tail test (non-directional HA)
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Represents the number of scores which are free to vary when calculating the statistic
Dependent upon the number of participants and number of groupsExample for correlation coefficient (r),
df = N (number of participants) – 2 Each test of significance has its own
formula for determining degrees of freedom
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1. Determine if significance test will be one-tailed or two-tailed;
2. Select a probability level;3. Compute a test of significance4. Consult the appropriate tables to
determine significance of your results Determined by the intersection of
probability level and df
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Parametric test are preferred because they are more powerful, but they require assumptions:
1.Normal population distribution2.Variables must be interval or ratio3.Randomized sample4.Variances of population comparison
groups are equal
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Nonparametric tests are less powerful, but they make no assumptions about the shape of the distributionUsed for nominal or ordinal data setsTakes a larger sample to reach same level
of significance as a parametric test
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Interval or Ratio Two groups:
t- test for independent groups t- test for dependent groups
Three or more groups:Analysis of variance (ANOVA) for
independent groups (F ratio)ANOVA for dependent groups (F)
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t-test is used to determine if 2 means are significantly different by comparing the actual mean observed with the difference expected by chance
t-value is compared to t-table values; if value is ≥ than table value, the null hypothesis is rejected
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Computes an F-ratio Total variance is divided into 2 sources:
Variance between groups (numerator)Variance within groups (denominator)
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Nominal Chi-square (X2)-
df = k (# groups or categories) -1
measure of difference between observed frequency with expected frequency