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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

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

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

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

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

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

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)

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

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

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

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

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)

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

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

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

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

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)

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

Computes an F-ratio Total variance is divided into 2 sources:

Variance between groups (numerator)Variance within groups (denominator)

Nominal Chi-square (X2)-

df = k (# groups or categories) -1

measure of difference between observed frequency with expected frequency