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2/10/11
 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 mean

Not 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 probability

The 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, and
A 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
false

Smaller 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 twotailed 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 (nondirectional HA)
 Represents
the number of scores which are
free to vary when calculating the statistic
 Dependent upon the number of participants
and number of groups

Example for correlation coefficient (r),
df = N (number of participants) – 2
 Each
test of significance has its own formula
for determining degrees of freedom
1.
2.
3.
4.
Determine if significance test will be onetailed or two-tailed;
Select a probability level;
Compute a test of significance
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 distribution
2. Variables must be interval or ratio
3. Randomized sample
4. Variances of population comparison groups
are equal
Nonparametric tests are less powerful, but
they make no assumptions about the shape
of the distribution


Used for nominal or ordinal data sets
Takes 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