Chapter 13:
Introductory
Inferential Statistics I:
Hypothesis Testing with Two Means
Outline 
Concepts 
I. Using Probability Distributions to Play the Odds 

B. Using Probability Distributions 
probability distributions: distributions that represent the theoretical patterns of expected “values of a random variable and of the probabilities of occurrence of these values” (Upton & Cook, 2002, p. 292) 
II. Reasoning With Statistical Hypothesis Testing 
research hypothesis: (symbolized H_{1}) “an expectation about events based on generalizations of the assumed relationship between variables” (Tuckman, 1999, p. 74) 
A. Determining Statistical Hypotheses 
null hypothesis: (symbolized H_{o}) a statistical hypothesis that states that there is no relationship between variables 
B. Decisions in Testing Statistical Hypotheses
For the
sake of argument, we assume that there are If finding results such as ours is quite probable when sampling from a population in which no relationships existed, we agree to continue assuming that any differences are just random; If it is very improbable that results such as ours could be found by sampling from a population in which no relationships exist, we reject the assumption that any differences are just random. 


determinism: the notion that the general course of events is determined by structures deemed to be fundamental 
1. Finding Unusual Occurrences

critical region: a portion of a probability distribution which, if our test statistic falls in that zone, will cause rejection of the null hypothesis statistically significant difference or relationship: as a result of a test of statistical significance, finding a relationship or effect size that is unlikely to have been found from random sampling error if the null hypothesis were true.
critical
value:
in statistical significance testing, the line that divides the critical
region from the rest of the distribution standard error: the standard deviation of a distribution of elements other than raw scores 
2. Choice and Errors in Testing Statistical Hypotheses 
Type I error: incorrectly rejecting the null hypothesis (claiming that the null hypothesis is untrue when it is true)
alpha risk:
the probability of committing a Type I error (for alpha risk of .05, 5%
of the distribution is in the critical region; for alpha risk of .01,
only 1% of the distribution is established as the critical region, and
so forth) 
C. The
Process of Examining Statistical Hypotheses 


central limit theorem: a statement that a sampling distribution of means tends toward normal distribution with increased sample size regardless of the shape of the parent population 
2. Computing the Test Statistics 
test statistic: in statistical hypothesis testing, a number computed from a statistical formula, “which is a function of the observations in a random sample” (Upton & Cook, 2002, p. 165) 
3. Finding the Critical Value 
onetailed tests: a test using a onetailed or directional material hypothesis that states the form of predicted differences and requires using a critical range on one side of a probability distribution. twotailed test: a test of a twotailed or nondirectional material hypothesis that does not state the form of predicted differences and requires using a critical range on both sides of a probability distribution. 
4. Rejecting or Failing to Reject the Null Hypothesis 

III. Comparisons of Two Means: The t test 
parametric
testing:
statistical
significance tests that
make
assumptions about populations from which the data were drawn; 
A. Forms
of the t Test 
onesample t test: an application of the t test that examines when a new sample mean differs from a known population mean, under conditions where the population standard deviation is unavailable 
2. t Test for Independent Samples 
t test for
independent samples: an application of the t test that
compares the means or two sample groups (one of which often is a control
or current condition) 
3. t Test for Dependent Samples 
t test for dependent samples: an application of the t test that compares the mean difference in two scores in which participants are matched or sampled twice 
4.
t Test for the Difference between Zero and an 
t test for the difference between zero and an observed correlation: used to test the statistical significance of a correlation and zero 
B. Determining Effect Sizes 
