Ch. 9 CDIS 455
CHAPTER 9: HYPOTHESIS TESTING
Charis Pow, Fall 2021
HYPOTHESIS
A hypothesis is defined as:
A proposed relationship between independent and dependent variables.
Involves a systematic 6-step process:
State the hypothesis.
Set level of risk.
Choose the sample size.
Determine the critical value.
Compute test statistic.
Make a decision about H0 (the null hypothesis).
1. STATE THE HYPOTHESIS
ALTERNATIVE HYPOTHESIS (HA or H1):
This is the statement of the expected result of a research study.
Illustrates a directional effect: suggests that the independent variable will affect the dependent variable somehow.
Example: "Drinking caffeine increases sustained attention to task."
NULL HYPOTHESIS (H0):
A statement of no difference or no relationship between variables or groups.
Example: "Drinking caffeine has no effect on sustained attention to task."
2. SET AN ACCEPTABLE LEVEL OF RISK
The level of risk represents the amount of error you are willing to accept before rejecting the null hypothesis (H0).
Alpha (α):
This is the threshold value to determine if a test statistic is statistically significant.
Best practice in research: set alpha at 0.05 as the criterion for rejecting or accepting H0.
Type 1 error: Rejection of a true H0 “false positive” - Ex: the test results say DO have “strep” but you actually Don’t.
Type II error: Accepting H0 when it’s actually false Ex: the test results say you Don’t have strep but you actually DO
3. CHOOSE SAMPLE SIZE
The sample size (n) affects several factors:
Probability (p) of the distribution.
Power of the test: the probability of rejecting H0 when it is actually false.
Important notes regarding sample size:
Larger sample sizes usually result in more powerful tests of H0.
Studies with small samples (n < 10) have a high risk of committing a Type II error (failing to reject a false null hypothesis).
4. DETERMINE CRITICAL VALUE
Critical Value (CV):
This is the cut-off point which defines the rejection region that can be used to make a decision on accepting or rejecting H0.
The CV is dependent on the alpha (α) value:
Using the predefined level of risk, one can look up the CV in a statistical table.
CV values are based on whether a 1-tailed or 2-tailed test is being conducted.
TAIL TESTING
1-TAILED TEST:
This test is based on a directional hypothesis.
Uses only one CV value depending on the direction studied.
Example: "College students will perform better on a memory task than elementary students."
2-TAILED TEST:
This is based on a non-directional hypothesis.
Uses both CV values, one at each end of the distribution.
Example: "College students and elementary students will perform differently on a memory task."
5. COMPUTE TEST STATISTIC
PARAMETRIC TESTS:
Include the following descriptive statistics:
Measures of central tendency: mean, median, mode.
Variability: standard deviation (SD), variance, range.
Correlational statistics denoted by "r," which indicates direction and degree of relationship.
Inferential Statistics:
Types include: T-test, Z-test, ANOVA, ANCOVA, MANOVA, etc.
NON-PARAMETRIC TESTS:
Examples include:
Mann-Whitney U (equivalent to the t-test).
Kruskal-Wallis (equivalent to ANOVA).
Chi-square tests.
6. MAKE DECISION ABOUT H0
Hypothesis testing is fundamentally a binary decision-making process; hypotheses are either accepted or rejected based on statistical tests.
Decision criteria:
Compare the computed statistic with the critical value (CV):
If the statistic value > CV, then reject H0.
If the statistic value < CV, then accept H0.
DECIDING TO REJECT OR ACCEPT H0
Rejecting the Null H0:
Accept the alternative hypothesis HA under the following conditions:
If p < α.
If t > CV.
If z > 1.96.
Outcomes indicate a "significant difference."
Failing to Reject the Null H0:
Accept H0 under the conditions:
If p > α.
If t < CV.
If z < 1.96.
Outcomes indicate "NO significant difference."
INTERPRETATION OF RESULTS
**Accepting or Rejecting the Null Hypothesis:
If you reject the null hypothesis:**
Indicates there is a significant difference between groups/treatments being studied, which may lead to clinical significance.
If you accept the null hypothesis:
Indicates there is NO significant difference found.
DISTRIBUTIONS IN STATISTICS
NORMAL DISTRIBUTION:
Characterized by a bell curve.
The mode is located at the center.
It is symmetrical and continuous across all scores.
OTHER DISTRIBUTIONS:
May exhibit skewness, kurtosis, and asymmetry with varying shapes.
Can have outliers affecting the distribution shape.
THE BELL CURVE
Normal Distribution describes data that vary randomly from the mean.
Normal Curve:
The resulting pattern of data forms a bell-shaped curve.
The Standard Normal Bell Curve:
Mean (average): 0.
Percentages regarding the distribution:
68% of the data falls within one standard deviation of the mean.
95% of the data falls within two standard deviations of the mean.
SYMBOLS IN STATISTICS
S: Sum
a: alpha
SD: standard deviation
Z: standard score
X: mean (average)
n: number of subjects
H0: null hypothesis
HA: alternative hypothesis
p: probability
CV: critical value
“r”: correlation
OTHER TERMS IN STATISTICS
Standard Error of Mean (SEM): Measures how far sample means are from the population mean.
Central Limit Theorem (CLT): States that, given a large enough sample size, the sampling distribution of the mean will be normally distributed.
Range: Compares variation between two sets of data.
Scale: Refers to the statistical analyses of data based on varying properties.
Standard Deviation: Reflects how data points are dispersed around the mean.
Variance: Measures the range of individual scores in comparison to one another.
REFERENCES
Meline, T. (2010). A research primer for communication sciences and disorders. Pearson.