Statistical Hypothesis
- This is a statement about the value of a population parameter (mean median, mode, variance,
standard deviation, proportion)
Statistical hypothesis testing - a method of making decisions using data, whether from a controlled
experiment or an observational study
- It is a set of procedures that culminates in either the rejection or the non-rejection of the null
hypothesis
- It involves the comparison of two hypothesis
> Null hypothesis
> Alternative hypothesis
Steps in Hypothesis Testing
1.
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State the null & alternative hypothesis
Null hypothesis
Statement of equality
Often used to signify the equivalence of population parameters
Alternative Hypothesis
➢ Usually the researcher hypothesis
➢ Uses <,> signs
Non-directional vs Directional
➢ Non-directional / two-tailed test
➢ Simply states that there is a difference in the groups being compared
➢ That the true value of the parameter is not equal to a hypothesized value
Directional / one tailed test
➢ specifies direction of disagreement with Ho
2. State the level of significance
➢ The probability level that is considered to low to warrant support of the hypothesis being tested
➢ This is usually set at 0.05, 0.1, or 0.01
3. Select the appropriate test statistic
➢ Factors to be considered:
A. Objective of the study
B. Design of the Study
C. Type of Variables
D. Level of measurement
E. Whether the samples are related or independent
F. Assumption about the test
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A. Objectives of the study
Descriptive
Inferential
B. Study Design
Cohort? Case – Control? Cross – Sectional?
C. Types of Variables
Qualitative or Quantitative?
D. Level of Measurement
Nominal? Ordinal? Ratio?
E. Related or Independent samples
Related – sample in one group is affected by the other group
Independent – probability of selection of samples in one group is not affected by the selection in
the other group
F. Assumption about the test
Parametric test – can be used if the assumptions about the parameter like normality,
independence and homogeneity hold true
Non-parametric – when the assumptions for the use of parametric tests are questionable in the
data
4. Determine the critical region
➢ Depends on the level of significance set by the investigator
➢ If the statistic computed for the sample data fall in this region, then there is a basis for rejecting
the null hypothesis
➢ Can be one-tailed or two-tailed based on the alternative
5. Compute the test-statistic
➢ It is important that before this step, the level of significance and the critical region have been set
to avoid manipulation of these entities after the test statistic has been computed to obtain
desired outcome.
➢ The computation differs depending on the test statistic used
➢ However, basic formula of a test statistic is
Test statistic= observed statistic – expected parameter under Ho ÷ standard error
6. Make a statistical decision
➢ Whether to reject or not to reject the null hypothesis
3 ways of making statistical decision
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Compare test statistic with critical region
Computed test statistic > C.R then reject Ho
Otherwise, do not reject the null hypothesis
Compare the p-value with a level of significance
If p-value < a, reject Ho
If p > a, do not reject Ho
Compare hypothesized (test) value with the confidence interval
If the hypothesized value does not fall within the confidence interval, then we reject the null
hypothesis
➢ Otherwise, then we cannot reject the null hypothesis
7. Draw Conclusion
➢ Reject Ho
- Conclude Ha
➢ Do not reject Ho
- Conclude that there is not sufficient evidence to say that Ha is true
Non-Rejection of Null Hypothesis
➢ This is not a proof that the null hypothesis is correct
➢ Factors that may affect the non-rejection
- Inadequate sample size
- Measurement problems
Hypothesis Testing for one proportion
➢ Deals with only one sample or group
➢ Hypothesis is that the population proportion is equal to a presumed / hypothesized value
➢ Null hypothesis
- Ho: P = Po
➢ Alternative hypothesis
➢ Ha: P = Po (two-tailed test)