Hypothesis Testing Process
Hypothesis tests are classified as one-tailed or two-tailed tests. The one-tailed test specifies the
direction of the difference, i.e., the null hypothesis, H0, is expressed in terms of the equation parameter ≥ something, or
parameter ≤ something.
For instance, in a before and after advertisement screening test, if the ad is expected to improve consumers’
disposition to try a new brand, then the hypothesis may be phrased as follows:
H0: null hypothesis: Dafter ≤ Dbefore
HA, research hypothesis: Dafter > Dbefore
Where D is the disposition to try the product, expressed as the proportion of respondents
claiming they will purchase the brand.
If the direction of the difference is not known, a two-tailed test is applied. For instance, if for
the same test, the marketer is interested in knowing whether there is a difference between men and women, in their
disposition to buy the brand, the hypothesis becomes:
H0: null hypothesis: Dmale = Dfemale
HA, research hypothesis: Dmale ≠ Dfemale
The standard process for hypothesis testing comprises the following steps:
- H0, HA: State the null and alternative hypothesis.
- α: Set the level of significance, i.e., the type I error. For most research studies this is set at 5%.
- Test statistic: Compute the test statistic. Depending on the characteristics of the test this is
either the z-score (standard score), the t-value, or the f-ratio.
- p-value: Obtain the p-value by referencing test statistic in the relevant distribution table. The
normal distribution is used for referencing the z-score, t distribution for the t-value and the f distribution
for the f-ratio.
- Test: Accept the research hypothesis HA (reject H0) if p-value < α.
Each of the test statistics is essentially a signal-to-noise ratio, where the signal is the relationship
of interest (for instance, the difference in group means), and noise is a measure of variability of groups.
If a measurement scale outcome variable has little variability it will be easier to detect change than
if it has a lot of variability (see Exhibit 34.19).
So, sample size is a function of variability (i.e., standard deviation).
A z-score (z) indicates how many standard deviations the sample mean is from the population mean.
$$ z = \frac{\bar x-μ}{s/\sqrt n} $$
Where x̄ is the sample mean, μ is the population mean, and σ=s/√n is the sample standard
deviation (refer CLT), and s is the standard deviation of the population.
Details of the t-test are provided in the section t-test, and the
f-ratio is covered in the section ANOVA.
Note: The data analysis add-in in excel provides an easy-to-use facility to conduct
hypothesis z, t and f tests. P-value calculators are also available online, for instance, at this Social Science Statistics
webpage.