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, H_{0}, 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:
H_{0}: null hypothesis: D_{after} ≤ D_{before}
H_{A}, research hypothesis: D_{after} > D_{before}
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:
H_{0}: null hypothesis: D_{male} = D_{female}
H_{A}, research hypothesis: D_{male} ≠ D_{female}
The standard process for hypothesis testing comprises the following steps:
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 33.19). 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.
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