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:

*H*: State the null and alternative hypothesis._{0}, H_{A}*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 H_{A}(reject H_{0}) 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 33.18). 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
web page.*

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