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: 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:

H₀: null hypothesis: D_male = D_female

H_A, research hypothesis: D_male ≠ D_female

The standard process for hypothesis testing comprises the following steps:

1. H₀, H_A: State the null and alternative hypothesis.
2. α: Set the level of significance, i.e., the type I error. For most research studies this is set at 5%.
3. 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.
4. 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.
5. Test: Accept the research hypothesis H_A (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 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.

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.