Formulating Statistical Hypotheses

A research hypothesis is a statement about the empirical world that can be tested against data. Communication scientists, for instance, may hypothesize that:

  • a television station reaches half of all households in a country,

  • media literacy is below a particular standard (for instance, 5.5 on a 10-point scale) among children,

  • opinions about immigrants are not equally polarized among young and old voters,

  • the celebrity endorsing a fundraising campaign makes a difference to people’s willingness to donate,

  • more exposure to brand advertisements increases brand awareness,

  • and so on.

As these examples illustrate, research hypotheses seldom refer to statistics such as means, proportions, variances, or correlations. Still, we need such statistics to test a hypothesis. The researcher must translate the hypothesis into a new hypothesis specifying a statistic in the population, for example, the population mean. The new hypothesis is called a statistical hypothesis.

Translating the research hypothesis into a statistical hypothesis is perhaps the most creative part of statistical analysis, which is just a fancy way of saying that it is difficult to give general guidelines stating which statistic fits which research hypothesis. All we can do is give some hints.

Research questions usually address shares, score levels, associations, or score variation. If a research question talks about how frequent some characteristic occurs (How many candies are yellow?) or which part has a particular characteristic (Which percentage of all candies are yellow?), we are dealing with one or two categorical variables. Here, we need a binomial, chi-squared, or exact test (see Figure 9.17).

If a research question asks how high a group scores or whether one group scores higher than another group, we are dealing with score levels. The variable of central interest usually is numerical (interval or ratio measurement level) and we are concerned with mean or median scores. There is a range of tests that we can apply, depending on the number of groups that we want to compare (one, two, three or more): t tests or analysis of variance.

Instead of comparing mean scores of groups, a research question about score levels can address associations between numerical variables, for example, Are heavier candies more sticky? Here, the score level on one variable (candy weight) is linked to the score level on another variable (candy stickiness). This is where we use correlations or regression analysis.

Finally, a research question may address the variation of numeric scores, for example, Does the weight of yellow candies vary more strongly than the weight of red candies? Variance is the statistic that we use to measure variation in numeric scores.