One-tailed Hypothesis test

What is a one-tailed Hypothesis test?

  • In a directional hypothesis test or a one-tailed test, the statistical hypotheses (H0 and H1) specify either an increase or a decrease in the population mean. That is, they make a statement about the direction of the effect.

For example:

    • A special training program has been expected to increase student performance (Marks obtained) in the class 12th CBSE board exam.
    • Now we are going to test that the average mark of students may increase from the previous year’s average marks.

    • This situation incorporates the directional prediction into the statement of H0 and H1.
    • The result is a directional test, or what commonly is called a one-tailed test.

Hypothesis for a Directional Test

  • In the first step of the hypothesis test, the directional prediction is incorporated into the statement of the hypotheses. Thus, the two hypotheses would state:

H0 : Average Marks are NOT increased.

(Before and after training -average marks are the same. The training program does not work.)

H1 : Average Marks are increased.

(The training program works as predicted.)

  • In the second step of the process, the critical region is located entirely in one tail of the distribution.

Measuring Effect Size

  • A measure of effect size is intended to provide a measurement of the absolute magnitude of a treatment effect, independent of the size of the sample(s) being used.
  • One concern with hypothesis testing is that a hypothesis test does not really evaluate the absolute size of a treatment effect.

Cohen’s d – Measuring and reporting effect size

  • Cohen’s d. Cohen (1988): Effect size can be standardized by measuring the mean difference in terms of the standard deviation. The resulting measure of effect size is computed as

  • The mean difference is determined by the difference between the population mean before treatment and the population mean after treatment.
  • The population mean after treatment is unknown. Therefore use the sample mean µt of the treated population.
  • The sample mean is expected to be representative of the population mean and provides the best measure of the treatment effect.

Evaluating the size of a treatment effect

Cohen’s d measures the degree of separation between two distributions, and a separation of one standard deviation (d = 1.00) represents a large difference.

  • Cohen’s d simply describes the size of the treatment effect and is not influenced by the number of scores in the sample.

Comparison of One-Tailed vs. Two-Tailed Tests

  • A two-tailed test is more rigorous and, therefore, more convincing than a one-tailed test.
  • The two-tailed test demands more evidence to reject H0 and thus provides a stronger demonstration that a treatment effect has occurred.
  • One-tailed tests should be used only in situations when the directional prediction is made before conducting analysis and there is a strong justification for making the directional prediction.
  • There is the argument that one-tailed tests are more precise because they test hypotheses about a specific directional effect instead of an indefinite hypothesis about a general effect.
  • Precaution: If a two-tailed test fails to reach significance, never follow up with a one-tailed test as a second attempt to salvage a significant result for the same data.

Concerns about Hypothesis Testing: Measuring Effect Size

There are two serious limitations to using a hypothesis test to establish the significance of a treatment effect.

The first concern is ⇒

  • The focus of a hypothesis test is on the data rather than the hypothesis.
  • When the null hypothesis is rejected, a strong probability statement is made about the sample data, not about the null hypothesis.
  • A significant result permits the conclusion: “This specific sample mean is very unlikely (p < .05) if the null hypothesis is true.” This conclusion does not make any definite statement about the probability of the null hypothesis being true or false.
  • The fact that the data are very unlikely suggests that the null hypothesis is also very unlikely, but we do not have any solid grounds for making a probability statement about the null hypothesis. It cannot be concluded that the probability of the null hypothesis being true is less than 5% simply by rejecting the null hypothesis with α = .05.

The second concern is ⇒

  • A significant treatment effect does not necessarily indicate a substantial treatment effect. In particular, statistical significance does not provide any real information about the absolute size of a treatment effect.
  • The test simply establishes that the results obtained in the analysis are very unlikely to have occurred if there is no treatment effect.
  • The hypothesis test reaches on conclusion by –
  1. calculating the standard error
  2. Difference between means
  3. Demonstrates that the obtained mean difference is substantially bigger than the standard error.

Also Read

Scroll to Top