one-tailed hypothesis

(noun)

a hypothesis in which the value of a parameter is specified as being either above or equal to a certain value or below or equal to a certain value

Related Terms

  • null hypothesis

Examples of one-tailed hypothesis in the following topics:

  • Directional Hypotheses and One-Tailed Tests

    • A one-tailed hypothesis is one in which the value of a parameter is either above or equal to a certain value or below or equal to a certain value.
    • The vast majority of hypothesis tests involve either a point hypothesis, two-tailed hypothesis or one-tailed hypothesis.
    • A one-tailed hypothesis is a hypothesis in which the value of a parameter is specified as being either:
    • An example of a one-tailed null hypothesis, in the medical context, would be that an existing treatment, $A$, is no worse than a new treatment, $B$.
    • A one-tailed test, showing the $p$-value as the size of one tail.
  • One- and Two-Tailed Tests

    • A probability calculated in only one tail of the distribution is called a "one-tailed probability. "
    • The null hypothesis for the two-tailed test is π = 0.5.
    • By contrast, the null hypothesis for the one-tailed test is π ≤ 0.5.
    • The one-tailed hypothesis is rejected only if the sample proportion is much greater than 0.5.
    • The alternative hypothesis in the two-tailed test is π ≠ 0.5.
  • Steps in Hypothesis Testing

    • Be able to state the null hypothesis for both one-tailed and two-tailed tests
    • The first step is to specify the null hypothesis.
    • For a two-tailed test, the null hypothesis is typically that a parameter equals zero although there are exceptions.
    • For a one-tailed test, the null hypothesis is either that a parameter is greater than or equal to zero or that a parameter is less than or equal to zero.
    • Failure to reject the null hypothesis does not constitute support for the null hypothesis.
  • Interpreting Significant Results

    • Consider the one-tailed test in the James Bond case study: Mr.
    • The null hypothesis for this one-tailed test is that π ≤ 0.5 where π is the probability of being correct on any given trial.
    • Bond is better than chance on this task.
    • Now consider the two-tailed test used in the Physicians' Reactions case study.
    • The validity of concluding the direction of the effect is clear if you note that a two-tailed test at the 0.05 level is equivalent to two separate one-tailed tests each at the 0.025 level.
  • The Null and the Alternative

    • In the hypothesis testing approach of Jerzy Neyman and Egon Pearson, a null hypothesis is contrasted with an alternative hypothesis, and these are decided between on the basis of data, with certain error rates.
    • One-tailed directional.
    • A one-tailed directional alternative hypothesis is concerned with the region of rejection for only one tail of the sampling distribution.
    • Two-tailed directional.
    • A two-tailed directional alternative hypothesis is concerned with both regions of rejection of the sampling distribution.
  • Exercises

    • What is the null hypothesis?
    • The probability value is computed assuming that the null hypothesis is true.
    • A study comparing a drug with a placebo on the amount of pain relief.
    • (A one-tailed test was used. )
    • Would a sample value of M= 60 be significant in a two-tailed test at the .05 level?
  • Creating a Hypothesis Test

    • Decide between a one-tailed or a two-tailed statistical test.
    • A one-tailed test assesses whether the observed results are either significantly higher or smaller than the null hypothesis, but not both.
    • A two-tailed test, on the other hand, assesses both possibilities at once.
    • It achieves so by dividing the total level of significance between both tails, which also implies that it is more difficult to get significant results than with a one-tailed test.
    • This image shows a graph representation of a two-tailed hypothesis test.
  • Factors Affecting Power

    • Power is higher with a one-tailed test than with a two-tailed test as long as the hypothesized direction is correct.
    • A one-tailed test at the 0.05 level has the same power as a two-tailed test at the 0.10 level.
    • A one-tailed test, in effect, raises the significance level.
    • The relationship between μ and power for H0: μ = 75, one-tailed α = 0.05, for σ's of 10 and 15.
    • The relationship between significance level and power with one-tailed tests: μ = 75, real μ = 80, and σ = 10
  • Two-sided hypothesis testing with p-values

    • In one-sided tests, we shade the single tail in the direction of the alternative hypothesis.
    • p-value = left tail + right tail = 2 × (left tail) = 0.4180
    • If the null hypothesis is true, we incorrectly reject the null hypothesis about 5% of the time when the sample mean is above the null value, as shown in Figure 4.19.
    • Then if we change to a one-sided test, we would use H A : µ < µ 0 .
    • If the null hypothesis is true, then we would observe such a case about 5% of the time.
  • Testing a Single Proportion

    • Do you have one group or two groups?
    • Therefore, we can perform a one proportion $z$-test to test this belief.
    • There is no reason to think how many cell phones one household owns has any bearing on the next household.
    • Determine the Critical Region(s): Based on our hypotheses are we performing a left-tailed, right tailed or two-tailed test?
    • We will perform a right-tailed test, since we are only concerned with the proportion being more than 30% of households.
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