Hypothesis Testing

• Hypothesis testing is a statistical method that is used in making statistical decisions using experimental data. Hypothesis testing is basically an assumption that we make about the population parameter
• Procedure in Hypothesis Testing

  1. State the null hypothesis and alternative hypothesis.
  2. Choose the level of significance.
  3. Select appropriate test statistic.
  4. Determine the critical values that divide the rejection and nonrejection regions (if the decision is to be based on P value it is not necessary to state the critical region).
  5. Compute for the value of the test statistic from the sample data.
  6. Make a statistical decision.
  7. State the conclusion.
• Two types of Statistical Hypothesis: Null Hypothesis and Alternative Hypothesis
• The null hypothesis states that a population parameter is equal to a value.
• The null hypothesis is often an initial claim that researchers specify using previous research or knowledge.
• It is a statement of no effect, relationship, or difference between two or more groups or factors.
• In research studies, a researcher is usually interested in disproving the null hypothesis.
• Null Hypothesis (H0 – “H sub Zero/ H null”)
• Null Hypothesis (H0 – “H sub Zero/ H null”)
• An alternative hypothesis states that the population parameter is different from the value of the population parameter in the null hypothesis.
• The alternative hypothesis is what you might believe to be true or hope to prove true.
• Alternative Hypothesis is the statement that there is an effect or difference. This is usually the hypothesis the researcher is interested in proving.
• The alternative hypothesis can be onesided (only provides one direction) or two-sided.
• We often use two-sided tests even when our true hypothesis is one-sided because it requires more evidence against the null hypothesis to accept the alternative hypothesis.
• In order to state the hypothesis correctly, the researcher must translate correctly the claim into mathematical symbols.
• H0 : parameter = specific value (two-tailed test)

  Ha : parameter ≠ specific value

  H0 : parameter = specific value (left-tailed test)

  Ha : parameter < specific value

  H0 : parameter = specific value (right-tailed test)

  Ha : parameter > specific value
• A Type I error, also known as a false positive, occurs when a null hypothesis is rejected when it is actually true. In other words, it is the incorrect rejection of a true null hypothesis.
• A Type II error, also known as a false negative, occurs when a null hypothesis is not rejected when it is actually false. In other words, it is the failure to reject a false null hypothesis.
• Level of significance is the probability of committing a Type I error is called the level of significance, denoted by the Greek letter alpha (α).
• The probability of committing a Type II error, denoted by β, is difficult to determine unless we have a specific alternative hypothesis.
• In hypothesis testing, the level of significance refers to the degree of significance in which we accept or reject the null hypothesis which is assumed as true.
• In hypothesis testing, 100% accuracy is not possible for accepting or rejecting a null hypothesis.
• So, we select a level of significance that is usually 0.01, 0.05 and 0.10.
• The Type I and Type II errors are related. A decrease in the probability of one results in an increase in the probability of other.
• The size of the critical region, therefore the probability of committing Type I error can always be reduced by adjusting the critical value(s)
• An increase in the sample size will reduce α and β simultaneously.
• If the null hypothesis is false, β is maximum when the true value of a parameter approaches the hypothesized value. The greater the distance between the true value and the hypothesized value, the smaller the β will be.
• P value less than 0.01 = Highly statistically significant (very strong evidence against the null hypothesis)
• P value 0.01 to 0.05 = Statistically significant (Adequate evidence against the null hypothesis)
• P value greater than 0.05 = Not Significant (Insufficient evidence against the null hypothesis)
• Statistical hypothesis – an assertion or conjecture concerning the population or more populations.
• Null hypothesis – the hypothesis or assumption about the population parameter we wish to test.
• Alternative hypothesis – the conclusion we accept when the data fail to support the null hypothesis.
• Significance level - a value indicating the percentage of sample values that is outside a certain limits, assuming the null hypothesis is correct; i.e. the probability of rejecting the null hypothesis
• Power of the test – the probability of rejecting the null hypothesis when it is false, i.e. it is measure of how well the hypothesis test is working.
• Test statistic – a statistic used in deciding whether to reject or to accept the null hypothesis.
• Confidence level – the probability that the parameter tested is within the specified values in the hypothesis.
• Critical value – the last number observed in passing from the acceptance region into the rejection region.
• Critical region or rejection region – part of the set of all possible values of a sample statistic for which the hypothesis to be tested is rejected
• Dependent samples – samples drawn from two populations in such a way that the elements were not chosen independently of one another, in order to allow a more precise analysis or to control for some extraneous factors