Hypothesis Testing

• Hypothesis Testing


  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.
• The Two Types of Statistical Hypothesis: Null and Alternative.
• H sub Zero or H null


  This symbol "H₀" is read as?
• 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.
• Null Hypothesis


  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.
• Some examples of null hypotheses are:

  1. There is no difference between the average ages of male and female customers.
  2. The intervention and control groups have the same survival rate (or, the intervention does not improve survival rate).
  3. There is no association between the atmospheric temperature and the total sales of fruit shake.
• Alternative Hypothesis


  This “H₁ or Hₐ“ is the symbol for__?
• 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 


  It is the statement stating that there is an effect or difference.
• Alternative Hypothesis 


  This is usually the hypothesis the researcher is interested in proving.
• Some examples Alternative Hypotheses are:

  1. The average age of male customers differs with the average age of female customers.
  2. The time to resuscitation from cardiac arrest is lower for the intervention group than for the control.
  3. There is an association between the atmospheric temperature and the total sales of fruit shake.
• The alternative hypothesis can be one-sided (only provides one direction) or two-sided.
• Two-sided tests 


  It is used when we require more evidence against the null hypothesis to accept the alternative hypothesis.
• 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.
• 1. H0 : parameter = specific value (two-tailed test) Ha: parameter ≠ specific value
  2. H0 : parameter = specific value (left-tailed test) Ha: parameter < specific value
  3. 3. H0 : parameter = specific value (right-tailed test) Ha: parameter > specific value


  What are the three possible sets of statistical hypotheses?
• What are some common phrases for hypothesis testing for this symbol ">"?

  • is greater than
  • is above
  • is higher than
  • is longer than
  • is bigger than
  • is increased
• What are some common phrases for hypothesis testing for this symbol "<"?

  • is less than
  • is below
  • is lower than
  • is shorter than
  • is smaller than
  • is decreased
• What are some common phrases for hypothesis testing for this symbol "≥"?


  • is greater than or equal to
  • is at least
  • is not less than
• What are some common phrases for hypothesis testing for this symbol "≤"?

  • is less than or equal to
  • is at most
  • is not more than
• What are some common phrases for hypothesis testing for this symbol "="?



  • is equal to
  • is exactly the same as
  • has not changed from
• What are some common phrases for hypothesis testing for this symbol "≠"?



  • is not equal to
  • is different from
  • has changed from
  • is not the same as
• What are the two possible errors in decision making when testing a statistical hypothesis?

  Type I error (α) and Type II error (β)
• Type I error


  It is 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.
• Type I error


  What type of error is shown in this situation? Let's say a medical researcher is conducting a clinical trial to test a new drug's effectiveness in treating a certain disease.

  
  

  Ho: The drug has no effect, meaning there is no difference between the treatment group (given the drug) and the control group (given a placebo).

  
  

  Decision: The researcher concludes that there is a significant difference between the treatment group and the control group.
•  Type II error


  It is 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.
• Type II error


  What type of error is shown in this situation? For example, a company manufacturing light bulbs claims that their bulbs have an average lifespan of 1000 hours. A consumer protection agency wants to test this claim and conducts a hypothesis test.

  
  

  Ho: The average lifespan of the bulbs produced by the

  company is indeed 1000 hours.

  
  

  Now, suppose that in reality, the average lifespan of the

  bulbs is not 1000 hours but is actually lower, let's say 900

  hours.
• Type II error leads to a false conclusion that the null hypothesis is true when it is actually false. 
• Level of Significance


  It is the probability of committing a Type I error.
• Level of Significance


  This is denoted by the Greek letter alpha (α).
• The probability of committing a Type II error, denoted by beta (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.
• If the null hypothesis is rejected, the

  probability of a type I error will be 10%, 5% or 1%, and the probability of a correct decision will be 90%, 95%, or 99%, depending on which level of significance is used.
• A 0.05 or 5% level of significance is chosen in designating a test of hypothesis, then there are about 5 chances in 100 that we would reject the hypothesis when it should be accepted. We are about 95% confident that we made the right decision.