Question

J. Kahl and R. White. 2004.

Identify theory leading to hypotheses

how did they test their hypotheses

summarize results-were hypotheses supported?

what is the key takeaway from the research paper? whatwas learned and what are the potential ramitifications for the tax profession?

Answer 1

Theory of Hypothesis:

Hypothesis Testing is a method of statistical inference. It is used to test if a statement regarding a population parameter is statistically significant. Hypothesis testing is a powerful tool for testing the power of predictions. A Financial Analyst, for example, might want to make a prediction of the mean value a customer would pay for her firm’s product. She can then formulate a hypothesis, for example, “The average value that customers will pay for my product is larger than $5”. To statistically test this question, the firm owner could use hypothesis testing. This example is further explored down below.

Hypothesis Testing is a critical part of the scientific method, which is a systematic approach of assessing theories through observation. A good theory is one that can make accurate predictions. For an Analyst who makes predictions, hypothesis testing is a rigorous way of backing up his prediction with statistical analysis.

Steps In Hypothesis Testing:

Here are the steps for hypothesis testing:

1. State the null hypothesis (H₀) and alternative hypothesis (H_a).
2. Consider the Statistical assumptions being made. Evaluate if these assumptions are coherent with the underlying population being evaluated. For example, is assuming the underlying distribution as a normal distribution sensible?
3. Determine the appropriate probability distribution and select the appropriate test statistic.
4. Select the Significance Level commonly denoted by the greek letter alpha (α), this is the probability threshold for which the null hypothesis will be rejected.
5. Based on the significance level and on the the appropriate test, state the decision rule.
6. Collect the observed sample data, and use it to calculate the test statistic
7. Based on your results you should either reject the null hypothesis, or fail to reject the null hypothesis. This is known as the statistical decision.
8. Consider any other economic issues that are applied to the problem. These are non-statistical considerations that need to be considered for a decision. For example, sometimes societal cultural shifts lead to changes in consumer behaviour, this must be taken in consideration in addition to the statistical decision for a final decision.

Summarization of results of Hypothesis:

There are two types of possible errors in hypothesis testing.

The binary nature of our decision, to reject or fail to reject the null hypothesis, gives rise to two possible errors. The table below illustrates all of the possible outcomes. A Type I Error arises when a true Null Hypothesis is rejected. The probability of making a Type I Error is also known as the level of significance of the test, which is commonly referred to as alpha (α). So, for example, if a test that has its alpha set as 0.01, there is a 1% probability of rejecting a true null hypothesis or a 1% probability of making a Type I Error.

A Type II Error arises when you fail to reject a False Null Hypothesis. The probability of making a Type II Error is commonly denoted by the greek letter beta (β). β is used to define the Power of a Test, which is the Probability of correctly rejecting a false null hypothesis. The Power of a Test is defined as 1-β. A test with more Power is more desirable, as there is a lower probability of making a Type II Error. However there is a tradeoff between the probability of making a Type I Error and the probability of making a Type II Error.

True Case Decision Ho True H. False Do not reject Ho Correct Decision Wrong Decision TYPE II ERROR Reject Ho Wrong Decision TYPE I ERROR Correct Decision

Key Takeways :

• Hypothesis testing is used to infer the result of a hypothesis performed on sample data from a larger population.
• The test tells the analyst whether or not his primary hypothesis is true.
• Statistical analysts test a hypothesis by measuring and examining a random sample of the population being analysed.