The Difference Between Alpha and P-Values

In conducting a test of significance or hypothesis test, there are two numbers that are easy to get confused. These numbers are easily confused because they are both numbers between zero and one, and are both probabilities. One number is called the p-value of the test statistic. The other number of interest is the level of significance or alpha. We will examine these two probabilities and determine the difference between them. Alpha Values The number alpha is the threshold value that we measure p-values against. It tells us how extreme observed results must be in order to reject the null hypothesis of a significance test. The value of alpha is associated with the confidence level of our test. The following lists some levels of confidence with their related values of alpha: For results with a 90 percent level of confidence, the value of alpha is 1 — 0.90 0.10.For results with a 95 percent level of confidence, the value of alpha is 1 — 0.95 0.05.For results with a 99 percent level of confidence, the value of alpha is 1 — 0.99 0.01.And in general, for results with a C percent level of confidence, the value of alpha is 1 — C/100. Although in theory and practice many numbers can be used for alpha, the most commonly used is 0.05. The reason for this is both because consensus shows that this level is appropriate in many cases, and historically, it has been accepted as the standard.  However, there are many situations when a smaller value of alpha should be used. There is not a single value of alpha that always determines statistical significance. The alpha value gives us the probability of a type I error. Type I errors occur when we reject a null hypothesis that is actually true. Thus, in the long run, for a test with a level of significance of 0.05 1/20, a true null hypothesis will be rejected one out of every 20 times. P-Values The other number that is part of a test of significance is a p-value. A p-value is also a probability, but it comes from a different source than alpha. Every test statistic has a corresponding probability or p-value. This value is the probability that the observed statistic occurred by chance alone, assuming that the null hypothesis is true. Since there are a number of different test statistics, there are a number of different ways to find a ​p-value. For some cases, we need to know the probability distribution  of the population.​​ The p-value of the test statistic is a way of saying how extreme that statistic is for our sample data. The smaller the p-value, the more unlikely the observed sample. Difference Between P-Value and Alpha To determine if an observed outcome is statistically significant, we compare the values of alpha and the p-value. There are two possibilities that emerge: The p-value is less than or equal to alpha. In this case, we reject the null hypothesis. When this happens, we say that the result is statistically significant. In other words, we are reasonably sure that there is something besides chance alone that gave us an observed sample.The p-value is greater than alpha. In this case, we fail to reject the null hypothesis. When this happens, we say that the result is not statistically significant. In other words, we are reasonably sure that our observed data can be explained by chance alone. The implication of the above is that the smaller the value of alpha is, the more difficult it is to claim that a result is statistically significant. On the other hand, the larger the value of alpha is the easier is it to claim that a result is statistically significant. Coupled with this, however, is the higher probability that what we observed can be attributed to chance.

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Koger Properties, Inc. Free Essays

Facts Before the merger, Michael Goodbread served as an audit partner in Touche Ross. In December 1988, Goodbread bought 400 shares of common stock from Koger Properties, Inc. After the effective year of the merger in 1989, Koger automatically became an audit client of Deloitte Touche instead. We will write a custom essay sample on Koger Properties, Inc. or any similar topic only for you Order Now Also, Goodbread got an identical position in Deloitte Touche in the same year. In the following year, Goodbread was assigned to be an audit engagement partner in association with Koger’s financial statements for the fiscal year which was ended on March 31, 1990. Goodbread was in charge of all facets of Koger audit. Then Goodbread signed the Koger â€Å"audit planning memorandum† on February 21, 1990. Audit planning for the engagement and field work was conducted from that time until June 27, 1990, on which date Goodbread signed the â€Å"audit report record† which was a formal completion of the Koger audit. During the operation, Goodbread sold all his 400 shares of Koger common stock on May 10, 1990. Issues Did Goodbread violate the SEC’s independence rules? 2. Was Goodbread’s equity interest qualified as a material investment? Was it relevant? 3. Under what conditions could Goodbread have later served as the audit engagement partner? Analysis The SEC strongly claimed that Goodbread violated its independence rules because of the following reasons. Rule 2-01(b) of SEC states, â€Å"an accountant will be considered not independent with respect to any person†¦ in which†¦ he, his firm or a member of his firm had, or was committed to acquire, any direct financial interest or any material indirect financial interest†¦ † Clearly, it was a direct financial interest for Goodbread to own 400 shares of Koger common stock in this situation. According to the Code of Professional Conduct, â€Å"Independence shall be considered to be impaired if: During the period of the professional engagement a covered member was committed to acquire any direct or material indirect financial interest in the client (ET  § 101. 1). † In Goodbread’s case, the fact was that he owned 400 shares of Koger common stock which were direct financial interest when he was the audit engagement partner who oversaw the audit of Koger. â€Å"Public confidence would be impaired by evidence that independence was actually lacking, and it might also be impaired by the existence of ircumstances which reasonable people might believe likely to influence independence (SAS  § 220. 03). † An auditor must not only be independent in fact which is related to the evidence that the public have, but must also avoid any actions that may likely seem to influence independence. No matter how many shares of Koger common stock Goodbread owned, it stil l affected his independence. The reason was the public tended to think that Goodbread would maximize his own benefit by unfaithfully making the audit decision for the company. The profession has established, through the AICPA’s Code of Professional Conduct, precepts to guard against the presumption of loss of independence (SAS  § 220. 04). † As an independent auditor, it is important to let the public maintain confidence in order to strength the belief of an audit’s profession. This will all be collapsed after realizing the auditor is holding common stock which is not supposed to. I believe that the investment was a material interest. Common stock has its true existing value knowing as an investment, because it is not just a piece of paper. Having the stock means that the stockholder has the ownership in a specific company. As an auditor, it is unlikely that the public will accept people like Goodbread claimed himself as an independent auditor to audit for the company since he was the one who had the great impact on the audit decisions. Goodbread might not think this way, but the public tended to think he would be biased when he dealt with the financial statements of the company. Therefore, the materiality of this investment was a relevant issue for Goodbread. He really needed to avoid this kind of situation which might lead outsiders to doubt his independence. Goodbread signed the Koger â€Å"audit planning memorandum† on February 21, 1990. It was since that date he had the full responsibility for being independent as an audit of Koger. If Goodbread could sell his 400 shares of Koger common stock before February 21, 1990, there would not be this kind of serious situation happening to him. However, the fact was he did not sell those stocks until May 10, 1990, so he completely lost the ability to be served as an audit engagement partner for the company legally. Conclusion After evaluating the codes and standard, it is not doubtful to see why the SEC took action against Goodbread. The public did not want to believe Goodbread was independent because of his partial ownership in Koger. Goodbread’s Koger ownership must be prohibited during the time of the Koger audit since he did not fully maintain his independence and was not legally responsible for the audit work. The auditor must be honest to claim himself as independent, and he must be away from any interest in the client. How to cite Koger Properties, Inc., Essay examples