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USING UNIVARIATE STATISTICAL ANALYSIS IN BUSINESS RESEARCH

USING UNIVARIATE STATISTICAL ANALYSIS IN BUSINESS RESEARCH. Hypothesis Testing . Classification of Univariate Methods. H ow can we get benefit from hypothesis tests?.

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USING UNIVARIATE STATISTICAL ANALYSIS IN BUSINESS RESEARCH

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  1. USING UNIVARIATE STATISTICAL ANALYSIS IN BUSINESS RESEARCH

  2. Hypothesis Testing

  3. Classification of Univariate Methods

  4. How can we get benefit from hypothesis tests?

  5. Let us assume that Ankara municipality decided not to allow the backers to produce bread under 300 grams. Later somebody has started to complain that X backer is producing bread under 300 grams. What should we do?

  6. No of course We took 100 breads as an example and weighted them. The average was 295 grams and the standard deviation was 3.45 grams. Is it enough to make a decision?

  7. Why? Because it is not scientific to make a decision by looking to the descriptive statistical indicators. So, what should we do? It is necessary to get advantages of hypothesis techniques.

  8. Stages of Hypothesis Testing

  9. Step 1: Formulate the hypothesis Formulate the null and alternative hypotheses. A null hypothesis H0is a statement of the status quo, one of no difference or no effect. If the null hypothesis is not rejected, no changes will be made.

  10. An alternative hypothesis H1is one in which some difference or effect is expected. Accepting the alternative hypothesis will lead to changes in opinions or actions. Thus, the alternative hypothesis is the opposite of the null hypothesis. A statistical test can have one of two outcomes: that the null hypothesis is rejected and the alternative hypothesis accepted, or that the null hypothesis is accepted and the alternative hypothesis is rejected.

  11. One-tailed test A test of the null hypothesis where the alternative hypothesis is expressed directionally. H1: μ >300 grs or H1: μ< 300 Two-tailed test A test of the null hypothesis where the alternative hypothesis is not expressed directionally. H1: μ1≠ μ2

  12. Reject Accept Accept Reject Reject Accept

  13. Step 2: Select an appropriate statistical technique To test the null hypothesis, it is necessary to select an appropriate statistical technique. The researcher should take into consideration how the test statistic is computed and the sampling distribution that the sample statistic (e.g. the mean) follows. The test statistic measures how close the sample has come to the null hypothesis.

  14. If the sample size is n>30 and the population variants is known z test will be applied. If the sample size is n>30 and the population variants is known z test will be applied.

  15. Step 3: Choose the level of significance Whenever we draw inferences about a population, there is a risk that an incorrect conclusion will be reached. Two types of error can occur.

  16. Type I error An error that occurs when the sample results lead to the rejection of a null hypothesis that is in fact true. Also called alpha error (α). Level of significance The probability of making a type I error. Type II error An error that occurs when the sample results lead to acceptance of a null hypothesis that is in fact false. Also called beta error (β)

  17. α: 0.01 High significance Degree of Freedom α: 0.05 medium significance Degree of Freedom α: 0.10 Low significance Degree of Freedom

  18. Step 4: Collect the data and calculate the test statistic Sample size is determined after taking into account the desired αand βerrors and other qualitative considerations, such as budget constraints. Then the required data are collected and the value of the test statistic is computed.

  19. Look at P 569

  20. Alternatively, the critical value of z, which will give an area to the right side of the critical value of 0.05, is between 1.64 and 1.65 and equals 1.645. Note that, in determining the critical value of the test statistic, the area to the right of the critical value is either α or α/2. It is α for a one-tailed test and α/2 for a two-tailed test.

  21. Steps 6 and 7: Compare the probability or critical values and make the decision If calculated z or t value is < Table value H0 accepted H1 rejected If Calculated z or t value is > Table value H0 rejected H1 accepted

  22. Calculation of Hypothesis Parametric Non-Parametric With Averages With Percentages N is not Known N is known

  23. Parametric Tests One population Two populations

  24. Parametric, Average and one population H0:  = 0 H1: 0 H0:  = 0 H1: 0 H0:  = 0 H1: 0 Claimed average

  25. Example 1 A pharmaceutical company produces pain relief pills. This company is claiming that its pills relief the pain in shorter time than the others. A consumer association attempt to test this claim. They applied the drug on 100 persons and saw that the pain had gone averagely in 28 minutes. The standard deviation of this average was found to be 10 minutes. Whereas, other pain relievers, headache known as troubleshooting time is 30 minutes. How this association has met the claims of this company? Test level is 0.01

  26. H0 accepted, H1 rejected This means that the claim of the firm is not true

  27. At which level of confidence the average of 28 minute can be acceptable? Z Table can be used. The value 2 against 00 is enough to find the ratio of 0.9772. 1-0.977= 0.023 is level of this confidence.

  28. Example 2 A battery producer claimed in one of his ad that his product Is longer than the other brands. Upon a complaint done by the competitors a research designed to test the claim. 25 batteries were bought randomly from different markets. The average weights was 17 minutes and the standard deviation 3 minutes while the average of other brands is 15 minutes. Is the producer right or wrong? Test it by using the level of 0.05

  29. To find the table value degree of freedom should be calculated. Degree of freedom is n-1. Therefore df is 25-1=24. If the significant level is 0.05 so table value is 1.71 Because the calculated value is biggest than the table value, H0 is rejected and H1 is accepted. In another words, the claim of the producer is right.

  30. Parametric, Average and two populations It is important to learn whether two samples which chosen from different population are similar or not. For example: Is the average wage different between two cities? N1 N2 n2 n1

  31. Example A firm has two different sale regions and wants to know whether the average weekly sales are equal or not. Two samples were drawn from these two areas. The average sales and standard deviations are as follows:

  32. Because the H1 is inequality so the test will be two tailed. In this case 0.05/2=0.025 To find the table value: 1-0.025=0.975 from the table 1.96

  33. Because the calculated value (1.93) is smaller than table value 1.96 H0 will be accepted and H1 will be rejected. In another words the average sale is similar in both regions.

  34. Example A tissue producer MELTEM advertised his products as the best absorber tissue in the market. The competitor of this firm NAZIK asked a research firm to test this claim then the research firm selected 20 packages of MELTEM and 30 packages of NAZIK from a market and tested them. How can we design the problem?

  35. Because the H1 is and there are two populations so the test will be left tailed and the df will be n1+n2-2= 20+30-2=48. If the significant level is 0.01 the table value will be: 2.41

  36. Because the calculated value (2.41) is bıgger than table value 2.77 H0 will be rejected and H1 will be accepted. In another words the tıssue of Meltem is absorbing more than Nazik.

  37. Parametric, Ratio with one population It is every time possible to find the arithmetical means and the standard deviation of the population. Ratio test is the best way to avoid this obstacle. This formula can be used. Here P0 represents the common opinion. P0+q0=1 The occurrence of an event+An event not to happened=1

  38. SEHER is a company which produces soap. It’s market share was 15%. After a comprehensive new advertising campaign, the company wanted to measure it’s market share. In a survey conducted on 1,000 people, 155 people have been determined to use the SEHER brand of soap. Is this campaign successful?

  39. H0: P0 = .15 (Thenew market share is still %15) H1: P0 .15 (Thenew market share is morethan%15) Z = 0.443 This is a Right-tail test at a 0.05 significance level. (1-0.05 =) 0.95 the table value is 1.65. Because the calculated value is smaller than the table value we will accept H0and reject H1. In another words the "market share (still) is 15%”.

  40. Parametric, Ratio with two independent population

  41. A research has done on Kazakh and Azerbaijani youth people on the clothing habits. Jeans wear rates shown in the table. Is there a difference between the rates of two of the country's young people wearing jeans?

  42. P1: The rate of wearingjeans of Kazak Youth P2: The rate of wearingjeans of Azeri Youth H0: P1 = P2 H1: P1 P2

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