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# Parametric Statistical Tool to Test Hypothesis

Research Methodology
by Randolph Reyes

by

Tweet## Randolph Reyes

on 18 February 2011#### Transcript of Parametric Statistical Tool to Test Hypothesis

Parametric Statistical Tool to Test Hypothesis What is parametric? also called conventional statistical procedures

use to test hypothesis with nominal and ordinal value

a sample statistic is obtained to estimate the population parameter

estimation process involves a sample , a sampling distribution, and a population "One finds the truth by making a hypothesis." David Douglas

Physicist at the University of Rochester 6-step hypothesis testing procedure 1. State the null hypothesis

2. Choose the statistical test

3. Select the desired level of significance

4. Compute the calculated difference value

5. Obtain the critical test

6. Interpret the test Selecting Tests using the Choice Criteria Recommended Statistical Techniques by Measurement Level and Testing Situation Measurement

Scale Parametric Test

+ places emphasis on the importance of assumptions

+ date are derived from interval and ratio measurements

+ observations are independent

+ sample data have a normal distribution The T-Test used to determine the special significance between a simple distribution mean and a parameter sample mean specified value to be tested sample standard deviation size of the sample NULL HYPOTHESIS ALTERNATIVE HYPOTHESIS First, compute the sample mean and standard deviation Second, compute the t-value A professor wants to know if her introductory statistics class has a good grasp of basic math. Six students are chosen at random from the class and given a math proficiency test. The professor wants the class to be able to score at least 70 on the test. The six students get scores of 62, 92, 75, 68, 83, and 95. Can the professor at least 90 percent certain that the mean score for the class on the test would be at least 70? by Randolph Reyes

MS Advertising Two sample test Nominal Ordinal Interval

&

Ratio TWO SAMPLE TEST Related Sample Independent Sample Mc Nemar Sign Test Wilcoxon matched-pairs

test T-Test for paired samples Fisher exact test x2 two-sample test median test Mann-Whitney U T-Test Z-Test Two-Independent Sample Test + The need to use two-independent sample test is often encountered in business research

+ Samples are independent if the response of the nth person in the second sample is not a funcion of the response of the nth person in the first sample

+ Independent sample are also called uncorrelated samples and unrelated samples

+ Samples which are NOT independent include before-after and panel studies of the same people, or matched-pairs studies of similar people T-Test formula When does Z-test used? used with large sizes (exceeding 30 for both independent samples) When does T-test used? appropriate with small sizes, normally distributed populations, and the assumption of equal population variances Z-Test formula the difference between the two population is associated with the pooled variance estimate PROBLEM Consider a problem might face a manager at KDL, a media firm that is evaluating account executive trainees. The manager wishes to test the effectiveness of two methods for training new account executives. The company selects 22 trainees, who are randomly divided into two experimental groups. One receives type A and the other type B training. The trainees are then assigned and managed without regard to the training they have received. At the year's end, the manager reviews the performances of the employees in these groups and finds the following results: Determine whether one training method is superior to the other: 1. Null hypothesis Ho: There is no difference in sales results produced by the two training methods

Ha: Training method A produces sales results superior to those of method B 2. Statistical test The T-Test is chosen because the data are at least interval and the samples are independent 3. Significance level a= .05 (one-tailed test) 5. Critical test value d.f.= 20, one-tailed test, a= .05

The critical value is 1.725 6. Interpretation Since the calculated value is higher taht the critical value (1.97>1.725), reject the nul hypothesis and conclude that training method A is superior Difference between Parametric and Non Parametric? A potential source of confusion in working out what statistics to use in analysing data is whether your data allows for parametric or non-parametric statistics.

The importance of this issue cannot be underestimated!

If you get it wrong you risk using an incorrect statistical procedure or you may use a less powerful procedure.

Non-paramteric statistical procedures are less powerful because they use less information in their calulation. For example, a parametric correlation uses information about the mean and deviation from the mean while a non-parametric correlation will use only the ordinal position of pairs of scores.

The basic distinction for paramteric versus non-parametric is:

If your measurement scale is nominal or ordinal then you use non-parametric statistics

If you are using interval or ratio scales you use parametric statistics.

Full transcriptuse to test hypothesis with nominal and ordinal value

a sample statistic is obtained to estimate the population parameter

estimation process involves a sample , a sampling distribution, and a population "One finds the truth by making a hypothesis." David Douglas

Physicist at the University of Rochester 6-step hypothesis testing procedure 1. State the null hypothesis

2. Choose the statistical test

3. Select the desired level of significance

4. Compute the calculated difference value

5. Obtain the critical test

6. Interpret the test Selecting Tests using the Choice Criteria Recommended Statistical Techniques by Measurement Level and Testing Situation Measurement

Scale Parametric Test

+ places emphasis on the importance of assumptions

+ date are derived from interval and ratio measurements

+ observations are independent

+ sample data have a normal distribution The T-Test used to determine the special significance between a simple distribution mean and a parameter sample mean specified value to be tested sample standard deviation size of the sample NULL HYPOTHESIS ALTERNATIVE HYPOTHESIS First, compute the sample mean and standard deviation Second, compute the t-value A professor wants to know if her introductory statistics class has a good grasp of basic math. Six students are chosen at random from the class and given a math proficiency test. The professor wants the class to be able to score at least 70 on the test. The six students get scores of 62, 92, 75, 68, 83, and 95. Can the professor at least 90 percent certain that the mean score for the class on the test would be at least 70? by Randolph Reyes

MS Advertising Two sample test Nominal Ordinal Interval

&

Ratio TWO SAMPLE TEST Related Sample Independent Sample Mc Nemar Sign Test Wilcoxon matched-pairs

test T-Test for paired samples Fisher exact test x2 two-sample test median test Mann-Whitney U T-Test Z-Test Two-Independent Sample Test + The need to use two-independent sample test is often encountered in business research

+ Samples are independent if the response of the nth person in the second sample is not a funcion of the response of the nth person in the first sample

+ Independent sample are also called uncorrelated samples and unrelated samples

+ Samples which are NOT independent include before-after and panel studies of the same people, or matched-pairs studies of similar people T-Test formula When does Z-test used? used with large sizes (exceeding 30 for both independent samples) When does T-test used? appropriate with small sizes, normally distributed populations, and the assumption of equal population variances Z-Test formula the difference between the two population is associated with the pooled variance estimate PROBLEM Consider a problem might face a manager at KDL, a media firm that is evaluating account executive trainees. The manager wishes to test the effectiveness of two methods for training new account executives. The company selects 22 trainees, who are randomly divided into two experimental groups. One receives type A and the other type B training. The trainees are then assigned and managed without regard to the training they have received. At the year's end, the manager reviews the performances of the employees in these groups and finds the following results: Determine whether one training method is superior to the other: 1. Null hypothesis Ho: There is no difference in sales results produced by the two training methods

Ha: Training method A produces sales results superior to those of method B 2. Statistical test The T-Test is chosen because the data are at least interval and the samples are independent 3. Significance level a= .05 (one-tailed test) 5. Critical test value d.f.= 20, one-tailed test, a= .05

The critical value is 1.725 6. Interpretation Since the calculated value is higher taht the critical value (1.97>1.725), reject the nul hypothesis and conclude that training method A is superior Difference between Parametric and Non Parametric? A potential source of confusion in working out what statistics to use in analysing data is whether your data allows for parametric or non-parametric statistics.

The importance of this issue cannot be underestimated!

If you get it wrong you risk using an incorrect statistical procedure or you may use a less powerful procedure.

Non-paramteric statistical procedures are less powerful because they use less information in their calulation. For example, a parametric correlation uses information about the mean and deviation from the mean while a non-parametric correlation will use only the ordinal position of pairs of scores.

The basic distinction for paramteric versus non-parametric is:

If your measurement scale is nominal or ordinal then you use non-parametric statistics

If you are using interval or ratio scales you use parametric statistics.