Recall back : Parametric and Nonparametric

Transcription

1 Recall back : Parametric and Nonparametric Parametric tests are based on assumptions about the distribution of the underlying population from which the sample was taken. The most common parametric assumption is that data are approximately normally distributed. Nonparametric tests do not rely on assumptions about the shape or parameters of the underlying population distribution. If the data deviate strongly from the assumptions of a parametric procedure, using the parametric procedure could lead to incorrect conclusions.

2 Recall back : Parametric and Nonparametric We should be aware of the assumptions associated with a parametric procedure and should learn methods to evaluate the validity of those assumptions. If we determine that the assumptions of the parametric procedure are not valid, use an analogous nonparametric procedure instead. Nonparametric methods were developed to be used in cases when we know nothing about the parameters of the variable of interest in the population (hence the name nonparametric).

3 Why Nonparametric? In more technical terms, this methods do not rely on the estimation of parameters (such as the mean or the standard deviation) describing the distribution of the variable of interest in the population. Two types of statistical procedures treated as nonparametric truly nonparametric procedures not concerned with population parameters distribution free procedures does not depend on the functional form of the population from which the sample has been drawn.

4 Goal Compare one group to one hypothetical value Compare two independent groups Compare two paired groups Binomial (Two Possible Outcomes) Parametric test Nonparametric test Sign Test Student s t-test Sign test Fisher's test McNemar's test Independent sample t-test Paired sample t-test Mann-Whitney U test Wilcoxon Sign Rank test Compare three or more independent groups Chi-square test One-way ANOVA Kruskal-Wallis test

5 Hypothesis-Testing Step 1 State the hypothesis, and identify the claim. Step 2 Based on 5% significance level, make a decision to reject or fail to reject the null hypothesis Reject null hypothesis if p-value Where, is significance level Type of test One tailed test Two tailed test p-value Sig.( two tailed ) 2 Sig.( two tailed ) 5

6 One sample t-test One sample t-test procedure tests whether the mean of a single variable differs from a specified constant. Data Considerations Data: The data should be at the interval or ratio level of measurement (quantitative variable). Assumptions: This test assumes that the data are randomly selected and normally distributed; however, this test is fairly robust to departures from normality.

7 One sample t-test via SPSS Select one or more variables to be tested against the same hypothesized value. Enter a numeric test value against which each sample mean is compared. Optionally, you can click Options to control the treatment of missing data and the level of the confidence interval. Step 1 : Select Analyze Menu Select Compare Means Click on One-samples T-test.

8 Step 2 : Click on appropriate Variable Click on the ARROW button into Test Variable(s) box. Step 3 : In Test Value box : type the value, e.g : 3 Step 4 : Click on OK. Step 2 Step 3 Step 4

9 Independent Sample t-test via SPSS The Independent samples t-test procedure compares means for two groups of cases. Ideally, for this test, the subjects should be randomly assigned to two groups Data Considerations Data : The data should be at the interval or ratio level of measurement (quantitative variable). The values of the quantitative variable of interest are in a single column in the data file. The procedure uses a grouping variable with two values to separate the cases into two groups. The grouping variable can be numeric (values such as 1 and 2, or 6.25 and 12.5) or short string (such as yes and no). Assumptions : This test assumes that the data are randomly selected, normally distributed, independence of groups, and homogeneity of variance. Step 1 : Select Analyze Menu Select Compare Means Click on Independent-samples T-test.

10 Step 2 : Click on the appropriate variable Click on the ARROW button into Test Variable box. Step 3 : Click on the appropriate variable Click on the ARROW button into Grouping Variable box. Step 4 : Click on Define Group Click on Continue Click on OK. Step 2 Step 4 Step 3 Step 4

11 Paired sample t-test via SPSS The Paired samples t-test procedure compares the means of two variables for a single group. It computes the differences between values of the two variables for each case and tests whether the average differs from 0. Data Considerations Data : For each paired test, specify two quantitative variables (interval or ratio level of measurement). For a matched-pairs or case-control study, the response for each test subject and its matched control subject must be in the same case in the data file Assumptions : Observations for each pair should be made under the same conditions. The mean differences should be normally distributed. Variances of each variable can be equal or unequal.

12 Step 1 : Select Analyze Menu Select Compare Means Click on Paired samples T-test. Step 2 : Clik on Both Variable Click on the ARROW button into Paired Variable box. Step 3 : Click on OK. Step 2 Step 3

13 One-Way ANOVA via SPSS One-Way ANOVA procedure produces a one-way analysis of variance for a quantitative dependent variable by a single factor (independent) variable. ANOVA is used to test the hypothesis that several means are equal. This technique is an extension of the independent sample t-test. In addition to determining that differences exist among the means, you may want to know which means differ.

14 Data Considerations Data : Factor variable (treatment variable) values should be integers, and the dependent variable should be quantitative (interval level of measurement). Assumptions : Each group is an independent random sample from a normal population. Analysis of variance is robust to departures from normality, although the data should be symmetric. The groups should come from populations with equal variances. To test this assumption, use Levene's homogeneity-of-variance test.

15 Step 1 : Select Analyze Menu Select Compare Means Click on One-way ANOVA. Step 2 : Click on the appropriate Variable Click on the ARROW button into Dependent List box. Step 3 : Click on the appropriate Variable Click on the ARROW button into Factor box. Step 4 : Click on OK. Step 2 Step 4 Step 3

16 Step 1 : If you need to do a further analysis, Click on Post Hoc. Step 2 : Select the appropriate statistics, eg : Bonferroni. Step 3 : Click on Continue. Step 2 Step 3

17 Nonparametric via SPSS Independent Sample : Wilcoxon Rank Sum Test/ Mann Withney U Test Analyze Nonparametric Test 2 Independent Samples Paired Sample : Wilcoxon Sign Rank Test Analyze Nonparametric Test 2 Related Samples More Than 2 Independent Sample : Kruskal Wallis Test Analyze Nonparametric Test K Independent Samples

18 Hands on : Perform Univariate Statistics via SPSS