Parametric & Non-Parametric Tests PDF

PARAMETRIC & NON-PARAMETRIC TESTS ‘- IAN D. BECOÑADO, MAEd Professor 1 Statistical Tests statistical methods that help reject or not reject our null hypothesis. They’re based on probability ‘- dist...

PARAMETRIC & NON-PARAMETRIC TESTS ‘- IAN D. BECOÑADO, MAEd Professor 1 Statistical Tests statistical methods that help reject or not reject our null hypothesis. They’re based on probability ‘- distributions and can be one-tailed or two-tailed, depending on the hypotheses that the researcher had chosen. Parametric or Non-parametric 2 Parametric Test those statistical tests that assume the data approximately follows a normal distribution, ‘- amongst other assumptions (examples include z- test, t-test, ANOVA). Important note — the assumption is that the data of the whole population follows a normal distribution, not the sample data. 3 Non-parametric Tests are those statistical tests that don’t assume anything about the distribute on followed by the ‘- data, and hence are also known as distribution free tests (examples include Chi-square, Mann-Whitney U). Nonparametric tests are based on the ranks held by different data points. 4  Parametric Test Non-parametric Test Paired T-test Wilcoxon Signed Rank Test ‘- Unpaired T-test Mann-Whitney U Test One way ANOVA Kruskal-Wallis H test Pearson’s Coefficient Spearman’s Coefficient 5 PARAMETRIC ‘- 6 Parametric Test Common parametric tests are focused on analyzing and comparing the mean or variance of data. ‘- The mean is the most commonly used measure of central tendency to describe data, however it is also heavily impacted by outliers. Thus it is important to analyze your data and determine whether the mean is the best way to represent it. 7 Parametric tests have a couple of assumptions that need to be met by the data: Normality Homogeneity of variance ‘- Independence Outliers 8 Normality the sample data come from a population that approximately follows a normal distribution. ‘- 9 Homogeneity of Variance the sample data come from a population with the same variance. ‘- 10 Independence the sample data consists of independent observations and are sampled randomly. ‘- 11 Outliers the sample data don’t contain any extreme outliers. ‘- 12 Outliers the sample data don’t contain any extreme outliers. ‘- 13 DEGREES OF FREEDOM ‘- 14 Degrees of Freedom essentially the number of independent values that can vary in a set of data while measuring statistical ‘- parameters. 15 Degrees of Freedom essentially the number of independent values that can vary in a set of data while measuring statistical ‘- parameters. 16 Let’s say you like to go out every Saturday and you’ve just bought four new outfits. You want to wear a new outfit every weekend of the month. On the first Saturday, all four outfits ‘- are unworn, so you can pick any. The next Saturday you can pick from three and the third Saturday you can pick from two. On the last Saturday of the month though, you’re left with only one outfit and you have to wear it whether you want to or not, whereas on the other Saturdays you had a choice. 17 Comparing Means One-sample (one-sample z-test or a one-sample t-test) ‘- Two-sample (two-sample z-test and a two- sample t-test) 18 One-sample (one-sample z-test or a one- sample t-test): one group will be a sample and the second group will be the population. Basically, comparing a ‘- sample with a standard value from the population. We are basically trying to see if the sample comes from the population, i.e. does it behave differently from the population or not. 19 Two-sample (two-sample z-test and a two- sample t-test): both groups will be separate samples. As in the case of one-sample tests, both samples must be ‘- randomly selected from the population and the observations must be independent of one another. 20 How do we choose between a z-test and a t-test? 1. If the population variance is known and the sample size is large (greater than or equal to 30) — we choose a z-test 2. If the population variance is known and‘-the sample size is small (less than 30) — we can perform either a z-test or a t-test 3. If the population variance is not known and the sample size is small — we choose a t-test 4. If the population variance is not known and the sample size is large — we choose a t-test 21 ‘- 22 T-TEST ‘- 23  T-TEST FOR INDEPENDENT SAMPLES ‘- IAN D. BECOÑADO, MAEd Professor 24 T-TEST FOR INDEPENDENT SAMPLES The T-test is a test of difference between two independent groups. The means are compared 𝑥1 against 𝑥2. ‘- 25 When do we use the T-test for independent samples? When we compare the means of two independent groups. When the data are normally distributed, 𝑆𝑘 = 0 and 𝐾𝑢 = ‘- 0.265. When data are expressed in interval and ratio. When the sample is less than 30. 26 Why do we use the T-test for independent samples? Because it is more powerful test compared with other tests of difference of two independent groups. ‘- 27 The following are the hour Male 𝑥1 Female 𝑥2 per week of the overtime 14 12 of 10 male and 10 female 18 9 nurses in Calbayog Dist. 17 11 Hospital. Test the null 16 5 ‘- hypothesis that there is no 4 10 significant difference 14 3 between the performance 12 7 of male and female nurses 10 2 in their overtime. Use the 9 6 t-test at 0.05 level of 17 13 significance. 28  Solving by the Stepwise Method I. Problem: Is there a significant difference between the performance of ‘- male and female nurses in their overtime? 29  Solving by the Stepwise Method II. Hypotheses: 𝐻0 : There is no significant difference between the ‘- performance of the male and female nurses in their overtime. 𝐻0 : 𝑥1 = 𝑥2 𝐻1: There is a significant difference between the performance of the male and female nurses in their overtime. 𝐻1 : 𝑥1 ≠ 𝑥2 30  Solving by the Stepwise Method III. Level of Significance: 𝛼 = 0.05 𝑑𝑓 = 𝑛1 + 𝑛2 − 2 ‘- = 10 + 10 − 2 = 18 𝑡. 05 = 2.101 tabular value at 0.05. 31 ‘- 32  Solving by the Stepwise Method IV. Statistics: T-test for two independent samples ‘- 33  Solving by the Stepwise Method V. Decision Rule: If the t-computed value is greater than or beyond the t-tabular ‘- / critical value, disconfirm 𝐻0. 34 How do you solve t-test for independent samples using a scientific pocket calculator? 1. Compute the sum of group 1 σ 𝑥1 and group 2 sum σ 𝑥2 2. Determine the number of the observations in group 1, 𝑛1 and group 2, 𝑛2 ‘- 3. Compute the sum of the squares of group 1, σ 𝑥1 2 and sum of the squares of group 2, σ 𝑥2 2. 4. Compute the means of group 1 and group 2. σ 𝑥1 σ 𝑥2 𝑥1 = the mean of group 1; 𝑥2 = the mean of group 2 𝑛1 𝑛2 35 How do you solve t-test for independent samples using a scientific pocket calculator? 5. Compute the 𝑆𝑆1 of group 1 and 𝑆𝑆2 of group 2 σ 𝑥1 2 𝑆𝑆1 = , σ 𝑥1 2 − sum of the squares of group 1 𝑛1 ‘- σ 𝑥2 2 𝑆𝑆2 = , σ 𝑥2 2 − sum of the squares of group 2 𝑛2 36 How do we use the T-test for independent samples? 𝑥1−𝑥2 Use the formula 𝑡 = 𝑆𝑆1+𝑆𝑆2 1 1 + 𝑛1+𝑛2−2 𝑛1 𝑛2 Where: 𝑡 = t-test ‘- 𝑥1 = the mean of group 1 𝑥2 = the mean of group 2 𝑆𝑆1 = the sum of squares of group 1 𝑆𝑆2 = the sum of squares of group 2 𝑛1 = the number of observation in group 1 𝑛2 = the number of observation in group 2 37  Solving by the Stepwise Method VI. Conclusion: Since the t-computed value of 2.88 is greater than the t-tabular value of 2.101 at.05 level of significance with 18 degrees of freedom, the null hypothesis is disconfirmed ‘- in favor of the research hypothesis. This means that there is a significant difference between the performance of the male and the female nurses in their overtime implying that the male nurses performed better than the female nurses considering that the mean/ average score of the male nurses of 13.1 is greater compared to the average score of female nurses of only 7.8. 38  Male 𝑥1 Female 𝑥2 The following are the 25 24 hours per week of the 23 23 overtimes of 10 male staff 27 22 and 10 female staff in a 39 30 ‘- EVMC. Test the null 42 41 hypothesis that there is no 33 30 significant difference 38 38 between the performance 28 25 of male and female staffs in their overtime. 31 33 41 38 39