Week 8 Statistical Test Part 1 PDF

Bioepidemiology Hypothesis, hypothesis! Paano ka tinest? Hanzel Tolentino, RMT, MPHc Faculty, College of Medical Laboratory Science Adviser, Medical Technology Innovative Society  Research...

Bioepidemiology Hypothesis, hypothesis! Paano ka tinest? Hanzel Tolentino, RMT, MPHc Faculty, College of Medical Laboratory Science Adviser, Medical Technology Innovative Society  Research Research process: Qualitative Quantitative 1. Epidemiology 1. Type of Statistics: Both but more on 2. Hypothesis Testing Descriptive Statistics 3. Type of Statistics: Both; Descriptive then 2. Description of data through Graphs Inferential Statistics 3. Summarization of data: Central Tendency Variation 4. Presentation of data:  Choosing the statistical test (parametric) Type of data 1. 2. Chi-square family T-test family 3. Correlation family Categorical Continuous Purpose Comparison Relationship Biostatics and epidemiology  Choosing the statistical test (parametric) Type of data 1. 2. Chi-square family T-test family 3. Correlation family Categorical Continuous Purpose Comparison Relationship Biostatics and epidemiology  Choosing the statistical test (parametric) Type of data 1. 2. Chi-square family T-test family 3. Correlation family Categorical Continuous Purpose Comparison Relationship Biostatics and epidemiology  t-Test Chi-Squared (requires identification of Correlation groups) 1 group 1-sample t-test Parametric Chi-squared test 2 group 2-sample unpaired t-test 2-sample paired t-test Person’s correlation Regression test 3+ group One-way ANOVA 1 group non- 1-sample Wilcoxon signed rank test parametric 2 group Spearman’s correlation Chi-squared test Wilcoxon Regression Mann Whitney test 3+ group Kruskal-Wallis test Biostatics and epidemiology Statistical Hypothesis Testing  t-Test Chi-Squared (requires identification of Correlation groups) 1 group 1-sample t-test Parametric Chi-squared test 2 group 2-sample unpaired t-test 2-sample paired t-test Person’s correlation Regression test 3+ group One-way ANOVA 1 group non- 1-sample Wilcoxon signed rank test parametric 2 group Spearman’s correlation Chi-squared test Wilcoxon Regression Mann Whitney test 3+ group Kruskal-Wallis test Biostatics and epidemiology Statistical Tests Part 1 Parametric (two sample means)  Use if n1 ≥30 and n2 ≥30 For Testing a Population Mean to compare the sample mean to the z test population mean. Test whether the average height of a sample of people is significantly different from the known population average height.  Suppose you know the average z test height of adults in a country is 170 cm with a standard deviation of 6 example cm. You take a sample of 50 adults and find the mean height is 172 1 cm. You want to know if this difference significant. is statistically  You want to test if there is a z test significant difference in average exam scores between two example different sections with 39 students each 2 Example #3: o Protoporphyrin levels were measured in two sample subjects. Sample 1 consisted of 35 adult male alcoholics with ring sideroblast 35 45 in the bone marrow. Sample 2 consisted of 40 apparently healthy adult non-alcoholic males. o Is there a significant difference between the protoporphyrin levels in the alcoholic population and non-alcoholic population? Given the gathered data. Using 1% level of significance. Example #3: 1. Formulate the Null (Ho) hypothesis and H0 - There is no significant difference Alternative (Ha) hypothesis. between the protoporphyrin levels in 2. Select the level of Significance (α). the alcoholic population and non- alcoholic population. 3. Determine the test statistic to be used. 4. Define the Area of Rejection. Ha - There is a significant difference between the protoporphyrin levels in 5. Compute for the values of the Statistical Test. the alcoholic population and non- alcoholic population. 6. Draw conclusion.  Ha - There is a significant difference between Example #3: the protoporphyrin levels in the alcoholic population and non-alcoholic population. 1. Formulate the Null (Ho) hypothesis and α: 1% or 0.01 Alternative (Ha) hypothesis. Tail: 2 tailed test 2. Select the level of Significance (α). Statistical test: z test 3. Determine the test statistic to be used. Critical Value: ±2.58 4. Define the Area of Rejection. Area of Rejection: 5. Compute for the values of the Statistical Test. AREA OF ACCEPTANCE 6. Draw conclusion. z test critical value Example #3: 1. Formulate the Null (Ho) hypothesis and Alternative (Ha) hypothesis. 2. Select the level of Significance (α). 3. Determine the test statistic to be used. 4. Define the Area of Rejection. 5. Compute for the values of the Statistical Test. 6. Draw conclusion. Example #3: 1. Formulate the Null (Ho) hypothesis and Alternative (Ha) hypothesis. 2. Select the level of Significance (α). 1.36 3. Determine the test statistic to be used. AREA OF ACCEPTANCE 4. Define the Area of Rejection. 5. Compute for the values of the Statistical Decision: Accept Ho Test. Remarks: There is no significant difference 6. Draw conclusion. between the protoporphyrin levels in the alcoholic population and non-alcoholic population. Example #4: 1. Formulate the Null (Ho) hypothesis and Alternative (Ha) hypothesis. Do the “z test E2” 2. Select the level of Significance (α). 3. Determine the test statistic to be used. 4. Define the Area of Rejection. 5. Compute for the values of the Statistical Test. 6. Draw conclusion. 20 81 SE A teacher claims that the mean score of students in his class is greater than 82 with a standard deviation of 20. If a sample of 81 students was selected with a mean score of 90 then check if there is enough evidence to support this claim at a 0.05 significance level.  1%, two tail Practice Compute for the Z test: Sample mean Population Population SD Sample size mean 46 34 20 123 57 67 10 354 89 45 5 456 45 34 10 123 23 23 20 345  t-Test Chi-Squared (requires identification of Correlation groups) 1 group 1-sample t-test Parametric Chi-squared test 2 group 2-sample unpaired t-test 2-sample paired t-test Person’s correlation Regression test 3+ group One-way ANOVA 1 group non- 1-sample Wilcoxon signed rank test parametric 2 group Spearman’s correlation Chi-squared test Wilcoxon Regression Mann Whitney test 3+ group Kruskal-Wallis test Biostatics and epidemiology  It is a parametric test used to test significant difference of small sample size. t test Paired t-test Independent t-test For comparison e.g.: height of males compared to height of females Use if data is categorical and/or continuous  Sample Size: useful for small sample sizes (typically under 30) but can also be applied to larger samples. Unknown Population Variance: Unlike the t test Z-test, which requires the population variance to be known, the t-test is used when the population variance is unknown and is estimated from the sample data. Assumption of Normality: The data should be approximately normally distributed, especially for small sample sizes  Paired t-test Independent t-test Determine whether the mean of A T-test asks whether a the differences between two difference between two groups’ paired samples differs from 0 (or averages is unlikely to have a target value) occurred because of random to compare the means from the chance in sample selection. same group at two different to compare the means of two times (for example, before and independent groups to after a treatment in a medical determine if there is a study) or under two different statistically significant difference conditions. It's useful for before- between them. For example,: and-after measurements or comparing the test scores of matched pairs. students from two different schools.  Comparing the effects of two t test different teaching methods on performance of two groups with 11 example students each. 1  Comparing the effect of a medical t test intervention on the same group of patients before and after the example treatment. 2  Checking whether the mean t test diameter of manufactured 24 ball bearings differs significantly from example the engineering specification 3 Example #4: Example #4: 1. Formulate the Null (Ho) hypothesis and H0 - There is no significant difference Alternative (Ha) hypothesis. between pretest and post test 2. Select the level of Significance (α). 3. Determine the test statistic to be used. Ha - There is a significant difference between pretest and post test 4. Define the Area of Rejection. 5. Compute for the values of the Statistical Test. 6. Draw conclusion.  Ha - There is a significant difference Example #4: between pretest and post test 1. Formulate the Null (Ho) hypothesis and α: 5% or 0.05 Alternative (Ha) hypothesis. Tail: two tailed test 2. Select the level of Significance (α). Statistical test: Paired T test 3. Determine the test statistic to be used. Critical Value: +/- 2.093 4. Define the Area of Rejection. Area of Rejection: 5. Compute for the values of the Statistical Test. AREA OF ACCEPTANCE 6. Draw conclusion. -2.093 2.093 t test critical value Paired t-test odf = n – 1 owhere n is the number of paired observations Independent/unpaired t-test odf = n1 + n2 – 2 owhere n1 and n2 are the sizes of the two samples Example #4: 1. Formulate the Null (Ho) hypothesis and Alternative (Ha) hypothesis. 2. Select the level of Significance (α). 3. Determine the test statistic to be used. 4. Define the Area of Rejection. 5. Compute for the values of the Statistical Test. 6. Draw conclusion. Example #4: 1. Formulate the Null (Ho) hypothesis and Alternative (Ha) hypothesis. 2. Select the level of Significance (α). 3.23 3. Determine the test statistic to be used. AREA OF ACCEPTANCE 4. Define the Area of Rejection. -2.093 2.093 5. Compute for the values of the Statistical Test. Decision: Reject Ho Remarks: There is a significant difference 6. Draw conclusion. between pretest and post test Example #5: Example #5: 1. Formulate the Null (Ho) hypothesis and H0 - There is no significant difference Alternative (Ha) hypothesis. between the two group. 2. Select the level of Significance (α). 3. Determine the test statistic to be used. Ha - There is a significant difference between the two group. 4. Define the Area of Rejection. 5. Compute for the values of the Statistical Test. 6. Draw conclusion. Example #5: 1. Formulate the Null (Ho) hypothesis and α: 1% or 0.01 Alternative (Ha) hypothesis. Tail: 2 tailed test 2. Select the level of Significance (α). Statistical test: Unpaired/Independent T test 3. Determine the test statistic to be used. Critical Value: ±2.845 4. Define the Area of Rejection. Area of Rejection: 5. Compute for the values of the Statistical Test. AREA OF ACCEPTANCE 6. Draw conclusion. -2.845 2.845 t test critical value Paired t-test odf = n – 1 owhere n is the number of paired observations Independent/unpaired t-test odf = n1 + n2 – 2 owhere n1 and n2 are the sizes of the two samples Example #5: 1. Formulate the Null (Ho) hypothesis and Alternative (Ha) hypothesis. 2. Select the level of Significance (α). 3. Determine the test statistic to be used. 4. Define the Area of Rejection. 5. Compute for the values of the Statistical Test. 6. Draw conclusion. Example #5: 1. Formulate the Null (Ho) hypothesis and Alternative (Ha) hypothesis. 2. Select the level of Significance (α). 3. Determine the test statistic to be used. -3.19 AREA OF ACCEPTANCE 4. Define the Area of Rejection. -2.845 2.845 5. Compute for the values of the Statistical Test. Decision: Reject Ho Remarks: There is a significant difference 6. Draw conclusion. between the two group. MANiFESTATiONS? CREDITS: This presentation template was created by Slidesgo, and includes icons by Flaticon, and infographics & images by Freepik