Introduction NUMERICAL DATA ANALYSIS. Introduction. Outline for each test. Independent sample t-test INDEPENDENT SAMPLE T-TEST

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1 Introduction NUMERICAL DATA ANALYSIS Univariable Univariate Analysis of Numerical Data (Parametric) Numerical data the outcome is numerical Univariable analysis concern with only 1 independent variable Univariate analysis concern with only 1 dependent variable Parametric normal distribution of the outcome variable Introduction Three most commonly used statistical test in this ; Independent t-test Paired t-test Outline for each test Introduction Assumptions Steps Procedures in SPSS Interpretation and results INDEPENDENT SAMPLE T-TEST Also known as a Student s t-test or a two-sample t-test A parametric test Used to mean of two independent samples when the outcome is continuous and the explanatory (dependent) variable is binary Compares the actual difference between the two means in relation to the variation in the data 1

2 Example in observational studies: Example: A cross sectional study to weight between students sitting in the first and second row. A case control study to HbA1c level between male and female patients Male Mean HbA1c Female Mean HbA1c Example in experimental studies: Comparing characteristics between patients in treatment and control s Intervention Control Steps in analysis Step 1: state hypothesis Step 2: set the significant level Step 5: Interpret and make conclusion Step 1: state hypothesis Null hypothesis There is no difference of weight between students sitting in the front row and the second row Alternative hypothesis There is a difference of weight between students sitting in the front row and the second row Step 2: set the significant level =0.05 The acceptable level in medical and health sciences 2

3 1. Random samples (samples are representative of the population) 2. The s and measurements are independent of each other 3. The outcome (dependent) variable is numerical data (interval or ratio) 4. The outcome variable is normally distributed in each 5. The variance between s is approximately equal (Homogeneity of variances) Male Mean HbA1c Female Mean HbA1c The first three assumptions are determined by the study design The fourth must be checked before analysis. If violated, a non parametric test or data transformation will be needed. If the fifth assumption is violated, adjustment to the t-value will be made. Check normality : statistically and graphically SPSS analyse Descriptive Explore 3

4 Check homogeneity of variance Levene s test Assumption 5: Homogeneity of variance Test statistics. If equal variance assumed, read the upper row. Step 5: Interpret and make conclusion Mean (SD) wound healing among non-smoker = (7.15) Mean (SD) wound healing among smoker = (7.13) t-statistics=-3.00, df=88, P=0.004 Mean difference = % CI of difference =-7.52, Step 5: Interpret and make conclusion Since the 95% CI does not cross 0, the P-value must be significant In this case, P=0.004 Conclusion: Reject null hypothesis 4

5 In text: The difference between mean (SD) of wound healing between non-smokers and smokers was statistically significant [31.29 (7.15) vs (7.13), P=0.004] PAIRED SAMPLE T-TEST In table: Table 1: Comparison of wound healing time (days) between non-smokers and smokers Variable Mean (SD) Mean diff. (95% CI) t-statistics Smoker Non-smoker (df) (n=42) (n=48) Wound healing (days) * P-value* (7.15) (7.13) (-7.52, -1.53) (88) Also known as a dependent sample t-test A parametric test Used to two dependent or related samples Same subject, measure twice or repeatedly Matched study design Closely related subjects (e.g. twin studies) Same subject, measure twice Matched study design Intervention Control Intervention Matched for age Control 5

6 Twin studies Intervention : twin 1 Twin Control : twin 2 Steps in analysis Step 1: state hypothesis Step 2: set the significant level Step 5: Interpret and make conclusion Step 1: state hypothesis Null hypothesis Satisfaction pre = Satisfaction post µ pre = µ post Alternative hypothesis Satisfaction pre Satisfaction post µ pre µ post Step 2: set the significant level =0.05 The acceptable level in medical and health sciences 1. Random samples (samples are representative of the population) 2. The s or measurements are dependent of each other 3. The outcome (dependent) variable is numerical data (interval or ratio) 4. The difference of outcome variable is normally distributed Intervention Control 6

7 To check normality of the difference, must compute the difference between pre and post Then check histogram of the difference Then check histogram of the difference Step 5: Interpret and make conclusion Mean (SD) of customer satisfaction pre = (11.89) Mean (SD) of customer satisfaction post = (16.36) Mean difference = % CI of difference = 33.59, t-statistics=17.93, df=79, P<

8 Step 5: Interpret and make conclusion Since the 95% CI does not cross 0, the P-value must be significant In this case, P<0.001 Conclusion: Reject null hypothesis In text: The difference between mean (SD) of customer satisfaction before and after campaign started was statistically significant [37.46 (11.89) vs (16.36), P<0.001] In table: Table 1: Comparison of customer satisfaction before and after campaign started Variables measurement, Mean (SD) mean difference Customer Satisfaction Score * Pre Post (95% CI) t-statistics (df) P-value* (11.89) (16.36) (33.59,41.98) (79) <0.001 ONE WAY ANOVA Analysis of variance Compare mean of > two Comparison using multiple independent t-test inflates type I error Group A Group B Group C Group A Group B Group C 8

9 Commonly used to; Compare characteristics among patients randomized into different treatment s Compare post treatment differences between treatment s Types of data: 1 independent variable (factor), categorical > two s. Example: A, B, C One Way 1 dependent (outcome) variable Numerical Example:, SBP Steps in analysis Step 1: state hypothesis Step 2: set the significant level Step 5: Interpret and make conclusion Step 1: state hypothesis Null hypothesis There is no difference in mean recovery time between patients in three different treatment s µ a = µ b = µ c Alternative hypothesis At least one treatment has a mean recovery time differ to another treatment µ a µ b µ c Step 2: set the significant level =0.05 The acceptable level in medical and health sciences 1. Random samples (samples are representative of the population) 2. The s and measurements are independent of each other 3. The outcome (dependent) variable is numerical data (interval or ratio) 4. The outcome variable is normally distributed within each s 5. The variance between s is approximately equal (Homogeneity of variances) 9

10 Group A Group B Group C The first three assumptions are determined by the study design The fourth must be checked before analysis. If violated, a non parametric test or data transformation will be needed. If the fifth assumption is violated, adjustment to the test must be made Check normality : statistically and graphically SPSS analyse Descriptive Explore 10

11 Check homogeneity of variance Levene s test Levene s test is not significant (P >.05). Equal variance is assumed Overall ANOVA test. If significant (P < 0.05), indicates at least one of the mean is different to one another To determine which pair has a different mean, must do post hoc test. 11

12 Post hoc test A procedure to determine which pair show different in means Involves multiple pairwise comparisons to test the mean differences between each pair If equal variance assumed Bonferroni, Scheffe, Tukey tests If equal variance not assumed Dunnett s C, Games-Howell Post hoc test Post hoc test Step 5: Interpret and make conclusion Drug A: M=62.55, SD=27.02 Drug B: M=68.16, SD=21.58 Drug C: M=45.10, SD=27.92 test is significant (P = 0.018) suggesting that at least one pair of mean recovery time between patients in different treatment s was significantly different. Conclusion: reject null hypothesis Step 5: Interpret and make conclusion Post hoc analysis using Bonferroni s procedure; Drug A vs drug B: MD=-5.61, 95% CI include 0, P > 0.95 Drug A vs. drug C: MD=17.45, 95% CI include 0, P=0.109 Drug B vs. drug C: MD=23.06, 95% CI does not include 0, P=0.021 In text: analysis suggest that recovery time differ significantly across the three drugs [f(2,58)=4.30, P=0.018] Post hoc analysis using Bonferroni s procedure suggest that the mean of recovery time between patients given drug B and C differ significantly Mean recovery time of patients given drug C was significantly faster d to patients given drug B (M=45.10, SD=27.92 vs. M=68.16, SD=21.58, P=0.021) 12

13 In table: In graphics; Table 1: Mean recovery time between patients give different type of drug Type of drugs N Recovery time, F-statistics (df) P-value* Mean (SD) Drug A (27.02) 4.30 (2, 58) Drug B (21.58) Drug C (27.92) * test Post-hoc analysis using Bonferroni s procedure indicates that only mean recovery time between patients given drug B and C differ significantly (P=0.021) In graphics; In graphics; Recap Compare numerical outcome variable between s 2 independent s independent t-test 2 dependent s paired t-test >2 independent s one way ANOVA Acknowledgement Assoc Prof Dr Wan Mohd Zahiruddin Wan Mohamad Assoc Prof Dr Sarimah Abdullah 13