Introduction to Statistical Analysis What is STATISTICS Statistics

Introduction to Statistical Analysis

What is STATISTICS? �Statistics fulfill one of the basic human needs. �A process to: �Manage - to clean and format the data in order to get a valid data which is feasible to be analyzed. �Analyze - to explore the data in order to answer the objective. �Interpret data - to convert the statistical interpretation to the common understanding.

Classification of Statistics � Descriptive Statistics - describe the data by summarizing them � Inferential Statistics - techniques, by which. . - inferences are drawn for the population parameters from the sample statistics OR - Conclusions were made for the population using a sample data

What is the Descriptive Statistics for? In any study…. Before answering the research question, we should recognize the characteristics of the sample - (e. g. age, gender, ethnicity, etc)

How to describe a categorical variable? �Statistics - Frequency - Relative frequency - Cumulative relative frequency �Figure/Chart - Bar - Pie

How to describe a numerical variable? �Statistics - Central tendency - Mean - Median (50 th Percentile) - Dispersion - Standard deviation - Inter-quartile range (IQR) (3 rd quartile – 1 st quartile) �Figure/Chart - Histogram/Frequency polygon - Box plot

Inferential statistics � With inferential statistics, we take a sample (a small subset of a larger set of data). � We then use this sample to draw inferences or make generalizations about the population from which the samples were drawn. Estimation (Confidence interval) • For e. g. : Estimation of mean, estimation of proportion Hypothesis test • For e. g. : Comparing means, comparing proportions, association between 2 variables

Estimation � In estimation, the sample is used to estimate a population parameter and a confidence interval about the estimate is constructed. � Estimation (CI) of mean: For e. g. : =16. 14, 95% CI = (15. 30, 16. 98) We are 95% sure that the mean duration of exercise of population will lie between 15. 30 and 16. 98 minutes/day. � Estimation (CI) of proportion: For e. g. : p =0. 37, 95% CI = (0. 27, 0. 47) We are 95% sure that the prevalence of the obesity in the population will be between 27% & 47%.

Hypothesis � Testable statement that describes s relationships of variables. � Derived from research questions. � Postulating the existence of: 1. A difference between groups. 2. An association among factors. � Null hypothesis (H 0): - Hypothesis to be tested, of no difference. � Alternative hypothesis (Ha): - Hypothesis that postulates that there is a treatment effect or a difference between groups. � The process of inferential statistics is to justify whether we have enough evidence (based on probability) to reject or fail to reject H 0.

Statistical Procedure Sample Size Data Collection Data Quality Statistical Analysis Interpretation

Sample Size

What Is Sample Size? �Sample size is: the number of units (persons, animals, patients, specific circumstances, etc. ) in a population need to be studied to represent the population.

Why We Need To Calculate Sample Size? �Guide : When to start and stop collecting? How are we going to collect it? �Minimum required sample: Depends on availability of the sample, time constraint, subject constraint and ethical issues �Study design : Influence the quality and accuracy of research �Economic : Waste of resources if not having the capability to produce useful

Process of Sample Size Determination

Journal sample size for pilot study

What Happened If Sample Size…. . Too small � Well conducted study may fail to answer its research question. � May fail to detect important effects � May estimate those effects imprecisely Sample size should be adequate to achieve a good precision in estimation Too large � Costly – the longer the study the higher it cost � Difficulties face – lack of manpower and time � Tiring – recruitment of outcome or subjects maybe tiring for a long time

Statistical Software: Website address � Power and sample size http: //biostat. mc. vanderbilt. edu/wiki/Main/Power. Sample. Size � Epi – Info Software http: //wwwn. cdc. gov/epiinfo/html/downloads. htm � Epi. Calc http: //www. brixtonhealth. com/epicalc. html � Sample size for Prevalence Studies. xls – Lin Naing � Sample size for Sensitivity and Specificity. xls – Lin Naing � Power Analysis and Sample Size (PASS) – most powerful but have to buy the license first http: //www. ncss. com/pass. html

Data Collection

Data CATEGORICAL Nominal • E. g. : gender, race NUMERICAL Ordinal • Logical ordering to the categories, e. g. : education level, pain severity Continuous • E. g. : age, weight, height Statistics: • Frequency & percentage • Relative frequency & percentage • Cumulative frequency & percentage Statistic: Central tendency & dispersion • Mean & SD(if normality assumed) • Median & IQR (if skewed) Figure/chart: • Bar • Pie Figure/chart: • Histogram • Boxplot

DATA ENTRY Before key-in – What to prepare? q INSTRUMENT/QUESTIONNAIRE ◦ Purpose and objective ◦ Variables and units ◦ Format q DATA DEFINITION/ DATA DICTIONARY ◦ Explain the summary of variables in terms of variable name, description, formatting and labelling (where necessary/applicable).

DATA DEFINITION/DATA DICTIONARY

Data Quality

DATA CLEANING DUPLICATES More than one observation having same patientid MISSING VALUES Blank cell without information. INCONSISTENCY 3 means nothing in the definition for ptgender EXTREME VALUES Value exceeds the upper limit. Definition: patientid - patient identification number. ptgender - 1 is Male and 2 is Female. height - defines from 1. 4 m till 1. 8 m. weight - defines from 50. 0 kg till 150. 0 kg.

Statistical Analysis

Type of Analysis Parametric Test Non-parametric Test Dependent Variable Numerical Data Two (Independent) -Categorical (e. g. smokers and nonsmokers) Independent t-test Mann-Whitney test > two (Independent) -Categorical (e. g. malay, chinese and indian) One-way ANOVA Kruskal-Wallis test Two (Dependent) -Categorical (e. g. pre and post intervention) Paired t-test Wilcoxon Signed Rank test -Numerical (e. g. weight in kg) Pearson’s correlation Spearman’s correlation Number of Groups

Type of Analysis Assumptions Number of Groups Assumptions Dependent Variable Categorical Data Two (Independent) -Categorical (e. g. smokers and nonsmokers) Chi-square test Fisher’s exact test > two (Independent) -Categorical (e. g. malay, chinese and indian) Chi-square test Fisher’s exact test Assumptions: Non-parametric Test ü The number of cells with Expected Count (EC) less than 5, must be less than 25% of the total number of cells. ü The smallest EC must be at least 2.

Example Study – numerical data �RQ: Is there any difference of time spent for exercise between obese and non-obese group? �Objective: To compare the mean duration of exercise between obese and non-obese group Assumption: ü Dependent variable should be approximately normally distributed for each category of the independent variable.

second Test statistic using SPSS STEP: Analyze >> Compare means >> Independent t test Analyze >> Descriptive Statistics >> Explore Click

third Make a decision Descriptive statistics of each variable Levene’s test result If P value > 0. 05(not sig. ), read the first row(Equal variances assumed). If P value < 0. 05(sig), read the second row(Equal variances not assumed). The Levene’s test is not significant.

Interpretation Table 1: Comparing mean duration of exercise between obese(n=37) and nonobese(n=63) respondents “ An independent-sample t-test indicated that duration of exercise were not significantly different between obese (Mean=16. 7, SD=4. 83) and nonobese (Mean=15. 8, SD=3. 88), t(98)=1. 06, p=. 291. Therefore, there is no significant association between duration of exercise and obesity. ”

Example Study – categorical data �Comparing 2 or more proportions. �RQ: Is there any association between gender and obesity group?

second Test statistic using SPSS Analyze >> Descriptive Statistics >> Crosstabs Click 1 Click 2

third Make a decision must be at least 2 must be less than 25%

fourth Interpretation Table 9: Association between gender and obesity “ A Chi-square test for independence indicated that the prevalence (proportion) of obesity between male and female are not significantly different (P=0. 753). Therefore, there is no significant association between gender and obesity. ”

Statistical Procedure Sample Size Data Collection Data Quality Statistical Analysis Interpretation

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