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This is an electronic version of the print textbook. Due to electronic rights restrictions, some third party content may be suppressed. Editorial review has deemed. Page 1. Introduction to Biostatistics. Larry Winner. Department of Statistics. University of Florida. July 8, Page 2. 2. Page 3. Contents. 1 Introduction. 7. Introduction to Biostatistics / Robert R. Sokal and F. James Rohlf. Dovcr cd. . is little in it that needs changing for an introductory textbook of biostatistics for an.

Sometimes, certain data may be converted from one form to another form to reduce skewness and make it to follow the normal distribution. The goal of using a matched test is to control experimental variability between subjects, thus increasing the power of the test. It is the probability of inability to detect the difference when it actually exists, thus resulting in the rejection of an active compound as an inactive. While performing these tests, it requires x and y variables to be normally distributed. Provides an extensive discussion on the position of statistics within the medical scientific process.

Skip to Main Content. Understanding Biostatistics Author s: First published: Print ISBN: About this book Understanding Biostatistics looks at the fundamentals of biostatistics, using elementary statistics to explore the nature of statistical tests. Key features: Discusses confidence intervals and p-values in terms of confidence functions.

Explains basic statistical methodology represented in terms of graphics rather than mathematical formulae, whilst highlighting the mathematical basis of biostatistics. Looks at problems of estimating parameters in statistical models and looks at the similarities between different models.

Provides an extensive discussion on the position of statistics within the medical scientific process. Discusses distribution functions, including the Guassian distribution and its importance in biostatistics.

Reviews "Overall, the book is well-written. The topics are presented in a logical progression as is the level of their mathematical difficulty.

Free Access. Summary PDF Request permissions. PDF Request permissions. Tools Get online access For authors. Various softwares are available free of cost for calculation of sample size and power of study. Lastly, appropriate allowances are given for non-compliance and dropouts, and this will be the final sample size for each group in study.

We will work on two examples to understand sample size calculation. The mean SD diastolic blood pressure of hypertensive patient after enalapril therapy is found to be 88 8. It is claimed that telmisartan is better than enalapril, and a trial is to be conducted to find out the truth. By our convenience, suppose we take minimum expected difference between the two groups is 6 at significance level of 0. In this case, minimum expected difference is 6, SD is 8 from previous study, alpha level is 0.

After putting all these values in computer program, sample size comes out to be If we take allowance to non-compliance and dropout to be 4, then final sample size for each group would be The mean hemoglobin SD of newborn is observed to be It was decided to carry out a study to decide whether iron and folic acid supplementation would increase hemoglobin level of newborn. There will be two groups, one with supplementation and other without supplementation.

Minimum difference expected between the two groups is taken as 1. In this example, SD is 1. It is a probability that study will reveal a difference between the groups if the difference actually exists. A more powerful study is required to pick up the higher chances of existing differences.

Power is calculated by subtracting the beta error from 1. Hence, power is 1-Beta. Power of study is very important while calculation of sample size. Power of study can be calculated after completion of study called as posteriori power calculation. This is very important to know whether study had enough power to pick up the difference if it existed.

In this case, power of study is too low to pick up the exiting difference. It means probability of missing the difference is high and hence the study could have missed to detect the difference. If we increase the power of study, then sample size also increases. It is always better to decide power of study at initial level of research. There are number of tests in biostatistics, but choice mainly depends on characteristics and type of analysis of data.

Sometimes, we need to find out the difference between means or medians or association between the variables. Number of groups used in a study may vary; therefore, study design also varies. Hence, in such situation, we will have to make the decision which is more precise while selecting the appropriate test. Inappropriate test will lead to invalid conclusions. Statistical tests can be divided into parametric and non-parametric tests. If variables follow normal distribution, data can be subjected to parametric test, and for non-Gaussian distribution, we should apply non-parametric test.

Statistical test should be decided at the start of the study. Following are the different parametric test used in analysis of various types of data. It is usually applicable for graded data like blood sugar level, body weight, height etc.

For example, when we want to compare effect of drug A i.

For example, when we compare the effects of drug A and B i. However, when there are 3 or more sets of data to analyze, we need the help of well-designed and multi-talented method called as analysis of variance ANOVA.

This test compares multiple groups at one time. It compares three or more unmatched groups when the data are categorized in one way. For example, we may compare a control group with three different doses of aspirin in rats. Here, there are four unmatched group of rats.

For example, effect of supplementation of vitamin C in each subject before, during, and after the treatment. Matching should not be based on the variable you are com paring. For example, if you are comparing blood pressures in two groups, it is better to match based on age or other variables, but it should not be to match based on blood pressure. The term repeated measures applies strictly when you give treatments repeatedly to one subjects.

Therefore, these tests are used routinely in many field of science. For example, you might measure a response to three different drugs in both men and women. This is a complicated test. Therefore, we think that for postgraduates, this test may not be so useful. They account for multiple comparisons, as well as for the fact that the comparison are interrelated. ANOVA only directs whether there is significant difference between the various groups or not. If the results are significant, ANOVA does not tell us at what point the difference between various groups subsist.

But, post test is capable to pinpoint the exact difference between the different groups of comparison. Therefore, post tests are very useful as far as statistics is concerned.

There are five types of post- hoc test namely; Dunnett's, Turkey, Newman-Keuls, Bonferroni, and test for linear trend between mean and column number. Select Dunnett's post-hoc test if one column represents control group and we wish to compare all other columns to that control column but not to each other.

Select the test for linear trend if the columns are arranged in a natural order i. Select Bonferroni, Turkey's, or Newman's test if we want to compare all pairs of columns. The Chi-square test is a non-parametric test of proportions. This test is not based on any assumption or distribution of any variable.

This test, though different, follows a specific distribution known as Chi-square distribution, which is very useful in research. It is most commonly used when data are in frequencies such as number of responses in two or more categories. Test of proportion: This test is used to find the significance of difference in two or more than two proportions.

Test of association: The test of association between two events in binomial or multinomial samples is the most important application of the test in statistical methods. It measures the probabilities of association between two discrete attributes. Two events can often be studied for their association such as smoking and cancer, treatment and outcome of disease, level of cholesterol and coronary heart disease. In these cases, there are two possibilities, either they influence or affect each other or they do not.

In other words, you can say that they are dependent or independent of each other. Thus, the test measures the probability P or relative frequency of association due to chance and also if two events are associated or dependent on each other. Varieties used are generally dichotomous e. If data are not in that format, investigator can transform data into dichotomous data by specifying above and below limit. Multinomial sample is also useful to find out association between two discrete attributes.

For example, to test the association between numbers of cigarettes equal to 10, 20, , and more than 30 smoked per day and the incidence of lung cancer. Since, the table presents joint occurrence of two sets of events, the treatment and outcome of disease, it is called contingency table Con- together, tangle- to touch.

In contingency table, we need to enter the actual number of subjects in each category. We cannot enter fractions or percentage or mean. Most contingency tables have two rows two groups and two columns two possible outcomes. The top row usually represents exposure to a risk factor or treatment, and bottom row is mainly for control. The outcome is entered as column on the right side with the positive outcome as the first column and the negative outcome as the second column.

A particular subject or patient can be only in one column but not in both. The following table explains it in more detail:. This is the limitation of this test. It only indicates the probability P of occurrence of association by chance. Yate's correction is not applicable to tables larger than 2 X 2.

When total number of items in 2 X 2 table is less than 40 or number in any cell is less than 5, Fischer's test is more reliable than the Chi-square test. This is a non-parametric test. This test is used when data are not normally distributed in a paired design. It is also called Wilcoxon-Matched Pair test.

It analyses only the difference between the paired measurements for each subject. If P value is small, we can reject the idea that the difference is coincidence and conclude that the populations have different medians. This test is generally used when two unpaired groups are to be compared and the scale is ordinal i. This is a non-parametric test, which compares three or more paired groups. In this, we have to rank the values in each row from low to high.

The goal of using a matched test is to control experimental variability between subjects, thus increasing the power of the test. It is a non-parametric test, which compares three or more unpaired groups. Non-parametric tests are less powerful than parametric tests.

Generally, P values tend to be higher, making it harder to detect real differences. Therefore, first of all, try to transform the data. Sometimes, simple transformation will convert non-Gaussian data to a Gaussian distribution. Non-parametric test is considered only if outcome variable is in rank or scale with only a few categories [ Table 1 ]. In this case, population is far from Gaussian or one or few values are off scale, too high, or too low to measure.

To explain some common difficulties, we will take one example and try to solve it. Suppose, we want to perform a clinical trial on effect of supplementation of vitamin C on blood glucose level in patients of type II diabetes mellitus on metformin. Two groups of patients will be involved.

One group will receive vitamin C and other placebo. In such trial, first problem is to find out the sample size. As discussed earlier, sample size can be calculated if we have S. D, minimum expected difference, alpha level, and power of study. If the previous study report is not reliable, you can do pilot study on few patients and from that you will get S. Minimum expected difference can be decided by investigator, so that the difference would be clinically important.

In this case, Vitamin C being an antioxidant, we will take difference between the two groups in blood sugar level to be Minimum level of significance may be taken as 0. After putting all the values in computer software program, we will get sample size for each group. After calculating sample size, next question is to apply suitable statistical test. We can apply parametric or non-parametric test.

If data are normally distributed, we should use parametric test otherwise apply non-parametric test. In this trial, we are measuring blood sugar level in both groups after 0, 6, 12 weeks, and if data are normally distributed, then we can apply repeated measure ANOVA in both the groups followed by Turkey's post-hoc test if we want to compare all pairs of column with each other and Dunnet's post-hoc for comparing 0 with 6 or 12 weeks observations only.

If we want to see whether supplementation of vitamin C has any effect on blood glucose level as compared to placebo, then we will have to consider change from baseline i. If we want to find out any difference between basic demographic data regarding gender ratio in each group, we will have to apply Chi-square test. To see whether there is any correlation between age and blood sugar level or gender and blood sugar level, we will apply Spearman or Pearson correlation coefficient test, depending on Gaussian or non-Gaussian distribution of data.

If you answer all these questions before start of the trial, it becomes painless to conduct research efficiently.

Statistical computations are now made very feasible owing to availability of computers and suitable software programs. Now a days, computers are mostly used for performing various statistical tests as it is very tedious to perform it manually. Free website for statistical softwares are www. Statistical methods are necessary to draw valid conclusion from the data. The postgraduate students should be aware of different types of data, measures of central tendencies, and different tests commonly used in biostatistics, so that they would be able to apply these tests and analyze the data themselves.

This article provides a background information, and an attempt is made to highlight the basic principles of statistical techniques and methods for the use of postgraduate students. The authors gratefully acknowledge to Dr. Source of Support: Conflict of Interest: None declared. National Center for Biotechnology Information , U.

Journal List Indian J Pharmacol v. Indian J Pharmacol. Ganesh N. Dakhale , Sachin K. Hiware , Abhijit T.

Shinde , and Mohini S. Sachin K. Abhijit T. Mohini S. Author information Article notes Copyright and License information Disclaimer. Correspondence to: Ganesh Dakhale, E-mail: This is an open-access article distributed under the terms of the Creative Commons Attribution-Noncommercial-Share Alike 3. This article has been cited by other articles in PMC. Abstract Statistical methods are important to draw valid conclusions from the obtained data.

Biometry, level of significance, parametric test, power of study, sample size. Introduction Statistics is basically a way of thinking about data that are variable. Types of Data Observations recorded during research constitute data. Measures of Central Tendencies Mean, median, and mode are the three measures of central tendencies. Standard Deviation In addition to the mean, the degree of variability of responses has to be indicated since the same mean may be obtained from different sets of values.

Correlation Coefficient Correlation is relationship between two variables. Open in a separate window. Figure 1. Standard Error of Mean Since we study some points or events sample to draw conclusions about all patients or population and use the sample mean M as an estimate of the population mean M 1 , we need to know how far M can vary from M 1 if repeated samples of size N are taken.

Applications of Standard Error of Mean: Applications of SEM include: Null Hypothesis The primary object of statistical analysis is to find out whether the effect produced by a compound under study is genuine and is not due to chance.

Level of Significance If the probability P of an event or outcome is high, we say it is not rare or not uncommon. Outliers Sometimes, when we analyze the data, one value is very extreme from the others.

One-tailed and Two-tailed Test When comparing two groups of continuous data, the null hypothesis is that there is no real difference between the groups A and B. Importance of Sample Size Determination Sample is a fraction of the universe. Factors Influencing Sample Size Include 1. Sample Size Determination and Variance Estimate To calculate sample size, the formula requires the knowledge of standard deviation or variance, but the population variance is unknown.

Frequently used sources for estimation of standard deviation are: Calculation of Sample Size Calculation of sample size plays a key role while doing any research. Power of Study It is a probability that study will reveal a difference between the groups if the difference actually exists. How to Choose an Appropriate Statistical Test There are number of tests in biostatistics, but choice mainly depends on characteristics and type of analysis of data.

When to apply paired and unpaired a. Table 1 Summary of statistical tests applied for different types of data. Softwares for Biostatistics Statistical computations are now made very feasible owing to availability of computers and suitable software programs. Acknowledgement The authors gratefully acknowledge to Dr. Footnotes Source of Support: References 1.

Rao KV. What is statistic? What is Biostatistics? Rao KV, editor.

A manual of statistical methods for use in health, nutrition and anthropology. New Delhi: Jaypee Brothers Medical Publisher P ltd; Statistics for clinicians. J Assoc Physicians India. Transforming data. Br Med J. Medhi B, Prakash A. Practical Manual of Experimental and Clinical Pharmacology.

Biostatistics in pharmacology; pp. Lang T. Twenty statistical errors even you can find in biomedical research article. Croat Med J. Guidelines for reporting statistics in journals published by the American Physiological Society. Prabhakara GN. Pearson's correlation. Biostatistics; pp. Ghosh MN.

Fundamentals of experimental pharmacology.