# Statistics for Medical Students

Statistics is an integral part of medical school. It helps students understand different aspects of medicine, such as medical diagnosis, treatments, and outcomes. Therefore, it is important to have some understanding of statistics for medical students to be successful in their future careers. This guide will provide an overview of the fundamentals of statistics for medical students. It will cover several topics, including types of variables, biases, confounding variables, normal distribution, z-tests and p-values, and what is a z score. In each section, we will provide an overview of the concepts, examples, and formulas. By the end of the guide, you should have a better understanding of the tools available to you to analyze and interpret data in medical practices. This knowledge will serve as a useful resource throughout your training and career.Statistics is a field of mathematics that helps us to better understand the world around us. It includes topics and techniques such as data analysis, hypothesis testing, and probability models. Medical students need to be familiar with these concepts to be able to interpret health-related studies, apply treatments based on scientific evidence, and make appropriate decisions. This guide will provide an overview of the key concepts in statistics that medical students should understand, such as types of variables, biases, confounding variables, normal distributions, z-tests, and p-values.Statistics is an essential part of understanding the medical world. As a medical student, learning about statistics is important to be able to interpret data and draw reliable conclusions. Statistics supports medical professionals to better understand issues like disease prevalence, diagnose patients and determine the most effective treatments. It may also guide policy decisions and help to inform public health discussions. The ability to collect, analyze and interpret data provides medical professionals with information that can help inform their decision-making. Statistics helps to answer questions such as: what are the trends in certain diseases? What is the predicted impact of a new drug? How does one population differ from another population? Answering these questions through statistical modeling can provide a wealth of information. Through this guide you will gain an understanding of the different types of variables, biases, confounding variables, normal distribution, hypothesis tests and z-scores. You will learn how these concepts are related, and how they can be applied to real-world situations. At the end of this guide, you should be comfortable understanding and applying error analysis techniques to data. You will also be better prepared to make informed decisions in the medical field, based on sound statistical reasoning.In this guide, we will be looking at statistics for medical students. Statisticians, scientists, and students of medicine rely on the analysis of data to draw meaningful conclusions from results of experiments and studies. Being comfortable and knowledgeable about the fundamentals of statistics is a key skill to master in any medical field, whether in research, clinical practice or population health. In this guide, we will cover the types of variables, biases, confounding variables, normal distributions, z-test and p-values, and what is a Z score. After reading this guide, you should have a better understanding of the important concepts associated with statistics that are relevant to medical students. Let�s begin!When learning about statistics, it is important for medical students to understand the types of variables as this forms the basis of data gathering and interpretation. Variables are simply measurements or facts that can be counted and categorized. Variables are typically put into four distinct categories; quantitative, discrete, nominal and ordinal.

### Quantitative Variables

Quantitative variables are numbers that can be combined to give meaningful information. Examples of quantitative variables include age, height, weight, number of siblings and temperature. Quantitative variables can be further broken down into two additional categories; continuous and discrete.

### Continuous Variables

Continuous variables can be any value within a range, meaning they could have multiple potential responses. For example, weight is a continuous variable as it is possible to weigh anything between zero and infinity. Another example of a continuous variable is blood pressure.

### Discrete Variables

Unlike continuous variables, discrete variables have a limit to possible values within a range. An example of a discrete variable is the number of siblings someone has, which obviously cannot exceed a certain amount. Other examples of discrete variables include the number of times you have gone to the cinema in the last month, how many illnesses someone has had in the past year and how many hours of sleep someone gets per night.

### Nominal Variables

Nominal variables are simply categorizations of data rather than numerical values. Examples of nominal variables include gender, eye color and ethnicity; since each of these variables can only be either one option or another. A nominal variable cannot be given a numeric value.

### Ordinal Variables

Ordinal variables are similar to nominal variables, but with one key difference; the categories can be ranked. Examples of ordinal variables include education level, as someone can graduate from high school, college or university. Ratings of movies also fall into the category of an ordinal variable, as reviews can be given on a 1-5 basis. An ordinal variable can differentiate between two options, but can also rank them in order of magnitude.

Quantitative variables are those that can be measured numerically and have a meaningful quantitative difference between values. Quantitative variables usually come in the form of real numbers and involve either continuous or discrete units of measurement. Continuous variables are those which can take an infinite number of values within a given range, such as time or temperature. Discrete variables, on the other hand, involve counting finite (whole number) values, such as the number of individuals in a group or the number of patients a doctor sees.Nominal variables are those that cannot be measured numerically, but can still be categorized in some way. These variables usually involve assigning labels to items and are often used to denote the various categories in a study. For example, in a study about genders, participants may be categorized as either male or female.Ordinal variables are similar to nominal variables in that they also do not involve numerical measurements, but involve the assignment of order to items. An example of an ordinal variable is how a doctor might rate patient pain on a scale of 1�10. Such variables enable us to place values or items into an order from smallest to largest.Data derived from originally collected data can provide information about trends and outcomes which cannot be determined from the original data itself. For example, if you had data on the number of students in a school over a five-year period, you could use this data to calculate a trend in the number of students over time. This would give you an overview not just of the raw numbers, but of how the numbers changed over the five years. Similarly, examining the average grade of the school's students could provide insight into how well those students were performing. By looking at the average grade, you can also determine how much of an increase or decrease that average grade experienced over the same period of time.

When collecting and analyzing data, it is important to classify variables correctly. Variables are classified based on the type of data they represent. Quantitative variables are numerical values that represent some sort of measurable quantity (such as age, height, weight). Discrete variables are a type of quantitative variable that take on discrete readings, like whole numbers (such as the number of students in a classroom). Nominal variables are categories that can be easily sorted into groups, such as gender, ethnicity and state of residence. Finally, ordinal variables are categories that can also be sorted into groups, but these groups can be rank ordered or have a certain hierarchy associated with them (like a rating scale from 1-5, or a ranking system).

Classifying variables correctly is important because it allows for deriving meaningful insights from the data collected. For instance, if the data collected is age, then it would be classified as a quantitative variable because it is a numerical value that can be measured. Knowing this, we can then look at the average age, median age, standard deviation, etc. Knowing how to correctly classify variables also helps when trying to analyze relationships between different variables.

Biases can have a huge impact on the results of any study or research. In this section, we'll discuss what biases are and how they can influence the outcome of medical studies. Biases, more simply put, are any systematic errors or distortions in research that can lead to false conclusions. They can be due to either the design of the study, the researcher's personal beliefs, or the way data is collected. All these can have an immediate and negative effect on the reliability of the results. Examples of biases include selection, measurement, observer, procedure, central tendency, and misclassification. **Selection bias** occurs when particular participants are chosen or excluded from a study, either intentionally or unintentionally. This may lead to false impressions or conclusions about the effects of a certain exposure on an outcome. **Measurement bias** refers to a change in the process of collecting data, leading to inaccurate results. Such bias can be caused by the use of flawed instruments or protocols for data collection. **Observer bias** occurs when the researcher's personal opinions, preconceived ideas, or expectations influence the outcome of a study. The same thing applies for **procedural bias**, which happens when particular procedures are used to evaluate the research results. **Central tendency bias**, on the other hand, typically arises when the means of data collection are inadequate. The results may unintentionally favor a particular outcome, influencing the accuracy of the study. Finally, **misclassification bias** is caused by wrongly coding data, leading to misinterpretation and inaccurate conclusions. This type of bias is especially important for research involving human subjects, as it can affect both the accuracy of the data as well as the privacy of the participants. It's important to be aware of possible biases when conducting medical studies, so that their effects can be minimized. By being aware of the different types of bias and how they manifest, medical students can carry out their research with confidence and accuracy.Bias is a systematic error that affects the outcome of a study. It can introduce incorrect or misleading ideas or conclusions into the research and lead to unreliable results. Biases can occur when there is a particular preference during the selection process, data collection, or evaluation of results. Examples of biases include selection bias, attrition bias, measurement bias, observer bias, procedure bias, central tendency bias, and misclassification bias. Selection bias occurs when the researcher chooses the sample in a biased way that does not accurately represent the population being studied. Attrition bias occurs when participants stop participating before the end of the study. Measurement bias occurs when the data collection instruments are used incorrectly or inaccurate measurements are taken. Observer bias occurs when the researcher�s expectations affect the interpretation of results. Procedure bias occurs when the research design does not account for all variables that may be relevant to the study. Central tendency bias occurs when the data is collected or analyzed in a way that does not take all possible values into consideration. Misclassification bias occurs when data is inaccurately categorized or classified.

Bias is an error that occurs when the researcher's decisions influence the data in a certain way, leading to inaccurate conclusions. There are three different types of biases: selection bias, attrition bias, and measurement bias.

Selection bias occurs when participants are chosen in a way that is not random. This type of bias can be prevented by selecting participants randomly. Attrition bias occurs when participants drop out of the study before it is completed, and the remaining participants may not be representative of the group as a whole. Measurement bias happens when incorrect instruments are used to measure the results. This type of bias can be prevented by using valid and reliable instruments.

It is important to acknowledge and address bias in studies, as it can lead to inaccurate or misleading conclusions. To ensure accuracy, researchers should be aware of the different types of bias and how they might affect the results.

When it comes to biases, it�s important for medical students to understand how these may affect the accuracy of statistical analysis. Observer bias is a type of bias that occurs when someone conducting the research projects their own opinions, beliefs, or subjective feelings onto the results. This can make the data hard to interpret or draw conclusions from as there is little objectivity. Procedure bias is also known as selection bias and is caused by using an unbalanced or improper sample selection process. It might not be an accurate representation of the population which can lead to inaccurate results. Central tendency bias happens when someone conducting the research only looks at the average result instead of considering the variation in the data. This could lead to an underestimation or overestimation of the effect of the study and cause unreliable results.Misclassification bias is the result of incorrectly classifying data due to poorly defined categories. This can cause the data to be misinterpreted and again lead to incorrect conclusions being made about the study. In conclusion, understanding the different types of biases and how they are formed is key for medical students who are dealing with statistical analysis. Being aware of the possible distortions that might occur in data will help ensure that the results are reliable and that any conclusions are accurate.

## Confounding Variables

It's important to understand the concept of confounding variables when studying the cause and effect of medical conditions, orientations or treatments. A confounding variable is an extraneous element that influences the outcome of a study and it can distort the results of research.

Confusing variables can be difficult to detect but they essentially create a false correlation. For example, if you were researching whether eating ice cream had an effect on short-term memory, you'd need to be aware of any other factors that may be influencing the results, such as the day of the week. It's likely that more people will eat ice cream on sunny days when compared to cold rainy days and as such, this could have an effect on the overall results.

It�s essential to be aware of how confounding variables might affect your studies. To do this, researchers will need to delineate exact causes and effects in order to fully explore any potential relationships. This helps to ensure that spurious correlations are not inadvertently created.

At the end of the day, it�s essential for medical students to be familiar with the concepts of confounding variables in order to draw valid conclusions from their studies and experiments.

Confounding variables are a type of variable that can affect a study's results by introducing errors and distorting the true relationship between the variable being studied (the exposure) and the outcome. By understanding how these confounding variables can affect research, medical students can learn how to interpret study outcomes more accurately. Confouding variables introduce bias into a study because they may be associated with both the exposure and the outcome. It is important to account for potential confounding variables in order to accurately interpret the results of a study. For instance, a medical researcher trying to measure the effects of smoking on lung cancer risk may find that there is an association between the two variables. However, if the researcher did not take potential confounding variables like age and gender into account, they could produce inaccurate results, as the older a person is, the higher their risk of lung cancer generally is, regardless of whether they smoke or not. Therefore, age and gender would be classified as confounding variables in this study. It is also important to note that confounding variables can cause a correlation between two variables, without one causing the other. For example, people who play football might have a higher rate of ACL injuries. However, the connection between playing football and ACL injuries does not necessarily mean that playing football causes ACL injuries. A potential confounding variable like the age of the players could be responsible for the correlation, as younger players tend to have higher injury rates due to their physical immaturity. By taking confounding variables into account, medical students can learn to understand the true relationship between variables and draw accurate conclusions from their studies.When we talk about correlations and causations, it is important to understand the difference between them. Correlation means two items are related but does not necessarily mean that one item causes the other. For example, statistics show that there is a positive correlation between the amount of ice cream consumed and the number of reported crimes. This does not necessarily mean that eating more ice cream causes more crime, but that an increase in either can be observed. On the other hand, causation implies that one event will cause the other. In order for an experiment to prove causation, it must meet certain criteria. The relationship must be strong, consistent, causal direction must be clear, and other variables must be taken into account. An example might be a new medication being tested to see if it decreases the symptoms of a particular condition. If the experiment shows that those taking the medication experience a decrease in symptoms, this could be evidence of causation.Confounding variables are variables that may affect the relationship between two other variables. It is important to identify these confounding variables before making any conclusions about the data since they can influence the results or change the overall outcome. For example, let's say a medical study is done to measure the effect of contemporary medicine on reducing mortality rates. Here, age would be a confounding variable as younger patients may not receive the same treatment as older patients and this could lead to a biased result. Other confounding variables can include lifestyle factors such as exercise, diet, and smoking. It is essential to take these variables into account when interpreting research results.

## Normal Distribution - 350 words

Normal distribution is a type of probability distribution that shows how often a set of data follows a certain pattern. It is sometimes referred to as a bell curve because it peaks in the middle and gradually falls off on either side. This type of distribution has many applications, particularly in medical sciences.

The normal distribution is described by its mean, median, and standard deviation. The mean is the sum of all the values in a data set divided by the number of pieces of data. The median is the middle value of a data set. The standard deviation is a measure of how far away each piece of data is from the average.

No matter what the mean and standard deviation are, the normal distribution will always take a similar shape. Every piece of data has an equal chance of occurring, so the shape of the data follows a predictable pattern. This is useful for medical students when conducting studies based on probability.

A useful way to understand normal distributions is through the concept of Z-scores. A Z-score measures the distance between a value in the data and the mean. The higher the Z-score, the farther a value is from the mean. Therefore, if a Z-score is negative, the value is lower than the mean, and if it is positive, the value is higher than the mean.

The normal distribution provides a powerful way to study the effect of an exposure or intervention on an outcome. By finding the differences between the means of two different groups, researchers can determine the effect of an intervention or exposure. Understanding the normal distribution is key for medical students who wish to gain insights from their studies.

Normal distribution is a type of probability distribution that has a bell-shaped curve, and is symmetric around the mean. This means that data points in a normal distribution will cluster around the average, with fewer points as the numbers move away from the mean in either direction. For example, if you plotted the heights of people in a normal distribution, most would be of medium height, with the curve going down as the numbers get taller and shorter. Normal distributions also follow certain properties. All normal distributions have the same probability no matter what part of the curve they are on. They also have an equal probability of being greater than the mean or less than the mean. Furthermore, all normal distributions have a kurtosis of 3 and a standard deviation of 1.These properties make it easy to measure how different one value is from the population. If a value is close to the mean, it has a low z-score; if it is further away from the mean, it has a higher z-score. Z-scores can also tell us how rare a value is. The greater the z-score, the rarer the value. So, for example, a person who is 7 feet tall would have a high z-score, indicating that they are very tall and rare.

In order to calculate z-values in a normal distribution, you'll need to use the formula:

**Z = (X-_) / _**

Where "X" stands for the value you're looking at, _ is the mean, and _ is the standard deviation.

In other words, for every dataset you analyze, the equation will calculate how far away any given data point is from the mean. It does this by measuring the number of standard deviation units away from the mean that the data point is. This is known as its Z score.

The Z score can also be used to determine whether a data point is statistically significant or insignificant. A Z score of 1.96 or higher indicates that the data point is significant, while a Z score of less than 1.96 indicates an insignificant data point.

When studying statistical data, it is important to understand the concept of sampling variation and standard error. Sampling variation occurs because practically no two samples will have identical properties. This difference between samples is known as variability. Standard error is a measure of how much variability is expected in a sample of statistics. It can be used to determine the likelihood that an observed difference between samples is large enough to be meaningful or likely due to random selection. The amount of variability in a sample of data is also referred to as the "margin of error" and is a key factor in the accuracy of the data.

## Z-Tests & P-Values

It is almost impossible for medical students to fully understand statistics without first understanding the concepts of hypothesis tests, z-tests and p-values. Hypothesis tests are used to study the effect of an exposure on an outcome. A hypothesis test typically involves calculating a statistic that measures the evidence against the null hypothesis. The null hypothesis is typically �no effect� or �no difference� between two groups being compared.

A z-test is a type of hypothesis test used in statistics. It makes use of the standard scores (z-scores) that measure the distance between a value and the mean in terms of the number of standard deviation units. Z-tests are often used to compare means between two larger samples or populations.

The p-value is the probability of obtaining the observed results if the null hypothesis is true. A low p-value indicates strong evidence against the null hypothesis, so you reject the null hypothesis. Typically, a p-value less than 0.05 is considered sufficient evidence to reject the null hypothesis.

It is important to remember that the p-value is not the probability that the null hypothesis is true, but rather the probability of observing the results that were found if the null hypothesis is true. Therefore, a p-value of 0.05 suggests a 5% chance of obtaining these results if the null hypothesis is true.

When studying the effect of an exposure on an outcome using a hypothesis test, we are interested in the confidence interval associated with the statistic. This is calculated using the equation: *Confidence Interval = Statistic +/- [Margin of Error] _ [Standard Error]*, where the Margin of Error is determined by the desired confidence level.

## Hypothesis Tests and P-Values

Hypothesis tests are statistical tests that allow us to explore the likelihood of certain assumptions being true. These tests take into account real world data, and by analysing this data, we can make inferences about what is true. To determine this level of certainty, we use the concept of a p-value.

A p-value is a number between 0 and 1. If the p-value is low, this indicates that the data suggests our assumption is true. A high p-value, however, indicates that there is not enough evidence to support the assumption. Generally, a p-value of less than 0.05 is considered statistically significant and this means that the hypothesis is true given the data provided.

When studying the effect of an exposure on an outcome, it is important to consider a few key factors. Firstly, the size of the sample used. A larger group of participants will provide more accurate results than a smaller sample. Secondly, the measure of the exposure needs to be determined. For example, if using smoking as an exposure, how much a person smokes needs to be measured accurately. Lastly, the measure of outcome needs to be determined. In the case of the smoking example, this could be a physiological or psychological affect, or even something more serious such as mortality.

When performing hypothesis testing, the confidence interval helps to indicate how uncertain you are about a particular estimate. It is calculated as the difference between your sample statistic (such as the mean) and its margin of error, which is the predicted sampling distribution of the statistic. To calculate the confidence interval, you need to use the following equation:

- Confidence Interval = Sample Statistic +/- Margin of Error

The margin of error is determined by the size of the sample, the level of confidence desired, and the variability of the population. For example, if you have a sample of 100 people with a 99% confidence level, the margin of error could be approximately 3%. This means that the true value for the statistic (such as the mean) could lie somewhere between 3% above or 3% below the sample statistic.

In addition, when calculating the confidence interval, you'll need to consider the Z-score associated with the desired confidence level. The Z-score refers to the number of standard deviation units away from the mean. For example, a confidence level of 95% would have a Z-score of 1.96, whereas a confidence level of 99% would have a Z-score of 2.58.

A Z score is a quantitative measure used to evaluate the difference between an individual�s score and the average (or mean) score of a group. It is expressed in terms of the number of standard deviation units away from the mean score of the given group. A Z score, also known as a standard score, is used to help compare scores that are from different distributions. It is a summary statistic that measures the distance between a particular value and the mean value of a dataset. Positive Z scores indicate that the value is above the mean, while negative Z scores illustrate that the score is below the mean. The magnitude of the Z-score helps to give a better understanding of how far away the particular value is from the mean. In medical statistics, Z scores can be used to determine if a patient's values are significantly different from the population mean. By examining a patient�s Z score for a particular outcome, a doctor can decide if the patient's outcome is expected or unexpected. This information can then be used to develop an appropriate treatment plan.To calculate a Z score, we need to know the value we are assessing, the mean of the data set, and its standard deviation. The formula for calculating Z-Score is:Z = (x - �)/ _ Where x is the value being compared, � is the mean of the data set and _ is the standard deviation of the data set. By understanding what a Z score is and how to calculate it, medical students will be able to accurately assess a patient�s results and develop an appropriate treatment plan.A Z score, also known as a standard score, measures how far away a particular data point is from the mean or average of a dataset. It is calculated by subtracting the mean from a value and then dividing by the standard deviation. It is expressed in terms of the number of standard deviation units away from the mean.For example, if a data set has a mean of 50 and a standard deviation of 10, then a Z score of 1 would be 60 because it is one standard deviation higher than the mean. This means that the value is one standard deviation above the mean. Conversely, a Z score of -1 would be 40, which is one standard deviation lower than the mean.

Z Score is an important statistical tool that medical students need to understand when studying specific data sets. This value measures the distance between a single value and the mean value of a group or set of data. It tells us how many standard deviations away from the mean our single value is.

To calculate a Z Score, simply subtract the mean from the value you wish to measure and divide that number by the standard deviation of the data set. For example, if the mean value of a data set is 25 and the standard deviation is 5, then the Z Score for a value of 27 would be (27-25)/5 = 2/5 = 0.4.

The advantage of using a Z Score is that it allows us to compare different sets of data and take into account any differences in variation or central tendency. Knowing a Z Score can also help medical students analyse data more effectively and make informed decisions.

The Z score is a measure of how many standard deviation units away from the mean a particular value lies. For example, if a value lies 1.2 standard deviation units away from the mean, then it's Z score would be 1.2. This is useful for helping medical students to compare and contrast values in a dataset. Z scores are important because they help to assess the relative importance of any given value within a set of numbers. For example, if a student was looking at two sets of patient data, they could calculate the Z scores of each set of data. If one set had a higher Z score than the other, it could be concluded that this set of data had a greater importance or influence on the outcome. Z scores can also be used to determine how likely it is that a certain value is to occur. For example, if a Z score is particularly high, then it is more likely that the value will occur than if the Z score is low. By understanding the likelihood of a certain value occurring, medical students can accurately form assumptions and predictions.