Applied Statistics For Health Care Professionals

Introduction

Statistics is everywhere. We use it to analyze our favorite sports teams, describe the weather, and even to predict what might happen in the future. The best way to understand applied statistics is by using them! In this article, you’ll learn about how statisticians use descriptive statistics, inferential statistics and hypothesis tests to answer questions about populations of interest.

Introduction to Statistics; Descriptive and Inferential Statistics

The first step to understanding statistics is to understand what it means to describe data. Descriptive statistics is the process of describing a set of numerical values or measures in terms of their distribution, or how they’re distributed relative to one another.

For example, suppose we have 20 students who took math tests and their scores are listed below:

Score Range Mean Median Mode SD I1 100-125 75 90 70 130 I2 100-125 110 90 50 120 II1 125-140 100 100 80 145 II2 125-140 115 85 60 140 III 125 135 90 70 150 IV 135 140 95 90 155 V 140 145 105 95 160 VI 145 150 110 100 165 VII 150 155 115 105 170 VIII 155 160 120 110 175 IX 160 165 125 115 180 X 165 170 130 120 185 XI 170 175 135 125 190 XII 175 180 140 130 195 XIII 180 185 145 135 200 XIV 185 190 150 140 205 XV 190 195 155 145 210 XVI 195 200 160 150 215 XVII 200 205 165 152 220 XVIII 205 210 170 154 225 XIX 210 215 173 156 230 XX 215 220 176 158 235 XXI 220 225 179 160 240 XXII 225 230 181 162 245 XXIII 230 235 184 164 250

Definition of Probability (theoretical)

Probability

Probability is a measure of the likelihood that an event will occur. It can be viewed as a number between 0 and 1, or by how often something happens in comparison to other things happening at the same time. Probability is often used in statistics to describe probability distributions (more on that later), but it’s also important for understanding randomness in our lives because it helps us understand why certain things happen more often than others.

Discrete and Continuous Distributions; Sampling Distributions

• Discrete distributions: values are only whole numbers.

• Continuous distributions: values can be any number in a specified range.

• Sampling distribution: the distribution of sample means used to estimate population parameters (e.g., mean, standard deviation and standard error) or predictability measures (e.g., probability).

The Normal Distribution, Z-scores, Characteristics of the Normal Curve

In this section, you’ll learn about the normal distribution and how to calculate a z-score. You’ll also learn about the characteristics of the normal curve.

What is a distribution?

A distribution describes how often something occurs in a population, based on an assumed mean (average) and standard deviation. For example, there are many ways to measure weight and height—for example: average weight/height among American adults is 70 kg/1 m2; average weight/height among American children aged 6-11 years old is 60 kg/1 m2; etcetera—but these measurements do not have any meaning unless they’re compared against each other within some context (for example: comparing them with respect to age). Without some way of making sense out of all these numbers though we could end up with rather meaningless statements like “the average American adult weighs 72 kgs.” A common method used to compare such data sets involves drawing their probability density function (PDF) curves on axes labeled “weight” versus “height” so that we see which range(s) contain most people within each category; if you look at those PDF curves I’ve drawn here then you’ll notice that they fit together like pieces in an jigsaw puzzle!

Critical Values for Normal Curve

The normal curve is symmetrical, meaning that the mean, median and mode all lie at the same point. The standard deviation (σ) is equal to 1.96 times the square root of variance; therefore, if we have n data points with a mean of μ and standard deviation σ then we have:

μ = MEAN(n) + ROUNDDOWN(1/2 * SQRT(variance))

Where MEAN(n) is simply called ‘the mean’ or ‘average’ value for each data point in our set; ROUNDDOWN() gives us an approximation by rounding down rather than up (i.e., using only integers greater than zero).

Critical Values for the Chi-Square Distribution

The critical values for the chi-square distribution are not the same as P-values. In fact, they are obtained from a table of critical values that includes the following:

• The value of α (the probability of a Type I error)

• The degrees of freedom (n – k), where n is your sample size and k is your number of categories in your variable set up to be tested against each other.

Sampling distributions – Standard Error of the Mean, Standard Error of Proportion, Standard Error of Difference

The standard error of the mean is a measurement that describes how closely your sample’s average value fits with its population value. It is calculated by taking the square root of (1/N) × (SD/N) where SD is standard deviation and N is sample size. In other words, it’s just like an average except that instead of measuring an entire group’s performance, you’re looking at individual scores on a test or exam.

The standard error of proportion (SEP) tells us how much variability there is in our results for a given measure: if we have 100 people taking a test and our results are normally distributed with a mean score equal to 60 and standard deviation equal 30 points then half will get scores between 50-60 while half will get scores above 70

Introduction to Hypothesis Testing; Type I and Type II Errors; Level of Significance (alpha)

Hypothesis tests are used to determine if a particular treatment or intervention is effective or not. The null hypothesis states that the difference in means between two groups will be equal to zero, and the alternate hypothesis states that this difference does not exist.

The level of significance (alpha) is an indicator of how confident we are about concluding whether or not our results support our hypotheses. It can range from 0% (highly confident) to 100%, with lower values indicating more confidence in your conclusion. The higher your alpha value, the less likely you’ll make an error when interpreting your results; however, this also means that there’s less room for error when conducting statistical analyses on your data set!

If you have an alpha value greater than 0%, then we consider ourselves 99% certain that our findings fully support our hypotheses; however, if we had been able to collect more information about each patient group before conducting statistical analysis—like age or gender—then we’d want another type of test performed first so as not risk making any mistakes while analyzing all those additional variables at once:

Constructing a Research Question/Hypothesis

When you’re designing a study, it is important to answer the following questions:

• What are the null and alternate hypotheses?

• How will they be tested?

The most common way to test a hypothesis is by conducting an experiment. To do so, you must first construct your research question (or statement) and formulate an appropriate hypothesis that matches this question. Once you have formulated your hypothesis, write out each part of it in detail before moving on to its testing phase.

Null and Alternate Hypothesis Representation

The null hypothesis is the default. It’s what you assume to be true, and it’s the most well-known form of testing. The alternate hypothesis is a specific statement about the variable: “The mean weight of adults in California is between 150 and 200 pounds.” This means that if your sample size isn’t large enough to provide conclusive evidence for either side (i.e., if you’re using a small sample size), then your data cannot support either point on this line but instead can only indicate whether or not there’s any difference between these two groups based on their average weight—a finding which may not be significant enough to reject or accept as factually accurate yet still interesting nonetheless!

One Sample Inferences About the Mean (Z-test)

A Z-test for the mean is used to test if the mean of a sample is significantly different from a hypothesized value.

For example, you may have collected data on the number of patients who had blood tests and found that 80% were positive for diabetes. You decide to use this information as part of your research project, but you want to make sure that it’s not just an outlier—that there aren’t any other strange results in your data set as well. If we look at our original data set (the one with all those zeros), we can see where it would be reasonable to say “there must be something wrong here!” because some values are extremely low or high compared with others:

One Sample Inferences About a Proportion (Z-test)

One sample inferences about a proportion is the same as one-way analysis of variance (ANOVA), but with fewer parameters. The null hypothesis is that the true proportion is equal to the hypothesized value, and the alternate hypothesis is that it’s not.

This can be expressed in terms of proportions:

• Suppose you want to know whether a restaurant serves more customers on Friday nights than any other day of week. You collect data from your restaurant’s receipts for six weeks and record how many customers came into your establishment during each hour of operation. You find that on Fridays there were 20% more customers than other days (the mean number of customers per hour). How many people would you expect come into your establishment on any given day?

Independent Samples t-test; Paired Samples t-test; Analysis of Variance (ANOVA) Test

In this section, you will learn about the following three tests:

• Independent samples t-test

• Paired samples t-test

• Analysis of variance (ANOVA) test

Intuitive understandings of applied statistics.

Statistics is the science of making inferences about populations based on samples. Statistical analysis is the process of deriving meaningful conclusions from data. Statistics is used in many fields, including medicine, psychology and education.

Statistics can be applied to all kinds of problems: healthcare research needs to assess how effective new drugs are at treating certain conditions; you might want to know if a certain type of exercise program helps people lose weight or improve their health; scientists use statistics when they study patterns in nature like weather patterns or animal behavior (e.g., why do some animals hibernate?).

Conclusion

The most important takeaway from this article is that you should approach statistics with an open mind. You can’t go through life without using it at some point, so it’s best to be prepared for when the inevitable happens! The next step is making sure you know how to apply what you learn in real-life situations. Hopefully this article has given some insight into how these tools work and why they matter for health care professionals.