Descriptive Statistics vs Inferential Statistics Bradley University Online

Descriptive statistics is used to describe and organize data while inferential statistics draw conclusions about the population from samples by using analytical tools. Inferential statistics is a field of statistics that uses several analytical tools to draw inferences and make generalizations about population data from sample data. Descriptive and inferential statistics are used to describe data and make generalizations about the population from samples. The table given below lists the differences between inferential statistics and descriptive statistics. As I mentioned above, you may use hypothesis testing, determining relationship among variables through correlation and regression, or you may make a predictions through a statistical model. Let’s say you wanted to know the favorite ice cream flavors of everyone in the world.

However, descriptive statistics does not allow us to make any conclusions beyond the data. Two important types of descriptive statistics include the Measures of Central Tendency and Measures of Dispersion. However, descriptive statistics will describe the characteristics of only this group of 100 families. This group of data that contains all the data that you are interested in describing is called population.

Range, standard deviation, variance, quartiles, and absolute deviation are the measures of dispersion. Even though inferential statistics uses some similar calculations — such as the mean and standard deviation — the focus is different for inferential statistics. Inferential statistics start with a sample and then generalizes to a population. Instead, scientists express these parameters as a range of potential numbers, along with a degree of confidence.

In Inferential Statistics, the focus is on making predictions about a large group of data based on a representative sample of the population. A random sample of data is considered from a population to describe and make inferences about the population. This technique allows you to work with a small sample rather than the whole population. Since inferential statistics make predictions rather than stating facts, the results are often in the form of probability. Multiple linear regression is a regression model that estimates the relationship between a quantitative dependent variable and two or more independent variables using a straight line.

I am Kusum Wagle, MPH, WHO-TDR Scholar, BRAC James P. Grant School of Public Health, Bangladesh. I have successfully led and coordinated different projects involving multi-sector participation and engagement. Moreover, I am also regularly involved in the development of different national health related programs and its guidelines. Inferential Statistics refers to a discipline that provides information and draws the conclusion of a large population from the sample of it.

In ANOVA, the null hypothesis is that there is no difference among group means. If any group differs significantly from the overall group mean, then the ANOVA will report a statistically significant result. A factorial ANOVA is any ANOVA that uses more than one categorical independent variable. Measures of central tendency give you the average for each response. The test statistic will change based on the number of observations in your data, how variable your observations are, and how strong the underlying patterns in the data are.

Categorizing Statistics

Virtually any quantitative data can be analyzed using descriptive statistics, like the results from a clinical trial related to the side effects of a particular medication. Combined with probability, inferential statistics becomes a very powerful tool for making inferences and predictions about large populations. This provides a quick method to make comparisons between different data sets and to spot the smallest and largest values and trends or changes over a period of time. If the pet shop owner wanted to know what type of pet was purchased most in the summer, a graph might be a good medium to compare the number of each type of pet sold and the months of the year. This same pet shop may conduct a study on the number of fish sold each day for one month and determine that an average of 10 fish were sold each day. The range is the difference between the highest value and the lowest value in a data set.

descriptive vs inferential statistics

A paired t-test is used to compare a single population before and after some experimental intervention or at two different points in time . If you want to compare the means of several groups at once, it’s best to use another statistical test such as ANOVA or a post-hoc test. Testing the combined effects of vaccination and health status (healthy or pre-existing condition) on the rate of flu infection in a population. The test statistic you use will be determined by the statistical test. In most cases, researchers use an alpha of 0.05, which means that there is a less than 5% chance that the data being tested could have occurred under the null hypothesis.


The Akaike information criterion is one of the most common methods of model selection. AIC weights the ability of the model to predict the observed data against the number of parameters the model requires to reach that level of precision. The confidence level is the percentage of times you expect to get close to the same estimate if you run your experiment again or resample the population in the same way.

descriptive vs inferential statistics

Here, weight is a single variable, we found a characteristic of this variable by finding the average weight. To understand the variation in the weight variable, we can explore this further by plotting a histogram or kernel density plot . This analysis of a variable itself is known as univariate analysis and we shall dwell on this further in the upcoming Univariate analysis article. The following example illustrates how we might use descriptive statistics in the real world. Apart from these tests, other tests used in inferential statistics are the ANOVA test, Wilcoxon signed-rank test, Mann-Whitney U test, Kruskal-Wallis H test, etc. ToolsDescriptive statistics mostly use following statistical measures i.e.

Public Health Notes

We have seen that descriptive statistics provide information about our immediate group of data. For example, we could calculate the mean and standard deviation of the exam marks for the 100 students and this could provide valuable information about this group of 100 students. Any group of data like this, which includes all the data you are interested in, is called a population. A population can be small or large, as long as it includes all the data you are interested in.

Therefore, inferential statistics uses probability theory to ascertain if a sample is representative of the population or not. This process of checking for samples being a true representation of the population is obtained by sampling. Though the important measures of central tendency parameters are mean, median, and Mode, other parameters also fall under Measures of location, which also help describe the data. Measure of central tendency refers to a single value that summarizes or describes a dataset. The USP of the measure of central tendency is that this single value represents the middle or the center value for the dataset.

A hypothesis test can be left-tailed, right-tailed, and two-tailed. Given below are certain important hypothesis tests that are used in inferential statistics. The tools used in descriptive and inferential statistics are measures of central tendency, measures of dispersion, hypothesis testing, and regression analysis. Inferential statistics is a branch of statistics that makes the use of various analytical tools to draw inferences about the population data from sample data.

The mean of a chi-square distribution is equal to its degrees of freedom and the variance is 2k. A histogram is an effective way to tell if a frequency distribution appears to have a normal distribution. Categorical variables can be described by a frequency distribution. Quantitative variables can also be described by a frequency distribution, but first they need to be grouped into interval classes. Also called the multiplier, the critical value is standard for these confidence level values. The margin of error is calculated by multiplying the critical value by the confidence level .

To understand the inferential statistics definition, we need to first understand what the term population means in statistics. Population refers to the entire raw data that you are interested in and need to analyse. Descriptive statistics, for instance, are applied to the entire population data.

As a researcher, you must know when to use descriptive statistics and inference statistics. Using both of them appropriately will make your research results very useful. It is also important to understand the difference between data and information.

A regression model can be used when the dependent variable is quantitative, except in the case of logistic regression, where the dependent variable is binary. The only difference between one-way and two-way ANOVA is the number of independent variables. A one-way ANOVA has one independent variable, while a two-way ANOVA has two. Significant differences among group means are calculated using the F statistic, which is the ratio of the mean sum of squares to the mean square error .

  • This means that the 99.78th percentile is the value below which 99.78% of the observations fall.
  • Hypothesis testing and regression analysis are the types of inferential statistics.
  • For this reason, it is necessary to do a simple linear regression analysis to prove whether height really has a significant influence on mathematical values.
  • Most simply, a confidence interval is a way to measure how well the sample reflects the population under study.
  • Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Most simply, a confidence interval is a way to measure how well the sample reflects the population under study. Suppose you were teaching a class of 25 students, and you wanted to know what the average score was for the test that you just gave. descriptive vs inferential statistics You would use descriptive statistics; you are interested in the performance of that particular set of students. One limitation of descriptive statistics is that they do not allow us to make any inferences about the population at large.

( Regression Analysis

Inferential statistics will use this data to make a conclusion regarding how many cartwheel sophomores can perform on average. Here, \(\overline\) is the mean, and \(\sigma_\) is the standard deviation of the first data set. Similarly, \(\overline\) is the mean, and \(\sigma_\) is the standard deviation of the second data set. In descriptive statistics, we can take a sample according to our interest and analyze data to present its properties.

Statology is a site that makes learning statistics easy by explaining topics in simple and straightforward ways. Sometimes we’re interested in estimating some value for a population. For example, we might be interested in the mean height of a certain plant species in Australia.

Top 10 Powerful Data Modeling Tools to Know in 2023

Inferential statistics can be defined as a field of statistics that uses analytical tools for drawing conclusions about a population by examining random samples. The goal of inferential statistics is to make generalizations about a population. In inferential statistics, a statistic is taken from the sample data (e.g., the sample mean) that used to make inferences about the population parameter (e.g., the population mean). In this method, the dispersion of the study data from the average is considered. The three measures of dispersion are range, variance, andstandard deviation. Range is the difference between the largest and smallest values in the data set.

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