Knowing how to work with statistics is essential if you are pursuing a career in data science. But have you ever taken a moment and considered what statistics genuinely are? To the average person, statistics are just a series of numbers and other random information that clever people use to prove their point. However, statistics is both a subtle and complex concept that requires a closer look.

Experts define statistics as a science or a branch of mathematics that encompasses the collecting, classification, analysis, interpretation, and presentation of numerical facts and data. Statistics are especially handy when analysts must work with vast populations that are too extensive for specific, detailed measurements. Statistics are necessary for drawing general conclusions that relate to datasets taken from a data sample.

Statistics have two distinctive branches: descriptive and inferential. Today, we look at inferential statistics. This article covers the definition, types of inferential statistics, the differences between descriptive statistics and inferential statistics, and more.

Do you know the difference between implying and inferring something? Implying involves giving information, while inferring involves receiving information. When a speaker implies something, they are suggesting something without expressly saying it. When a listener infers something, they deduce or reach a conclusion based on reasoning and evidence, rather than from an explicit bit of information.

That goes a lot towards defining inferential statistics. This branch of statistics takes a random data sample from a portion of the population to make predictions, draw conclusions based on that information, and generalize the results to represent the data on-hand.

The best way to get an accurate analysis when using inferential statistics involves identifying the population being measured or studied, creating a sample for that portion of the population, and using analysis to factor in any sampling errors.

If a data analyst took the data results and didn't make any projections, inferences, or generalizations, they would practice descriptive statistics. More on that later.

Inferential statistics employ four different methodologies or types:

- Parameter Estimation. Analysts take a statistic from the sample data and use it to make an informed guess about a population’s mean parameter. It uses estimators such as probability plotting, Bayesian estimation methods, rank regression, and maximum likelihood estimation.
- Confidence Intervals. Analysts use confidence intervals to get an interval estimation for the chosen parameters. They are used to discover the margin of error in research to determine whether if it will affect the testing.
- Regression Analysis. Regression analysis is a series of statistical processes that estimate the relationship between a dependent variable and a set of independent variables. This analysis uses hypothesis tests to determine if the relationships observed in the sample data actually exist in the population.
- Hypothesis Test. Analysts try to answer research questions by using sample data and making assumptions involving the population parameters. This test determines if the measured population has a higher value than another data point in the analysis. In this practice, you are trying to find the error margin by multiplying the mean’s standard error by the z-score.

Inferential statistics have two primary purposes:

- Create estimates concerning population groups
- Testing hypotheses to draw conclusions involving populations

For example, a data analyst could randomly sample a group of 11th graders in a given region and gather SAT scores and other personal information. Using inferential statistics and the data sample, the researcher could make estimates and test hypotheses regarding 11th graders in the whole country.

Or a political consultant could gather voter information from a specific precinct and establish how many people voted for each presidential candidate. Equipped with that information, the consultant could project how voters would vote for a particular referendum question.

Analysts can also use inferential statistics to predict which movies or television shows have a greater likelihood of success. Data culled from test screenings and focus groups help analysts estimate how viewers will react to a new program and its potential viewership nationwide. We’ll revisit this idea later.

Inferential statistics employ statistical models to help data analysts to compare their sample data with other samples or earlier related research. Most analysts use statistical models called the generalized linear model, including methods like ANOVA (Analysis of Variance), t-tests, regression analysis, and others that produce linear or straight-line probabilities and results.

Say, for instance, you have sample data about an upcoming new television show, gleaned from a sample of the population that watched an “as-yet-unreleased” TV pilot episode. You could use that data to generate a set of descriptive statistics that describe your sample, including:

- Sample mean
- Sample standard deviation
- Creation of a boxplot or bar chart
- A description of the shape of the sample’s probability distribution

That’s a straightforward presentation of the facts, with no speculation or guesswork. But with inferential statistics, you could take that same sample data and try to figure out whether the data can predict if the rest of the national viewing audience will like it.

There are even different ways to predict the outcome, from calculating the z-score to post-hoc testing. Z-scores, also known as standard scores, show how far away a given data point is from the mean, pinpointing its location relative to the bell curve, otherwise known as normal distribution. Post-hoc testing analyzes experimental data results, often based on a familywise error rate (the chance of arriving at a false conclusion in a group of hypothesis tests). Common post-hoc tests include:

- Bonferroni Procedure
- Dunn’s Multiple Comparison Test
- Rodger’s Method
- Dunnett’s Correction

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Now that we know what inferential statistics is, how does it differ from descriptive statistics? We’ve already pointed out that descriptive statistics present data plainly and directly with no speculation on other analytical possibilities, so that’s a start.

Inferential statistics takes random samples of data from a segment of the population and makes inferences about the population as a whole. So, if you asked 100 people if they preferred Cola A or Cola B, and 60 of them chose Cola A, inferential statistics builds on that and assumes that those survey results would be valid for the soda-drinking population in general.

On the other hand, descriptive statistics never take things that far. It tells you that, in one survey conducted in one location, 60 percent of the people surveyed liked Cola A better, and that’s that.

If it appears that inferential statistics is a more complex concept than descriptive statistics, that’s because it is. Descriptive statistics tell you how things stand, based on your data. Inferential statistics uses that data to make a logical leap in predicting future outcomes. Naturally, inferential statistics need more tools to accomplish this ambitious goal, and some of the tools are very complex and involve hard number-crunching, graphing, and charting.

In summary, descriptive statistics give you a single, clear snapshot of your current data findings. Inferential statistics take that same data and make projections based on the data’s results.

Incidentally, we should note that the two statistics share one common trait — they both rely on the same dataset.

Whether you’re interested in descriptive or inferential statistics, the fields of data science and data analytics offer many opportunities for motivated professionals. It’s good to learn both.

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