Inferential statistics is a highly practical field of study where both learners and practitioners often find themselves asking a lot of questions. This article guides you through five common inferential statistics questions, fully explained to dispel the ambiguity that sometimes surrounds this fascinating area of statistics.

Why Inferential Statistics Matters

While descriptive statistics, probability theory, and probability distributions are core foundational areas of statistics, it’s in inferential statistics where most of the concepts are put together in a very practical fashion: statistical inference processes are widely used in research, business, and policy-making, to name a few. Through a repertoire of tools with diverse purposes such as hypothesis testing, it also bridges the gaps between raw data and actionable decisions and insights, constituting an important asset for professionals outside traditional statistics, such as data scientists, marketers, and analysts.

5 Inferential Statistics Questions with Explanations

1. What is the difference between descriptive and inferential statistics?

While descriptive statistics focuses on summarizing and describing facts and characteristics in your data -like average values per variable, skewness, and so on-, inferential statistics goes a step further and makes predictions or generalizations about larger populations through more elaborate techniques like hypothesis testing, confidence intervals, and regression analysis.

2. What is a confidence interval, and how can it be interpreted?

A confidence interval provides a range of plausible values for a parameter that describes a data population — like a mean or a proportion — based on a sample, together with a level of confidence that the range contains the true population value of that parameter.

Suppose 100 households are surveyed about their monthly electricity usage, yielding a sample mean of 500 kWh with a 95% confidence interval of [475 kWh, 525 kWh]. The 95% means that if the sampling and experiment were tried infinitely many times, about 95% of the resulting intervals would contain the true population mean. Narrower confidence intervals (like [490 kWh, 510 kWh]) signify more precise estimates, whereas wider intervals imply higher uncertainty in the estimate.

3. What is the p-value in hypothesis testing, and how it is used?

The p-value is a helpful statistical metric used in hypothesis testing to evaluate the likelihood of obtaining the observed data, under the assumption that the null hypothesis (explained shortly) is true. Given two data samples of students’ scores before and after introducing a new teaching method, let us suppose that you’re testing whether the new method improves average test scores. In this scenario, a p-value of 0.03 would mean that assuming the null hypothesis (that the new teaching method has no effect) is true, there is a 3% probability of observing the given difference in average scores — or a more extreme one — purely due to random variation. This low probability, in other words, is an indicator of differences between groups of average scores being statistically significant.

If the p-value were higher than 0.05, this would suggest that the observed difference in average scores is not statistically significant at the 5% significance level. This means there is insufficient evidence to reject the null hypothesis, and any observed difference might reasonably be attributed to random variation rather than the effect of the new teaching method.

4. What is the null hypothesis, and how does it differ from the alternative hypothesis?

The null hypothesis is a starting point or “status quo” assumption that there is no effect or relationship between what we’re studying: rejecting it normally means providing evidence that the effect or relationship being tested does exist. For example, when testing if a new medication reduces glucose levels, our null hypothesis would be, “This medication does not affect glucose levels.” Data are then collected to determine if there’s strong enough evidence to reject this default assumption. While it is possible to gather sufficient evidence to reject the null hypothesis with a specified level of confidence (typically when a p-value is below 0.05), the alternative hypothesis — which describes the existence of an effect or relationship — cannot be proven true with absolute certainty. This approach enforces scientific rigor by requiring substantial evidence before claiming the existence of any real effects.

5. What is the difference between parametric and non-parametric statistical tests?

Parametric tests make a series of assumptions about the underlying distribution and characteristics of the data, such as normality (which means the data follows a normal or Gaussian distribution), homogeneity of variances (equal variances across several data groups), etc. They include well-known tests like the t-test (used for comparing means of two groups), ANOVA (for comparing means across multiple groups), and Pearson’s correlation (for analyzing linear relationships between variables). Importantly, using parametric tests requires meeting the aforesaid assumptions to ensure the validity of the conclusions; otherwise, the results obtained cannot be deemed reliable.

Meanwhile, non-parametric tests become handy when no parametric assumptions like normality can be made. This is the case of certain types of datasets like ordinal data, ranked data, heavily skewed data, or datasets with outliers causing the non-reliance on results of parametric tests. Given their versatility, they are particularly helpful for testing aspects like differences in medians, ranks, or distributions, as well as for analyzing binary, categorical, or ordinal data. Common examples of non-parametric tests and their uses are:

• Mann-Whitney U test: a test utilized to compare the medians of two independent groups
• Wilcoxon signed-rank test: used to compare paired data groups -like “before” vs. “after” measurements- without normality assumptions
• Kruskal-Wallis test: the non-parametric counterpart to ANOVA to compare medians among multiple groups

You can find more about the types of parametric and non-parametric tests, along with guidelines for choosing the right test for your problem, in this article.

Wrapping Up

 
This article explained five burning questions anyone interested in inferential statistics often comes across. From confidence intervals to p-values to types of statistical tests, the explained questions provide a compass to help you better navigate the ample variety of statistical inference tools and methods.