Difference Between Descriptive vs Inferential Statistics
Table of Contents
- jaro Education
- 24, June 2024
- 3:00 pm
Statistics is the basis of data analytics because it is the key instrument for recognizing trends and patterns in large numerical data sets. This field in math involves two levels: Descriptive vs Inferential Statistics. In this case, we explore the difference between descriptive and inferential statistics, their types, and their importance. Though some methods of measurement can overlap, their objectives are at a rather wide distance. Thus, it is of utmost importance to identify the key differences between descriptive and inferential statistics analysis.
What is Descriptive Statistics?
The analysis of data is termed descriptive statistics, which assists in describing, presenting, and giving an important summary of data. It is an easy way of describing our data. Descriptively, we find that statistics is very helpful in presenting our raw data in an effective/meaningful manner through numericals, or graphs, or tables. In the absence of descriptive statistics, it would be difficult to do:
It enables us to be able to visualize data, particularly when we are dealing with a vast amount of data.
The use of descriptive statistics will therefore help us to be in a position to display the information in a more meaningful manner, which enables easier interpretation of data. The only thing to note, however, is that the latter is a common kind of statistic that is performed on previously known data.
What is Inferential Statistics?
Data is taken on the sample, and conclusions or inferences are drawn in inferential statistics, making conclusions concerning the greater population from which the sample was taken. The inferential goal As noted in the introduction, the inferential goal of the project is to get to know more about the history of Shoreline Library SMS.
The purpose of statistics is to draw conclusions from a sample of observations and then apply these conclusions to the population. It characterizes the likelihood of the qualities of the sample by probability theory. The most popular methods are hypothesis tests, Analysis of variance, etc.
As an example, consider that our data of interest is the exam marks of all the Indian students. However, it is not possible to gauge the marks of all the students in India in the exams. Now, we are going to measure
the symbols of a small sample of students, such as 1000 students. Such a sample will now constitute a great number of Indian students. This is one of the samples we would take into consideration.
Statistical study to be able to study the population from which it emerges. The mechanism of the attainment of the objectives is known as:
This is what is known as sampling. However, what should be emphasized is that the sample obtained should be representative of the population. That is, it is essential that the sample should be an accurate representation of either the population, or it would result in sampling error and consequently
incorrect findings.
How Do the Types of Descriptive Statistics Help in Data Analysis?
Descriptive statistics could be compared with the tools of the world of statistics as the summary ones. At school, when you are writing a school project, doing market research, or studying business trends, these kinds of statistics can be used to interpret raw numbers easily and clearly and concisely. When, instead of sorting through heaps of data, they need to mark tendencies, dynamics, and other discoveries in a few clicks, descriptive statistics can be a thing.
We will decompose why the varieties of descriptive vs inferential statistics analysis, such as mean, median, mode, range, and standard deviation, can have such a strong influence in rendering facts more reasonable. No confusing technical terms, no brain-twisting math; no learning how to do it, but how to apply it in real life.
1. Central Tendency Measures
Central tendency, the term used, means the centre or mean of a set of data. It provides the answer to the following question: What is a typical or the most frequent value?
- Mean (Average)
Most individuals associate the term average and think with the mean. When you are compiling a data set, all you do is add the sum of all the numbers and divide the answer by the total number of numbers in this set.
For example, when five students score 70, 75, 80, 85, and 90 on a test, the mean would be (70+75+80+85+90)/5 = 80. It provides a brief overview of performance.
- Median
The centre point of the numbers in a line is the median. For an odd number of values, the median is located in the middle. In this case, the median is calculated as the average of the two middle values.
The usefulness of the median is that it does not change with very large or very small figures, which are referred to as outliers. Among a list of earnings such as 20K, 25K, 30K, 1L, the median will give a more accurate impression of the average earnings as compared to the mean.
- Mode
A mode is the value that occurs most in a set of data.
Example: In a shoe shop, when the numbers 7, 8, 8, 8, 9, 10 are sold as follows (7, 8, 8, 8, 9, 10), then the mode is 8.
This assists the businesses in learning the preferences of the customers.
2. Measures of Dispersion (Spread)
Whereas central tendency helps us know where the centre lies, dispersion helps us know how widely spread the data is. This aids in the appreciation of variability, whether the values are stable or not.
- Range
The difference between the largest and smallest values in an index of a dataset is the range.
Examples: The scale of the temperature may also be interpreted as: the lowest temperature during a week = 18 o C and the highest = 32 o C, then the range = 14 o C: 32 o C – 18 o C.
It provides a close indication of the volatility of the values.
- Variance
Variance is the extent to which values in the data set deviate from their mean. When the variance is higher, it implies that the values are sharply distributed.
It is mostly applied in higher-level analysis and forms the pillar of standard deviation.
- Standard Deviation
This is the most popular and important statistical tool. It reveals to you how narrow or wide the range is in which the data points are tightly grouped around the mean.
Example: Assuming that the average on a test was 80 and most of the students scored an average of 78-82, then the standard deviation would be low, and this implies that the scoring was consistent.
3. Frequency Distribution
This will demonstrate how frequently you find each value or set of values in your data. You do not just write the list of numbers, but create groups to identify patterns better.
The example would be: Suppose 5 students had A, 10 had B, 8 had C, and 2 had D. A frequency table will assist you in getting a view of the number of students who are in the same grade categories.
Graphical Methods to Display Frequency Distributions:
- Bar Charts are awesome when you want to compare two categories, such as grades or survey questions.
- Histograms: These are helpful in the display of the range of continuous data, such as age or weight.
- Pie Charts: These are the best charts to display percentages, such as market share or budget distribution.
Such images simplify the visualization of large amounts of data significantly, and they work wonders on a presentation or a report!
How the Types of Inferential Statistics Methods Simplify Hypothesis Testing?
Inferential statistics enables us to generalise or make a guess about a population based on a sample observation. Inferential statistics, unlike descriptive vs inferential statistics, in which we only summarise and analyze data, allows us to make generalizations beyond the data at hand.
Inferential statistical methods are of several types, as each of them is used in different cases. Here is a summary of the most popular of them:
1. Hypothesis Testing
Hypothesis testing is a tool that is employed to arrive at decisions based on the features of a population using a sample. It is a process of determining whether an assumption (termed a hypothesis) is valid with statistical evidence.
Example:
An organization would be interested to see whether a new training regime enhances the performance of the employees. They take sample statistics of the workers who completed the program and then test the hypothesis to find whether there exists a statistically significant improvement.
Standardized tests:
- T-test: Uses the values of the means of two distributions.
- Z-test: Applied in the occurrence of a large sample size or a known population variance.
- Chi-square test: Tests whether there is a relationship between categorical variables.
- ANOVA (Analysis of Variance): It is used to compare the means of 3+ groups.
2. Confidence Intervals
A confidence interval is an estimate of a range of values in which a population parameter (such as a mean or a proportion) is believed to fall, with some defined level of confidence (most often 95 percent).
Example:
Suppose a survey indicates that 60 percent of the respondents choose product A; a 95 percent interval estimate is taken as [56%, 64%]. This implies that with 95 percent confidence, the actual preference within the population is recorded to be anywhere between 56 and 64 percent.
3. Regression Analysis
Regression analysis in this case is applied to analyze the association of a single dependent variable with one or more independent variables.
Form of regression:
- Simple Linear: Examines the correlation of two variables (e.g., income vs spending).
- Multiple Regression: It uses more than a single predictor variable group (e.g., to examine the impacts of income, education level, and age on spending).
Example:
A firm may employ the tool of regression to determine the impact of advertisement investment (independent variable) on sales (dependent variable).
4. Correlation Analysis
The correlation analysis would determine the relationship between two variables with the degree of closeness and direction.
Key term:
Correlation coefficient (r): It is between -1 and +1.
+1: It is a perfect relationship (positive)
R-1 = perfect negative relationship
0 = no correlation
Example:
A positive correlation between exercise and happiness may be arrived at by a study where, as the levels of exercise increase, the same happens to happiness levels.
5. Analysis of Variance (ANOVA)
ANOVA is applied where the means of three or more groups are compared to determine whether one of the groups differs significantly.
Example:
An investigator would like to know whether three colleges would score differently on a math test. ANOVA will allow an understanding of whether any of the colleges are characterised by some significant difference in their effectiveness.
6. Bayesian Inference
Bayesian Inference Bayesian Inference Bayesian Inference is a method of statistical inference, where the probability of a hypothesis is updated in light of new evidence using the Bayes Theorem.
Example:
Suppose you have an 80 percent degree of belief that a coin is fair, then you flip the coin and observe heads 8 times out of 10 throws, then Bayesian inference can assist you in changing your opinion regarding the fairness of the coin in light of the new evidence.
7. Non-Parametric Tests
They are the tests that do not presuppose that the data have a particular distribution (e.g., Gaussian distribution). They come in handy, particularly when the data has an ordinal distribution or is not normally distributed.
Common examples:
- Mann-Whitney U test
- Wilcoxon Signed Rank Test
- Kruskal-Wallis Test
Example:
Where the test scores are strongly skewed or are those with outliers, it is possible to analyze them better and efficiently using non-parametric tests.
Why Descriptive and Inferential Statistics Essential for Data Analysis?
Two major tools of data analysis are descriptive vs inferential statistics, whose functions are different but complementary. The raw data can be simplified and summarised in an easy-to-understand form with the aid of descriptive vs inferential statistics that can be presented in the form of averages, percentages, tables, and charts. This will be a clear and immediate look at the data to see how it has certain patterns, trends, and distributions. Inferential statistics, on the other hand, take a step further by enabling the analysts to predict a greater population using a sample of the population. Hypothesis testing, confidence interval, and regression analysis are some of the techniques that data scientists and researchers can use to make informed decisions on data without necessarily identifying the entire dataset.
The two statistics branches combined present the full picture of working with data—descriptive vs inferential statistics enable comprehending what is going on in the stake, whereas inferential statistics tell how or what might proceed. When addressing situations in such spheres as business, healthcare, education, and social sciences, the integration of the two practices will
Major Difference Between Descriptive and Inferential Statistics
| Basis of Comparison | Descriptive Statistics | Inferential Statistics |
|---|---|---|
| Definition | Summarizes and presents raw data in a meaningful way | Makes predictions or generalizations about a population based on a sample |
| Purpose | To describe the characteristics of a dataset | To conclude or make decisions beyond the available data |
| Scope | Focuses only on the data that is collected | Goes beyond the collected data to make estimates or test hypotheses |
| Techniques Used | Mean, median, mode, standard deviation, tables, graphs | Hypothesis testing, confidence intervals, regression, ANOVA, etc. |
| Data Requirement | Uses complete data from a population or sample | Uses data from a sample to infer about the population |
| Results | Results are Static and certain | Here, the results are Probabilistic and uncertain |
| Examples | Calculating average marks in a class | Predicting election results based on a voter sample |
| Application | Data summarization and presentation | Decision-making and forecasting |
| Visualization Tools | Bar charts, pie charts, histograms, and tables | Not typically visual, more statistical computations |
Conclusion
Descriptive vs inferential statistics are important categories in statistics. Descriptive vs inferential statistics focus on summarizing data to reveal its characteristics and patterns. Meanwhile, inferential statistics use sample data to make predictions and draw conclusions about a larger population.
Both types of statistics are essential for data analysis, complementing each other to provide a complete understanding of datasets. This blog has explained these concepts clearly, highlighting their differences with practical examples. Understanding descriptive vs inferential statistics helps analysts and researchers make informed decisions in their work across different fields.
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