# Parameter vs Statistic: Unpacking the Key Differences

- Author: Noreen Niazi
- Last Updated on: January 14, 2024

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ToggleKnow which is best and most precise in data analysis between Parameter or statistics? If you are unaware of what distinguishes parameters from statistics, this guide will be helpful to you.

Parameters and Statistics are key words in statistics, and data analysis is fundamental to understanding the nuances between them. In this article, I will discuss the essential aspects of parameter vs statistic and how they are used in statistical data analysis.

## Introduction to Parameter vs Statistic

Both variables and means are important concepts in data analysis, statistics and handling of information. When we mention the Parameter , it is a characteristic of a population, while an average represents that

But what does one mean by population? A population is a complete collection of people or things that we are interested in studying. A sample, on the other hand is a part of the population that we analyze and collect data from.

For instance, the mean height of all adults in a city. These are all adults in the city, and we randomly select a random group of adults from this population to measure their height considered as an observational sample.

## Parameter vs Statistic: Key Differences

Parameter vs statistic both look the same for their purpose. But there are some key differences between both of them.

The** main difference** between parameters and statistics is their relationship to the population and the sample. Parameters are** characteristics of the population,** while statistics are **characteristics of the sample**. Parameters are f**ixed and unknown**, while statistics **can vary and are calculated from the sample**.

**Another key difference **is that parameters are usually estimated using** inferential statistics**, while statistics are calculated using **descriptive statistics**. Inferential statistics involve making ut the population based on the sample data, while descriptive statistics summarize the sample data.

## Importance of Parameter vs Statistic in Data Analysis

It is because parameters and statistics are important in data analysis; they enable us to make conclusions about the population based on what we find from sample data. These concepts are only able to highlight the sample and not the population.**Example**

For example, assume we want to assess whether new drugs for treating a specific disease are effective. To accomplish this, we should carry out a **randomized controlled study** using the pool of patients with the disease and give half of them drug and other half placebo. We can then determine the difference in the proportion of patients who recover within each group. Statistic is the difference in sample, and parameter refers to the population. **With inferential statistics**, we can develop a hypothesis test to conclude if the difference in samples is statistically significant and generalizable.

## Parameters and Statistics in Data Analysis

There are many parameters and statistics. Here are a few:

**Population means and sample mean**: The mean of the population is the average value of a particular variable across the whole population. However, the variable average in the sample is known as the sample mean. To get the population means, the sample mean is calculated.**Population proportion and sample proportion**: A variable’s population proportion is its portion over the entire population, whereas its sample proportion is its proportion within the sample. To calculate the population proportion, one uses the sample proportion.**Population variance and sample variance:**A variable’s variability throughout the entire population is known as the population variance, but its variability inside a sample is known as the sample variance. To calculate the population variance, one uses the sample variance.

## How to Calculate Parameters and Statistics

We need formulas that depend on the variable type and the measurement level to calculate parameters and statistics. Here are a few examples:

**Population means:**Calculating the population mean involves adding up all of the population’s values and dividing by the total number of values.

$$\text{Population means}(\mu)=\frac{\text{sum of all values in population}}{\text{number of values}}$$

**Sample mean:**When calculating the sample mean, the sample size is divided by the sum of all the sample values.

$$\text{Sample means}(\bar{x})=\frac{\text{sum of all values in sample}}{\text{number of values}}$$

**Population proportion:**The population proportion is calculated by dividing the number of individuals with a certain characteristic by the total population size. It is donated by P.**Sample proportion**: The sample proportion is calculated by dividing the number of individuals in the sample with a certain characteristic by the sample size. It is denoted by p.

## Common Misconceptions about Parameters and Statistics:

It’s a frequent fallacy that the sample statistic always underestimates the population parameter when discussing parameters and statistics. While occasionally being true, this is not always the case. Depending on the sampling technique and the population’s variability, the sample statistic may also represent an unbiased or exaggerated estimate of the population parameter.

Another common misunderstanding is that the accuracy of the estimate depends on the sample size. A higher sample size can lessen the estimate’s variability, but this does not imply that the estimate will be more accurate. The sampling strategy and population variability both affect how accurate the estimate is.

## When to Use Parameters and Statistics in Data Analysis

Data analysis should consider parameters and statistics every time we seek to make conclusions about the population from sample data. Scientific research often involves trying to test population hypotheses based on sample data.

But sometimes, parameters and statistics may not be required or suitable in certain circumstances. For instance, if our interest is limited to descriptions of the sample data and we do not want inferences about anything that concerns population parameters then we can use descriptive statistics without estimating.

## Parameter vs Statistic: Which One to Use?

Whether to use a parameter or statistic depends on the study issue and the level of inference that is required. We must use inferential statistics to estimate population parameters in order to make conclusions about the population. Sample data can be described using descriptive statistics only, without calculating the population factors.

## Conclusion: The Importance of Understanding Parameters and Statistics in Effective Data Analysis

In summary, both statistics and data analysis rely on the notions of parameters and stats. The differences between the population have to be known in order to analyse and infer about them from sample data effectively. Able to calculate parameters and statistics, we might estimate population parameters estimates on the data from sample.

## References

- Statistics.com. (https://www.statistics.com)
- Laerd Statistics. (https://statistics.laerd.com)
- Khan Academy. (https://www.khanacademy.org)
- Investopedia. (https://www.investopedia.com)
- ThoughtCo. (https://www.thoughtco.com)
- Stat Trek. (https://stattrek.com)
- Simply Psychology. (https://www.simplypsychology.org)
- CliffsNotes. (https://www.cliffsnotes.com)
- Coursera. (https://www.coursera.org)
- Statista. (https://www.statista.com)

## FAQs

There is a difference between the roles of parameters and statistics. A parameter is a numerical value that depicts some characteristic of a population, while statistic notations refer to some kind of spiritum number.

A2: Parameters are used to make inferences on a population, which in turn guide the decision-making processes. On the other hand, statistics are derived from sample data and used to estimate or infer population parameters.

Certainly. A parameter is an average income of all residents in a city. A statistic would be the average income of a subset of residents.

Inferential statistics utilize sample stats to draw conclusions about population parameters. It is about reaching conclusions on a population using sample and accepting an element of doubt.

Very rarely, when the whole population is surveyed (census), it can happen that both sample and population values are equal to create a statistic as well as parameter.