Statistics vs. Parameters: A Comparative Study

While performing research, you often come across the terms statistics and parameters. They play a crucial role in ascertaining the sample size. Statistics give a small value of the target population, while parameters offer a summary of a small group of people. Moreover, statistical data is derived from the measurements of elements in a sample. In contrast, parameters are derived from the calculations of the units of the population. Students pursuing their education in statistics or researching any subject often confuse statistics with parameters. However, both are quite different concepts. If you are one of these students, this blog will be of great help to you. Here, we have explained the concepts, uses, and differences between statistics vs. parameters. Read along to get more details.

What are Statistics?

Statistics refers to any practice or science of gathering and examining large quantities of data, especially to serve the function of inferring proportions in a whole from those in a representative sample. In simple terms, statistics is any measurement that showcases the features of a sample. Here, a sample is a subset of a population.

Here are some examples of statistics:

• The mean height of a model of 1000 seven-year-old brown oak trees planted as a part of an effort to reforestation
• The variance in traveling times of a sample of 1750 daily commuters employed in Manhattan
• The median age of a sample of 4,000 nurses working in the United States of America

In these illustrations, the measurements like mean, variance, and median are all statistics that explain some features of a sample.

The samples in these illustrations were:

• 1000 seven-year-old brown oak trees
• 1750 commuters
• 4,000 nurses working in the U.S.A.

These samples were all gathered from larger populations:

• All the 7-year-old brown oaks planted in the reforestation effort
• The population of all commuters working in Manhattan
• The population of all nurses working in the U.S.A.

What is a Parameter?

In statistics, a parameter is a numerical feature of an entire population. Here, a population is the whole cluster of people, objects, organizations, regions, species, procedures, and cases studied during research.

Here are some examples of parameters:

• The standard life expectancy of Europeans
• The standard deviation of heights for all the NBA players
• The ratio of tickets that go unsold during a baseball tournament

In each of these examples, the quantifications like the average, the standard deviation, and the proportion are all parameters that assist in defining some characteristics of a population. The populations in these examples are the following:

• The whole American population
• The entire set of players in the NBA
• Tickets that went on sale for a baseball tournament

When estimating parameters, we can use confidence intervals. They are similar to fishing with a net instead of a hook. Here, you can analyze a collection of values from a sample and assess how likely it is to include the accurate population parameter at any stage of confidence:

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Differences between Statistics and Parameters

Here is a comparative study of Statistics vs. Parameter.

Statistics vs. Parameters: Types of Numerical

Here is the difference between statistics and parameters in terms of their numerical features:

• Statistics: It assumes parameters using sample data.
• Parameters: These are the fixed numerical values for populations.

Statistics vs. Parameters: Type of Values Offered

Both the Statistics and parameters are useful for data analysis, but they offer different types of values.

• Statistics: It gives values for population inferences.
• Parameters: It gives accurate values.

Statistics vs. Parameter: Definition of Elements

Both statistics and parameters describe some elements, but they are completely different.

• Statistics: It defines samples.
• Parameters: It defines populations.

Statistics vs. Parameters: Volume of Groups Analyzed

The values of statistics and parameters are both determined by groups. However, the volume differs.

• Statistics: Statistics about a group can be determined if the group is large and has many immeasurable and changeable elements.
• Parameters: For a small group, we can easily determine precise parameters.

Statistics vs. Parameter: Types

The subtypes of statistics and parameters are also different.

What are the Different Types Of Statistics?

Statistics are broadly classified into two types:

Descriptive statistics

It permits researchers to define their data based on its aspects or qualities. Examples of descriptive statistics are:

• Values of frequency: It highlights the recurrence of specific values.
• Values of central tendency: It illustrates average or common values.
• Measures of dispersion or variation: It depicts the distribution of data.
• Measures of position: It permits researchers to compare one set of data to another.

Inferential statistics

It permits researchers to examine the results of the population and draw conclusions from the samples of the population studied. Here are some prominent examples of inferential statistics:

T-test: It refers to the tools that are used to examine if the mean of a population alters with the mean assumed by a researcher.

• Confidence interval: It is the range of data values for a parameter unknown to the researcher.
• Contingency table: It refers to the frequency distribution of variables.
• Pearson correlation: It indicates the power of a linear relationship between two data values.
• Bi-variate regression: The connection between two data values
• Multi-variate regression: It is the connection between three or more values.

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What are the Different Types of Parameters?

There are primarily two types of parameters:

Measures of central tendency

It lets researchers know the position of central values around a specific point on a scale. It includes 3 elements:

• Mean: To measure the mean, count together all the data values in a set and split them by the total number of data values in the set. For example, if your data set is 1, 5, 2, 4, and 8, you will add them to get 20 and divide them by 5. You will get a mean score of 4.
• Median: The median is the central numeral in the set when the set is arranged from lowest to highest. For example, the median of 1, 5, 2, 4, and 8 is the number in the middle. It is 2.
• Mode: The mode is the number that comes up most often within the set. For example, the mode of 1, 5, 2, 4, and 8 is 0 because there are no repeated numbers. However, if the set includes 1, 1, 2, 4, and 8, then the mode is 1 because it appears twice while the other numbers appear once.

Measures of variation

• It lets the researchers know the position of the scattered numbers based on the central values of a data set. Measures of variation have the following elements:
  Range: It is the difference between the smallest and biggest values in the data set. For example, the range of 1, 5, 2, 4, and 8 is 7, because if the lowest number (1) is deducted from the highest number (8), the value derived is 7.
• Standard deviation: The standard deviation provides researchers with an estimated idea of how much the mean of each value in a data set differs from its center value. It is calculated by taking away the mean from a specific value in the data set. For example, if the mean of a data set is 5, then the standard deviation of a data value of 1 is -4.
• Variance: The variance of a set of data is the average of squared distances from its mean. Researchers employ an intricate mathematical formula to determine the value. The variance of the data sets 1, 5, 2, 4, and 8 is 6.

Statistics vs. Parameter: Uses

Statistics and parameters are required for different reasons.

Why Do We Need Statistics?

The information gathered through statistics helps researchers answer questions, predict outcomes, and continue their research on the subject. Additionally, the researched findings help resolve industry-related problems, prevent bringing changes to the world, and stop coming across additional similar challenges in the future by offering them resources to recognize and meet a requirement. For example, a manufacturing company can benefit from research on the type of packaging its consumers prefer since the findings can be used to determine the packaging to select for the products.

What are the Uses of Parameters?

Parameters are primarily used when research requires values for data from every section of a population. Researchers can also use these parameters as the foundation for other research and make important decisions about how to proceed with the research.
Example: A health insurance organization may employ parameters from the total expenditure on the cost of the policyholder’s healthcare to determine the premium for the next year.

Statistics vs. Parameter: Symbols

To distinguish between measurements that are statistics and measurements that are parameters, use the following notation.

Note: The notation for parameters often employs uppercase or Greek letters, while the notation for statistics is frequently lowercase or Roman letters.

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Examples of Parameter and Statistics

Here are a few more examples of parameters and statistics. It will help you understand the difference between Statistics vs. Parameters more deeply.

Parameters

• The range of age groups in a ballet company
• Mode of regular visits to a website
• The proportion of NFL members playing on behalf of the team presently who have experienced a major concussion

Statistics

• The mean (or average) earnings for a sample of American journalists
• Median square footage of one hundred 2-bedroom hall kitchen homes listed for sale in Austin, Texas
• The standard deviation of weights for 1500 tuna caught in the Mediterranean

Statistics vs. Parameter: A Comparison Table

Conclusion

Statistics and parameters are both important parts of any research analysis. Though they both refer to a specific group, still there are major differences between them. The discussion above highlights the prominent differences between Statistics vs. Parameters. Primarily, statistics refers to the numbers of a sample of a population while parameters refer to the entire population itself.