In order to be confident in our ability to use a sample to draw inferences about a population, we need to make sure that we have a representative sample — that is, a sample in which the characteristics of the individuals in the sample closely match the characteristics of the overall population.
If our sample is not similar to the overall population, then we cannot generalize the findings from the sample to the overall population with any confidence. To maximize the chances that you obtain a representative sample, you need to focus on two things:. Make sure you use a random sampling method. There are several different random sampling methods that you can use that are likely to produce a representative sample, including:. Random sampling methods tend to produce representative samples because every member of the population has an equal chance of being included in the sample.
Make sure your sample size is large enough. Fortunately, you can use online calculators to plug in these values and see how large your sample needs to be. To answer these questions we can perform a hypothesis test , which allows us to use data from a sample to draw conclusions about populations. For example, we might be interested in the mean height of a certain plant species in Australia. Instead of going around and measuring every single plant in the country, we might collect a small sample of plants and measure each one.
Then, we can use the mean height of the plants in the sample to estimate the mean height for the population. However, our sample is unlikely to provide a perfect estimate for the population.
For example, suppose we want to know if hours spent studying per week is related to test scores. To answer this question, we could perform a technique known as regression analysis. So, we may observe the number of hours studied along with the test scores for students and perform a regression analysis to see if there is a significant relationship between the two variables. If the p-value of the regression turns out to be significant , then we can conclude that there is a significant relationship between these two variables in the overall population of students.
In summary, the difference between descriptive and inferential statistics can be described as follows:. Descriptive statistics use summary statistics, graphs, and tables to describe a data set. This is useful for helping us gain a quick and easy understanding of a data set without pouring over all of the individual data values. Inferential statistics use samples to draw inferences about larger populations. Depending on the question you want to answer about a population, you may decide to use one or more of the following methods: hypothesis tests, confidence intervals, and regression analysis.
If you do choose to use one of these methods, keep in mind that your sample needs to be representative of your population , or the conclusions you draw will be unreliable.
Your email address will not be published. Skip to content Menu. Posted on January 15, November 12, by Zach. There are two main branches in the field of statistics: Descriptive Statistics Inferential Statistics This tutorial explains the difference between the two branches and why each one is useful in certain situations. Descriptive Statistics In a nutshell, descriptive statistics aims to describe a chunk of raw data using summary statistics, graphs, and tables.
Common Forms of Descriptive Statistics There are three common forms of descriptive statistics: 1. There are two popular types of summary statistics: Measures of central tendency : these numbers describe where the center of a dataset is located.
Examples include the mean and the median. Measures of dispersion : these numbers describe how spread out the values are in the dataset. Examples include the range , interquartile range , standard deviation , and variance. Example of Using Descriptive Statistics The following example illustrates how we might use descriptive statistics in the real world. We are interested in understanding the distribution of test scores, so we use the following descriptive statistics: 1.
Summary Statistics Mean: Graphs To visualize the distribution of test scores, we can create a histogram — a type of chart that uses rectangular bars to represent frequencies. Tables Another easy way to gain an understanding of the distribution of scores is to create a frequency table.
Inferential Statistics In a nutshell, inferential statistics uses a small sample of data to draw inferences about the larger population that the sample came from. The Importance of a Representative Sample In order to be confident in our ability to use a sample to draw inferences about a population, we need to make sure that we have a representative sample — that is, a sample in which the characteristics of the individuals in the sample closely match the characteristics of the overall population.
How to Obtain a Representative Sample To maximize the chances that you obtain a representative sample, you need to focus on two things: 1.
There are several different random sampling methods that you can use that are likely to produce a representative sample, including: A simple random sample A systematic random sample A cluster random sample A stratified random sample Random sampling methods tend to produce representative samples because every member of the population has an equal chance of being included in the sample. Common Forms of Inferential Statistics There are three common forms of inferential statistics: 1. Inferential statistics are produced through complex mathematical calculations that allow scientists to infer trends about a larger population based on a study of a sample taken from it.
Scientists use inferential statistics to examine the relationships between variables within a sample and then make generalizations or predictions about how those variables will relate to a larger population.
It is usually impossible to examine each member of the population individually. So scientists choose a representative subset of the population, called a statistical sample, and from this analysis, they are able to say something about the population from which the sample came.
There are two major divisions of inferential statistics:. Techniques that social scientists use to examine the relationships between variables, and thereby to create inferential statistics, include linear regression analyses , logistic regression analyses, ANOVA , correlation analyses , structural equation modeling , and survival analysis.
When conducting research using inferential statistics, scientists conduct a test of significance to determine whether they can generalize their results to a larger population. Common tests of significance include the chi-square and t-test.
These tell scientists the probability that the results of their analysis of the sample are representative of the population as a whole. Although descriptive statistics is helpful in learning things such as the spread and center of the data, nothing in descriptive statistics can be used to make any generalizations. In descriptive statistics, measurements such as the mean and standard deviation are stated as exact numbers. Even though inferential statistics uses some similar calculations — such as the mean and standard deviation — the focus is different for inferential statistics.
Inferential statistics start with a sample and then generalizes to a population. This information about a population is not stated as a number. Instead, scientists express these parameters as a range of potential numbers, along with a degree of confidence. Actively scan device characteristics for identification. Use precise geolocation data.
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