Which refers to the process of using sample statistics to draw conclusions about true population parameters?
Video TranscriptOkay in this problem, we have multiple questions to answer. This first 1 has to deal with a definition right. The process of using samples statistics to draw conclusions about true population parameters is called statistical. Inference right. We'Re using statistics of this is a statistical inference. We'Re using statistic statistic inference to infer right and what that word means infer is that i'm drawing a conclusion based on an incomplete picture. Okay, so i'm using an incomplete picture, but i have enough of the picture to be able to take make an inference about the whole all right. So this next 1, which of the following statistics, is not a measure of central tendency. Will the arithmetic means is the average the median is in the middle and the mode is the 1 that occurs. The most q 3 is the 1 that that's like the top quarter. That'S the third of the top quarter, so that doesn't tell us. What'S in the middle, it tells us what's above, so that is going to be the correct answer for that. That is not a measure of the central tendency. Now, the next 1, the smaller the spread of scores around the arithmetic, mean means the smaller. This standard deviation and the smaller the variance and the smaller of the inter cortile range. It means that all of those numbers are going to get smaller. So that's going to be all of the above all of the above all right. So the difference between all of those are getting smaller because the spread is smaller, which of the following is sensitive to extreme values. Well, that is going to be the arithmetic mean the arithmetic mean, is going to be sensitive to extreme values, all right, so the next 1 that we have is, let me see true false a population with 200 elements has an arithmetic mean of 10 point from this Information, it can be shown that the popular that the standard deviation is 15 point that is going to be false, all right, just because we know the average we have to have a different. We have to have a different set of what sort i'm looking for observations to be able to show what the standard deviation is. Okay, just because we know what the mean is doesn't mean that we know what the standard deviation is. That is false in a sample size of 40. This sample mean is 15 point, and then in this case the sum of all observations is 600 on now. That is true. That is true right, because the whole process of finding the means is adding up. All of the samples all of the data and the sample and then dividing by the number in our sample, so we're going to be 40 times 15, and that gives us 600 point. So that is true right and i believe, let me check. Yes, that is the last 1, so we are done. Show
Inferential statistics lets you draw conclusions about populations by using small samples. Consequently, inferential statistics provide enormous benefits because typically you can’t measure an
entire population. However, to gain these benefits, you must understand the relationship between populations, subpopulations, population parameters, samples, and sample statistics. In this blog post, learn the differences between population vs. sample, parameter vs. statistic, and how to obtain representative samples using random sampling. Related post:
Difference between Descriptive and Inferential Statistics Populations can include people, but other examples include objects, events, businesses, and so on. In statistics, there are two general types of populations. Populations can be the complete set of all similar items that exist. For example, the population of a country includes all people currently within that country. It’s a finite but potentially large list of members. However, a population can be a theoretical construct that is potentially infinite in size. For example, quality improvement analysts often consider all current and future output from a manufacturing line to be part of a population. Populations share a set of attributes that you define. For example, the following are populations:
Before you begin a study, you must carefully define the population that you are studying. These populations can be narrowly defined to meet the needs of your analysis. For example, adult Swedish women who are otherwise healthy but have osteoporosis. Population vs SampleIt’s virtually impossible to measure a whole population completely because they tend to be extremely large. Consequently, researchers must measure a subset of the population for their study. These subsets are known as samples. Typically, a researcher’s goal is to draw a representative sample from their target population. A representative sample mirrors the properties of the population. Using this approach, researchers can generalize the results from their sample to the population. Performing valid inferential statistics requires a strong relationship between the population and a sample. In a later section, you’ll learn about the importance of representative samples and how to obtain them. A statistical inference is when you use a sample to infer the properties of the entire population from which it was drawn. Learn more about making Statistical Inferences. Subpopulations can Improve Your AnalysisSubpopulations share additional attributes. For instance, the population of the United States contains the subpopulations of men and women. You can also subdivide it in other ways such as region, age, socioeconomic status, and so on. Different studies that involve the same population can divide it into different subpopulations depending on what makes sense for the data and the analyses. Understanding the subpopulations in your study helps you grasp the subject matter more thoroughly. They can also help you produce statistical models that fit the data better. Subpopulations are particularly important when they have characteristics that are systematically different than the overall population. When you analyze your data, you need to be aware of these deeper divisions. In fact, you can treat the relevant subpopulations as additional factors in later analyses. For example, if you’re analyzing the average height of adults in the United States, you’ll improve your results by including male and female subpopulations because their heights are systematically different. I’ll cover that example in depth later in this post! Parameter vs StatisticA parameter is a value that describes a characteristic of an entire population, such as the population mean. Because you can almost never measure an entire population, you usually don’t know the real value of a parameter. In fact, parameter values are nearly always unknowable. While we don’t know the value, it definitely exists. For example, the average height of adult women in the United States is a parameter that has an exact value—we just don’t know what it is! The population mean and standard deviation are two common parameters. In statistics, Greek symbols usually represent population parameters, such as μ (mu) for the mean and σ (sigma) for the standard deviation. A statistic is a characteristic of a sample. If you collect a sample and calculate the mean and standard deviation, these are sample statistics. Inferential statistics allow you to use sample statistics to make conclusions about a population. However, to draw valid conclusions, you must use particular sampling techniques. These techniques help ensure that samples produce unbiased estimates. Biased estimates are systematically too high or too low. You want unbiased estimates because they are correct on average. In inferential statistics, we use sample statistics to estimate population parameters. For example, if we collect a random sample of adult women in the United States and measure their heights, we can calculate the sample mean and use it as an unbiased estimate of the population mean. We can also perform hypothesis testing on the sample estimate and create confidence intervals to construct a range that the actual population value likely falls within. Learn more about Parameters vs Statistics. The law of large numbers states that as the sample size grows, sample statistics will converge on the population parameters. Additionally, the standard error of the mean mathematically describes how larger samples produce more precise estimates. Related posts: Measures of Central Tendency and Measures of Variability Representative Sampling and Simple Random SamplesIn statistics, sampling refers to selecting a subset of a population. After drawing the sample, you measure one or more characteristics of all items in the sample, such as height, income, temperature, opinion, etc. If you want to draw conclusions about these characteristics in the whole population, it imposes restrictions on how you collect the sample. If you use an incorrect methodology, the sample might not represent the population, which can lead you to erroneous conclusions. Learn more about Representative Samples. The most well-known method to obtain an unbiased, representative sample is simple random sampling. With this method, all items in the population have an equal probability of being selected. This process helps ensure that the sample includes the full range of the population. Additionally, all relevant subpopulations should be incorporated into the sample and represented accurately on average. Simple random sampling minimizes the bias and simplifies data analysis. I’ll discuss sampling methodology in more detail in a future blog post, but there are several crucial caveats about simple random sampling. While this approach minimizes bias, it does not indicate that your sample statistics exactly equal the population parameters. Instead, estimates from a specific sample are likely to be a bit high or low, but the process produces accurate estimates on average. Furthermore, it is possible to obtain unusual samples with random sampling—it’s just not the expected result. Methods for collecting a representative sample include the following:
Additionally, random sampling might sound a bit haphazard and easy to do—both of which are not true. Simple random sampling assumes that you systematically compile a complete list of all people or items that exist in the population. You then randomly select subjects from that list and include them in the sample. It can be a very cumbersome process. Random sampling can increase the internal and external validity of your study. Learn more about internal and external validity. Conversely, convenience sampling does not tend to obtain representative samples. These samples are much easier to collect but the results are minimally useful. Let’s bring these concepts to life! Related post: Sample Statistics Are Always Wrong (to Some Extent)! Example of a Population with Important SubpopulationsSuppose we’re studying the height of American citizens and let’s further assume that we don’t know much about the subject. Consequently, we collect a random sample, measure the heights in centimeters, and calculate the sample mean and standard deviation. Here is the CSV data file: Heights. We obtain the following results:  Because we gathered a random sample, we can assume that these sample statistics are unbiased estimates of the population parameters. Now, suppose we learn more about the study area and include male and female as subpopulations. We obtain the following results. Notice how the single broad distribution has been replaced by two narrower distributions? The distribution for each gender has a smaller standard deviation than the single distribution for all adults, which is consistent with the tighter spread around the means for both men and women in the graph. These results show how the mean provides more precise estimates when we assess heights by gender. In fact, the mean for the entire population does not equal the mean for either subpopulation. It’s misleading! During this process, we learn that gender is a crucial subpopulation that relates to height and increases our understanding of the subject matter. In future studies about height, we can include gender as a predictor variable. This example uses a categorical grouping variable (Gender) and a continuous outcome variable (Heights). When you want to compare distributions of continuous values between groups like this example, consider using boxplots and individual value plots. These plots become more useful as the number of groups increases. This example is intentionally easy to understand but imagine a study about a less obvious subject. This process helps you gain new insights and produce better statistical models. Using your knowledge of populations, subpopulations, parameters, sampling, and sample statistics, you can draw valuable conclusions about large populations by using small samples. For more information about how you can test hypotheses about populations, read my Overview of Hypothesis Tests. When you take measurements, ensure that your measurement instruments and test scores are valid. To learn more, read my post Validity. What is the process of drawing a sample from a population?There are 4 key steps to select a simple random sample.. Step 1: Define the population. Start by deciding on the population that you want to study. ... . Step 2: Decide on the sample size. Next, you need to decide how large your sample size will be. ... . Step 3: Randomly select your sample. ... . Step 4: Collect data from your sample.. What is the process of drawing a sample from a conclusion?statistical inference. The process of drawing a sample from a population and then carrying out statistical analysis on the sample in order to make conclusions about the entire population is called statistical inference.
What is the process of making estimates about the population parameter from a sample is called?The process of using a sample to make inferences about a population is called statistical inference. Characteristics such as the population mean, the population variance, and the population proportion are called parameters of the population.
Which sampling method allows to draw valid conclusions about population?Stratified sampling involves dividing the population into subpopulations that may differ in important ways. It allows you draw more precise conclusions by ensuring that every subgroup is properly represented in the sample.
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