Comparing Two Samples Part 3

Difference Between Descriptive and Inferential Statistics: Descriptive Statistical vs. Inferential Comparison Descriptive vs Inferential Statistics Statistics is the discipline of collecting, analyzing and presenting data. Statistics theory is divided into two branches on the basis of the information it produces through data analysis. What are descriptive statistics? Descriptive statistics is the branch of statistics that quantitatively describes the main characteristics of a data set. To represent the characteristics of a data set as accurately as possible, the data is summarized using graphical or numerical tools. The values of the variables of interest are graphically summarized by tabulating, grouping, and graphing. The frequency distribution and the relative distribution of the frequency graphs are such representations. They depict the distribution of values throughout the population. Numerical summarization involves calculating descriptive measures such as mean, mode, and mean. Descriptive measures are further classified into two categories; They are measures of central tendency and measures of dispersion/variance. The measures of central tendency are mean/mean, mean, and mode. Each has its own level of application and benefit. Where one might fail, the other might better represent the data set. As the name implies, measures of dispersion involve measuring the distribution of data. Range, standard deviation, variance, percentages and interquartile ranges, and coefficient of variance are measures of dispersion. They provide information on the spread of the data. A simple example of using descriptive statistics is to calculate a student's grade point average. In essence, the GPA is a weighted average of student outcomes and is a reflection of that particular student's overall academic performance. What are inferential statistics? Inferential statistics is the branch of statistics that draws conclusions about the population of interest from a set of data obtained from a sample subject to random changes, observation, and sampling. In general, results are obtained from a random sample of the population, and the results from the sample are then generalized to represent the entire population. A sample is a subset of a population, and measures of descriptive statistics for data gained from a sample are simply called statistics. Measures of descriptive statistics obtained from a sample analysis are known as parameters when applied to the population, and they represent the total population. Inferential statistics focuses on how to generalize the statistics obtained from the sample as accurately as possible to represent the population. One factor of concern is the nature of the sample. If the sample is biased, then the results are also biased, and parameters based on these do not represent the entire population correctly. Therefore, sampling is one important study of inferential statistics. Statistical assumptions, statistical decision theory, estimation theory, hypothesis testing, design of experiments, analysis of variance, and regression analysis are prominent topics of study in inferential statistics theory. A good example of inferential statistics in action is predicting the outcome of an election before voting by ballot. What is the difference between descriptive and inferential statistics? • Descriptive statistics focus on summarizing the data collected from the sample. This technique produces measures of central tendency and dispersion that represent how the values of the variables are concentrated and dispersed. • Inferential statistics generalize statistics obtained from a sample to the general population to which the sample belongs. The measures of the population are called as parameters. • Descriptive statistics only provide a summary of the characteristics of the sample obtained from the data, but in inferential statistics, the measure is used from the sample to infer the characteristics of the population. • In inferential statistics, parameters were obtained from a sample, but not the entire population; Thus, there is always some uncertainty in comparison to the true values. What does it mean for a confidence interval to include zero? What does it mean for a confidence interval to include zero? Zero is the null value of the operand (in this case the difference is in the means). If the 95% confidence interval includes a null value, there is no statistically significant or significant difference between the groups. What happens if the confidence interval does not contain zero? When the hypothesis is zero, there is a simple relationship between hypothesis testing and confidence intervals: if the interval contains zero, the null hypothesis cannot be rejected at the specified confidence level. If the interval does not contain zero, the null hypothesis can be rejected. How do you know if the confidence interval is important? If the confidence interval does not contain the null hypothesis value, the results are statistically significant. If the value of P is less than alpha, then the confidence interval will not contain the value of the null hypothesis. Does the 99% confidence interval contain a zero? 05, which is the traditional limit for "importance". "Having zero in the individual's confidence interval means that the effect of the treatment has no effect." : This is often how these confidence intervals are interpreted, but this is wrong. What does it mean for a confidence interval to include zero? Related Questions Does it include the mean confidence interval? The probability that the confidence interval includes the true mean value within the population is called the confidence level in the CI. You can calculate the CI for any confidence level you want, but the most commonly used value is 95%. How do you know that the confidence interval contains zero? It is important to note that all values in the confidence interval are equal probability estimates of the true value of (μ1-μ2). If there is no difference between the population mean, then the difference will be zero (i.e. (μ1-μ2). = 0). Does the 95% confidence interval contain 0? Significance testing and confidence intervals. There is a close relationship between confidence intervals and tests of significance. Specifically, if the statistic differs significantly from 0 at the 0.05 level, the 95% confidence interval will not contain 0. Can the confidence interval be greater than 1? If the confidence interval includes or intersects (1), there is insufficient evidence to conclude that the groups are statistically significantly different (no difference between study forms). Stick to confidence intervals (prediction periods of regression). P values are often misleading. How do you explain the 95% confidence interval? The correct interpretation of the 95% confidence interval is that we are "95% confident that the population parameter lies between X and X." How do you explain the confidence interval for the study? CI is a numerical range used to describe search data. For example, for the results of a weight study, the CI may be from 53 to 71 kg. This period of 53 to 71 kg is where there is a 95% certainty that the true weight will be (if you use a 95% CI). What is the difference between 95 and 99 confidence intervals? Significance level is a statistical term that indicates how likely you are to be wrong. With a 95 percent confidence interval, you have a 5 percent chance of being wrong. The 99 percent confidence interval may be greater than the 95 percent confidence interval (for example, plus or minus 4.5 percent instead of 3.5 percent). Can the confidence interval include zero? If the confidence interval (with the confidence level you chose) includes 0, then you think 0 is a reasonable probability of the true value of the difference. In general, "significant" people usually mean that they no longer believe the null hypothesis (0) is a reasonable probability. How do you explain 90 confidence intervals? A 90% confidence level means that we expect 90% of the interval estimates to include the population parameter; The 95% confidence level means that 95% of the intervals will include the parameter; and so on and so on. What is an example of a confidence interval? The confidence interval is the average of your score plus and minus the variance of that estimate. For example, if you create a confidence interval with a 95% confidence level, you are confident that 95 of 100 times the estimate will fall between the upper and lower values defined by the confidence interval. What does confidence interval 1 mean? The confidence interval indicates the level of uncertainty about the effect measurement (the accuracy of the effect estimate) which in this case is expressed as OR. If the confidence interval exceeds 1 (eg 95% CI 0.9-1.1) then there is no difference between the study arms. What is the purpose of the confidence period? The confidence interval shows the probability of a parameter falling between a pair of values around the mean. Confidence intervals measure the degree of uncertainty or certainty in the sampling method. They are often generated with 95% or 99% confidence levels. How do you explain the relative confidence interval for risk? RR 1.00 means that the event risk is identical in the exposed and control samples. RR less than 1.00 means that the risk is lower in the exposed sample. RR greater than 1.00 means that the risk is increased in the exposed sample. How is the confidence interval related to the value of P? The p-value relates to a test against the null hypothesis, and the parameter value is usually zero (no relationship). The wider the confidence interval in the parameter estimate, the closer one of its extreme points is to zero, and a p value of 0.05 means that the 95% confidence interval only touches zero. What does rejecting the null hypothesis mean? If there is less than 5% chance of an extreme result such as the sample result if the null hypothesis is true, then the null hypothesis will be rejected. When this happens, the result is said to be statistically significant. What does it mean when 95 confidence intervals overlap? If those periods overlap, they conclude that the difference between groups is not statistically significant. If there is no overlap, the difference is large. What is Z for the 95th confidence interval? The z* value for the 95% confidence level is 1.96. After putting the value of z* and the standard deviation of the population and sample size into the equation, a margin of error of 3.92 is found. The formulas for the confidence interval and the margin of error can be combined into a single formula. Why is the 95th confidence interval the most common? Get the confidence level as high as you can! Well, as the level of confidence increases, so does the margin of error. This means that the interval is wider. For this reason, 95% confidence intervals are the most common. Can the 95th confidence interval be greater than 1? If the ratio is 1, then the two groups are equal. Hence, if the 95% CI of the ratio contains the value 1, the p-value will be greater than 0.05. Alternatively, if the 95% CI does not have the value 1, then the p-value is less than 0.05. What is the level of confidence in the research? The trust level tells you how confident you are or whether your data is representative of the entire community. Most researchers seek a 95% confidence level, which means you can be 95% sure that the results reflect the opinions of the entire population. Which confidence interval is wider, 95 or 80? The confidence level is usually set in the range from 99% to 80%. The 95% confidence interval will be wider than 90%, which in turn will be wider than 80%. Confidence interval for two different percentages of the population Confidence intervals are one part of inferential statistics. The basic idea behind this topic is to estimate the value of an unknown population parameter using a statistical sample. Not only can we estimate the value of a parameter, but we can also adapt our methods to estimate the difference between two related parameters. For example, we might want to find the difference in the percentage of male voters in the United States who support a particular piece of legislation compared to the voting public. We will see how to do this type of calculation by creating a confidence interval for the difference between the relative populations. In the process we will examine some of the theories behind this account. We will see some similarities in how to construct a confidence interval for a single population percentage as well as a confidence interval for the difference between two means of a population. generalities Before looking at the specific formula we'll be using, let's think about the general framework that fits this type of confidence interval. The form of the confidence interval type we will be looking at is given by the following formula: Estimate +/- margin of error Many confidence intervals are of this type. There are two numbers we need to calculate. The first of these values is the parameter estimate. The second value is the margin of error. This margin of error explains the fact that we have an estimate. The confidence interval provides us with a set of possible values for our unknown parameter. Circumstances We must ensure that all conditions are met before making any account. To find a confidence interval for the difference between two ratios, we need to make sure that the following comment: We have two simple random samples from a large population. Here "large" means that the population is at least twenty times larger than the sample size. Sample sizes will be denoted by n 1 and n 2 . Our people have been selected independently of each other. There are at least ten successes and ten failures in each of our samples. If the last item in the list is not met, there may be a way around this. We can modify the construction of the confidence interval plus four and get strong results. As we move forward, we assume that all of the above conditions are met. Samples and population ratios Now we are ready to build our confidence interval. We begin by estimating the difference between our population proportions. Each of these population ratios is estimated by the sample ratio. These sample ratios are statistics found by dividing the number of successes in each sample, and then dividing by the respective sample size. The first population ratio is denoted by p1. If the number of success cases in our sample from this population is k 1, then we have a sample ratio of k 1 / n 1. We denote this statistic by p 1 . We read this symbol as "p 1 -hat" because it looks like the symbol p 1 with a hat on top. In a similar way we can calculate the proportion of a sample from our second group. The parameter of this group is p2. If the number of successes in the sample from this population is k 2 , and our sample ratio is p 2 = k 2 / n 2. These two stats become the first part of our confidence interval. The estimate of p 1 is p 1 . The estimate of p 2 is p 2. So the estimate of the difference p 1 - p 2 is p1 - 2. p Distribution of samples due to different proportions of the sample Next we need to get the margin of error formula. To do this, we will first consider the sampling distribution of p 1 . This is a binomial distribution with a probability of success for the p1 and n1 experiments. The mean of this distribution is the ratio p1. The standard deviation of this type of random variable has a variance of p 1 (1 - p 1) / n 1 . The sampling distribution for p 2 is similar to that of p 1 . Just change all the indices from 1 to 2 and we have a binomial distribution with mean p 2 and variance of p 2 (1 - p 2 ) / n 2 . We now need some results from mathematical statistics in order to determine the sampling distribution of p 1 - p 2 . The mean of this distribution is p 1 - p 2 . Due to the fact that the variances add together, we see that the variance of the sampling distribution is p 1 (1 - p 1 ) / n 1 + p 2 (1 - p 2 ) / n 2. The standard deviation of the distribution is the square root of this formula. There are two types of adjustments we need to make. The first is that the standard deviation formula for p 1 - p 2 uses the unknown parameters of p 1 and p 2 . Of course if we really knew these values, it wouldn't be an interesting statistic problem at all. We will not need to estimate the difference between p1 and p2.. instead we can simply calculate the exact difference. This problem can be fixed by calculating a standard error instead of a standard deviation. All we have to do is replace the population proportions with the sample proportions. Standard errors are calculated based on statistics rather than parameters. The standard error is useful because it effectively estimates the standard deviation. What this means for us is that we no longer need to know the value of the parameters p1 and p2 . . Since these sample proportions are known, the standard error is given by the square root of the following expression: p. 1 (1 - p. 1) / n 1 + p. 2 (1 - p. 2) / n 2. The second element we need to address is the particular shape of our sample distribution. It turns out that we can use the normal distribution to approximate the sampling distribution for p 1 - p 2 . The reason for this is somewhat technical, but is explained in the next paragraph. Both p 1 and p 2 have a binomial sampling distribution. Each of these binomial distributions can be well approximated by a normal distribution. Thus p 1 - p 2 is a random variable. It is formed as a linear combination of two random variables. Each of these normal distributions are approximated. Therefore the sampling distribution of p 1 - p 2 is also normally distributed. confidence interval formula We now have everything we need to compile the confidence interval. The estimate is (p 1 - p 2) and the margin of error is z * [p 1 (1 - p 1) / n 1 + 2p (1 - 2) p / n 2.] 0.5. The value we enter for z* is determined by the level of confidence C. Commonly used values for z* are 1.645 for the 90% confidence and 1.96 for the 95% confidence. These z* values refer to the portion of the standard normal distribution where C is the exact percentage of the distribution between -z* and z*. The following formula gives us a confidence interval for the difference between the relative populations: (p 1 - p2 ) +/- z * [ 1p(1 - 1 p) / n 1 + 2 (1p - Examples of confidence intervals for means 2 ) /pn 2. ] 0.5