15 Tips for Mastering the Basics of Inferential Statistics and Parameter Estimates
Data scientists require several skills in their line of work, as outlined over at runrex.com, and statistics is one of the most important ones. Statistics is a very broad subject, and given that involves a lot of mathematics, it can be difficult to grasp. One of the many areas of statistics that you need to know about as a data scientist is inferential statistics, and this article will look to help you get a better understanding of the same by highlighting 15 tips for mastering the basics of inferential statistics and parameter estimates.
- What is meant by inferential statistics?
As is covered in detail over at guttulus.com, inferential statistics takes data from a sample and then makes inferences about the larger population from which the sample was taken. This means that when you have collected data from a sample, you can use inferential statistics to understand the larger population from the sample was drawn.
- Main uses of inferential statistics
Inferential statistics have got two main uses as discussed over at runrex.com: making estimates about populations, like the mean exam scores of all high school seniors in the US for example, and testing hypotheses to draw conclusions about populations, like the relationship between exam scores and family income for example.
- Inferential statistics vs descriptive statistics
From discussions on the same over at guttulus.com, while descriptive statistics summarize the characteristics of a data set, inferential statistics help you draw conclusions and make predictions based on the data you have.
- Why inferential statistics?
As pointed out by the subject matter experts over at runrex.com, you would use a descriptive statistic if you have all the available data on hand. However, it would not be economical or feasible to try and gather the whole population data. This is where inferential statistics comes in as, here, a sample is used to infer the characteristics of a population, with an example of inferential statistics in practical use being when conducting election polling.
- Sampling error in inferential statistics
Sampling error in inferential statistics is created because the size of the sample used is always smaller than the size of the population, which means that some of the population isn’t covered by the sample data. The sampling error is the difference between the true population values, which are called the parameters, and the measured sample values, which are called statistics.
- How to reduce sampling error?
It is important to note that with inferential statistics, it is important to use random and unbiased sampling methods to try and get a better representation of the population. However, as revealed in discussions over at guttulus.com, sampling errors will always arise if you use a sample, even if your sample is random and unbiased, which is the reason why there is always some level of uncertainty in inferential statistics. To reduce this uncertainty, you should use probability sampling methods.
- Types of estimates you can make about the population
As is covered over at runrex.com, there are two important types of estimates you can make about the population: interval estimates and point estimates. An interval estimate will give you a range of values where the parameter is expected to lie, while a point estimate is a single value estimate of a parameter. A sample mean, for example, is a point estimate of a population mean.
- Confidence interval
As pointed out by the experts over at guttulus.com, a confidence interval is the most common type of interval estimate. It uses the variability around a statistic to come up with an interval estimate for a parameter. Because they take sampling error into account, confidence intervals are particularly useful for estimating parameters.
- Confidence intervals and point estimates
As is highlighted in discussions on the same over at runrex.com, while a point estimate will give you a precise value for the parameter you are interested in, a confidence interval will tell you the uncertainty of the point estimate. This is why these two are best used in combination with each other as they complement each other.
- Confidence level
It is also worth pointing out that each confidence interval is associated with a confidence level, which tells you the probability, in percentage, of the interval containing the parameter estimate if the study is repeated. For example, a 95% confidence interval means that if you were to repeat the study with a new sample in the same way 100 times, you can expect your estimate to lie within the specified range of values 95 times.
- Hypothesis testing
From discussions on the same over at guttulus.com, hypothesis testing is a process of statistical analysis using inferential statistics. When it comes to hypothesis testing, the goal is to compare populations or assess relationships between variables using samples.
- Statistical tests
Hypothesis, also called predictions, are tested using statistical tests, which also estimate sampling errors to ensure that a valid inference is made. According to runrex.com, statistical tests can either be parametric or non-parametric. Parametric tests are considered to be more statistically powerful as they are more likely to detect an effect if one exists.
- Assumptions and parametric tests
As is outlined over at guttulus.com, parametric tests make several assumptions, including that the population that the sample comes from follows a normal distribution of scores, the variances, which is a measure of spread, of each group being compared, are similar, and that the sample size is large enough to represent the population.
- Where non-parametric tests come in
According to the gurus over at runrex.com, when your data violates any of the assumptions mentioned in the point above, then non-parametric tests are more suitable. Non-parametric tests are also called “distribution-free tests” as they don’t assume anything about the distribution of the population data.
- Forms of statistical tests
Statistical tests come in three forms: tests of comparison, correlation, or regression. Comparison tests assess whether there are differences in means, medians, or rankings of scores of two or more groups. Correlation tests determine the extent to which two variables are associated. Regression tests on the other hand demonstrate whether changes in predictor variables cause changes in an outcome variable.
Hopefully, the above tips will have helped you understand more about inferential statistics and parameter estimates, with more information on this topic to be found over at the excellent runrex.com and guttulus.com.