Basics introduction to inferential statistics
Overview: The aim of inferential statistics is to draw inferences concerning population characteristics based on sample data. Within this framework, sample statistics are used as estimators of corresponding population parameters. The process is necessarily probabilistic in nature, as parameter estimates are computed from the limited information contained in a sample. It is generally assumed that observations on variables of interest are randomly and independently sampled from a population of observations. This means that the likelihood of selecting one observation is unrelated to the likelihood of selection another. Parameter estimates can come in the form of point and interval estimates. Confidence intervals are used to provide an estimated range of values that may overlap with the true value of a population parameter. When an interval method is not utilized, then a computed sample statistic is simply treated as a point estimate of a corresponding population parameter. The videos and Powerpoints below demonstrate how to use SPSS to generate point and interval estimates of a population mean and a population proportion.
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General introduction to basic concepts necessary to understand inferential statistics (June 2020): Video, Excel file
This video discusses the following concepts:
- Point estimates
- Confidence intervals
- Sampling error
- Standard error of the mean
- Sampling distribution of the mean
Generating a confidence interval around a sample mean using SPSS (June, 2020): video, SPSS data file, Powerpoint demo
Description: The video provides a short demo of how to obtain 90% and 95% confidence intervals around a sample mean using the Explore menu in SPSS. The Powerpoint provides the same steps, but also the computational details behind the intervals constructed in the demonstration.
Generating a confidence interval around a sample proportion using SPSS / Clopper-Pearson intervals (June, 2020): video, SPSS data file
Description: This video demonstrates how to obtain confidence intervals around a sample proportion in SPSS. Specifically I focus on generating Clopper-Pearson exact confidence intervals in the video demonstration.
Note 1: Ordinarily one would not construct confidence intervals for the proportion of cases falling into each group on your variable as I did in this video. However, this was done to illustrate how you can reset your target group when constructing interval estimates for proportions for either group.
Note 2: Clopper-Pearson intervals are formed using the binomial sampling distribution (see https://en.wikipedia.org/wiki/Binomial_proportion_confidence_interval). An alternative method (not shown in the video, but can be included in textbooks) is to use the z-distribution to construct a symmetric interval around the proportion (this approach is called the 'normal distribution approximation'). That approach, however, is best used when the sample proportion is near .50 [i.e., not close to 0 or 1] and/or your sample size is large. As your proportion gets closer to 0 or 1 (i.e., the boundaries for proportions), then larger and larger samples would be required to construct symmetric confidence intervals where one of the bounds does not end up falling outside the range of 0 and 1.
Generating a confidence interval around sample proportion / normal distribution approximation: Powerpoint, Excel file
The Powerpoint discusses the normal theory approximation to constructing confidence intervals around sample proportions. The Excel file can be downloaded and used as a calculator to easily generate confidence intervals using this method.
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Older videos
Introductory concepts and SPSS applications (video), Powerpoint, SPSS data file
Creating a confidence interval around a sample mean using SPSS (video), SPSS data file
Creating a confidence interval around a sample proportion (video), SPSS data file