A Summary of Parametric Methods | Inferences for Correlation | STAT1201S_7260_62711 Courseware | The University of Queen ... 11/26/22, 8:14 AM Course > Module 8 > Inferen ... > A Sum ... A Summary of Parametric Methods The confidence intervals and tests we have discussed so far have all been parametric methods. These methods work by using a sample statistic to estimate some parameter of ¯ the population. For example, the sample mean x is used to estimate the population mean u and the sample least-squares slope b1 is used to estimate the population slope ß1. This process also involves making an assumption about the distribution of the estimate of the parameter, and so far we have assumed that it is a Normal distribution. The Central Limit Theorem says that this is okay for large enough samples, but we have to be more careful about checking the assumption for smaller samples. We will look at some nonparametric procedures in Module 12 which avoid having to make the normality assumption. In essence then we have only really looked at one method of inference. Every confidence interval has had the form estimate+t* se(estimate), though for proportions we used z* instead of t *. We have used Greek letters to denote population parameters so we will now use the letter 0 to denote an arbitrary parameter (such as u or ß1). We can then write the above general confidence interval more mathematically as Ô+++se(Ô). Similarly, every significance test has had the form se(estimate) estimate - hypothesised t = , or, in mathematical notation, https://learnx.uq.edu.au/courses/course-v1:UQ+STAT1201S_7260_62711+LearnX/courseware/ad8872e1907d449cba1ee391ae2279de/f7ccba77cde7 ... 1/3
11/26/22, 8:14 AM A Summary of Parametric Methods | Inferences for Correlation | STAT1201S_7260_62711 Courseware | The University of Queen ... < 0 - 00 t = , se(0) where 00 is the value of 0 given by the null hypothesis. All we need to calculate a confidence interval or a test statistic is the appropriate standard error for the estimate we are using, as listed in the following table. (Note that the standard error formulas related to linear regression are included for interest only - in practice we will always obtain these from R.) Parameter Estimate Standard Error ? ô se( ¯ s ? x p p p(1-p) 1 n H1 - H2 ¯ ¯ ? 1 S2 + P1-P2 P1 -12 PI (1-P1) P2(1-P2) + n2 ? r ? 1-12 m-2 Bo b0 1 ¯ 2 x + SU n ¯ ? (x ;- x)2 https://learnx.uq.edu.au/courses/course-v1:UQ+STAT1201S_7260_62711+LearnX/courseware/ad8872e1907d449cba1ee391ae2279de/f7ccba77cde7 ... 2/3
11/26/22, 8:14 AM A Summary of Parametric Methods | Inferences for Correlation | STAT1201S_7260_62711 Courseware | The University of Queen ... ?1 b1 ˆ ?? y ? ¯ V? (x; - x)2 ¯ 1 (x *- x)2 SUN n -+ ¯ ? (x ;- x)2 ¯ (x *- x)2 sug 1+-+ 1 ¯ n ? (x ;- x)2 https://learnx.uq.edu.au/courses/course-v1:UQ+STAT1201S_7260_62711+LearnX/courseware/ad8872e1907d449cba1ee391ae2279de/f7ccba77cde7 ... 3/3