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- https://stats.libretexts.org/Courses/Cerritos_College/Introduction_to_Statistics_with_R/08%3A_Estimating_Unknown_Quantities_from_a_Sample/8.04%3A_Estimating_Population_Parametersknitr::kable(data.frame(stringsAsFactors=FALSE, Symbol = c("$s$", "$\\sigma$", "$\\hat{\\sigma}$", "$s^2$", "$\\sigma^2$", "$\\hat{\\sigma}^2$"), What.is.it = c("Sample standard deviation", "Populatio...knitr::kable(data.frame(stringsAsFactors=FALSE, Symbol = c("$s$", "$\\sigma$", "$\\hat{\\sigma}$", "$s^2$", "$\\sigma^2$", "$\\hat{\\sigma}^2$"), What.is.it = c("Sample standard deviation", "Population standard deviation", "Estimate of the population standard deviation", "Sample variance", "Population variance", "Estimate of the population variance"), Do.we.know.what.it.is = c("Yes - calculated from the raw data", "Almost never known for sure", "Yes - but not the same as the sample standard dev…
- https://stats.libretexts.org/Courses/Cerritos_College/Introduction_to_Statistics_with_R/02%3A_Introduction_to_R/2.13%3A_Using_CommentsBefore discussing any of the more complicated stuff, I want to introduce the comment character, #. It has a simple meaning: it tells R to ignore everything else you’ve written on this line. seeker <- ...Before discussing any of the more complicated stuff, I want to introduce the comment character, #. It has a simple meaning: it tells R to ignore everything else you’ve written on this line. seeker <- 3.1415 # create the first variable lover <- 2.7183 # create the second variable keeper <- seeker * lover # now multiply them to create a third one print( keeper ) # print out the value of 'keeper'
- https://stats.libretexts.org/Courses/Cerritos_College/Introduction_to_Statistics_with_R/15%3A_Regression_in_R/15.12%3A_Model_SelectionIf we ignore the low level details, it’s fairly obvious what the AIC does: on the left we have a term that increases as the model predictions get worse; on the right we have a term that increases as t...If we ignore the low level details, it’s fairly obvious what the AIC does: on the left we have a term that increases as the model predictions get worse; on the right we have a term that increases as the model complexity increases. where N is the number of observations, p is the number of predictors in the full model (not including the intercept), and k is the difference in the number of parameters between the two models.
- https://stats.libretexts.org/Courses/Cerritos_College/Introduction_to_Statistics_with_R/15%3A_Regression_in_RThe goal in this chapter is to introduce linear regression, the standard tool that statisticians rely on when analysing the relationship between interval scale predictors and interval scale outcomes. ...The goal in this chapter is to introduce linear regression, the standard tool that statisticians rely on when analysing the relationship between interval scale predictors and interval scale outcomes. Stripped to its bare essentials, linear regression models are basically a slightly fancier version of the Pearson correlation (Section 5.7) though as we’ll see, regression models are much more powerful tools.
- https://stats.libretexts.org/Courses/Cerritos_College/Introduction_to_Statistics_with_R/04%3A_Summarizing_Data_Visually_Using_R/4.07%3A_Saving_Image_Files_Using_R_and_RstudioIf you’re running R through Rstudio, then the easiest way to save your image is to click on the “Export” button in the Plot panel (i.e., the area in Rstudio where all the plots have been appearing). T...If you’re running R through Rstudio, then the easiest way to save your image is to click on the “Export” button in the Plot panel (i.e., the area in Rstudio where all the plots have been appearing). The reason for this is that my experience with the graphical device provided by Rstudio has led me to suspect that it still has a bunch on non-standard (or possibly just undocumented) features, and so I don’t quite trust that it always does what I expect.
- https://stats.libretexts.org/Courses/Cerritos_College/Introduction_to_Statistics_with_R/09%3A_Hypothesis_Testing/9.04%3A_Making_DecisionsAt this point, our hypothesis test is essentially complete: (1) we choose an α level (e.g., α=.05, (2) come up with some test statistic (e.g., X) that does a good job (in some meaningful sense) of com...At this point, our hypothesis test is essentially complete: (1) we choose an α level (e.g., α=.05, (2) come up with some test statistic (e.g., X) that does a good job (in some meaningful sense) of comparing H0 to H1, (3) figure out the sampling distribution of the test statistic on the assumption that the null hypothesis is true (in this case, binomial) and then (4) calculate the critical region that produces an appropriate α level (0-40 and 60-100).
- https://stats.libretexts.org/Courses/Cerritos_College/Introduction_to_Statistics_with_R/19%3A_Bayesian_Statistics/19.02%3A_Bayesian_Hypothesis_TestsSuppose, for instance, the posterior probability of the null hypothesis is 25%, and the posterior probability of the alternative is 75%. The alternative hypothesis is three times as probable as the nu...Suppose, for instance, the posterior probability of the null hypothesis is 25%, and the posterior probability of the alternative is 75%. The alternative hypothesis is three times as probable as the null, so we say that the odds are 3:1 in favour of the alternative.
- https://stats.libretexts.org/Courses/Cerritos_College/Introduction_to_Statistics_with_R/06%3A_Describing_Data_With_Numbers_Using_R/6.02%3A_Measures_of_VariabilityIn practice, this leads to two different measures, the “mean absolute deviation (from the mean)” and the “median absolute deviation (from the median)”. From what I’ve read, the measure based on the me...In practice, this leads to two different measures, the “mean absolute deviation (from the mean)” and the “median absolute deviation (from the median)”. From what I’ve read, the measure based on the median seems to be used in statistics, and does seem to be the better of the two, but to be honest I don’t think I’ve seen it used much in psychology.
- https://stats.libretexts.org/Courses/Cerritos_College/Introduction_to_Statistics_with_R/18%3A_Basic_Programming/18.04%3A_Writing_FunctionsWhenever the function is called, R executes the statements in the curly braces, and then outputs the contents of VALUE to the user. As you can see, when you type the name of a function at the command ...Whenever the function is called, R executes the statements in the curly braces, and then outputs the contents of VALUE to the user. As you can see, when you type the name of a function at the command line, R prints out the underlying source code that we used to define the function in the first place. The doubleMax() function identifies the largest value in the inputs, by passing all the user inputs to the max() function, and then doubles it.
- https://stats.libretexts.org/Courses/Cerritos_College/Introduction_to_Statistics_with_R/17%3A_Preparing_Datasets_and_Other_Pragmatic_Matters/17.11%3A_Other_Useful_Data_StructuresThe reason for these differences is that for this is that, for both data frames and matrices, the “row and column” version exists to allow the human user to interact with the object in the psychologic...The reason for these differences is that for this is that, for both data frames and matrices, the “row and column” version exists to allow the human user to interact with the object in the psychologically meaningful way: since both data frames and matrices are basically just tables of data, it’s the same in each case.
- https://stats.libretexts.org/Bookshelves/Applied_Statistics/Learning_Statistics_with_R_-_A_tutorial_for_Psychology_Students_and_other_Beginners_(Navarro)/17%3A_Bayesian_Statistics/17.03%3A_Why_Be_a_BayesianAny time that you aren’t exactly sure about what the truth is, you should use the language of probability theory to say things like “there is an 80% chance that Theory A is true, but a 20% chance that...Any time that you aren’t exactly sure about what the truth is, you should use the language of probability theory to say things like “there is an 80% chance that Theory A is true, but a 20% chance that Theory B is true instead”. To me, this is the big promise of the Bayesian approach: you do the analysis you really want to do, and express what you really believe the data are telling you.
