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- https://stats.libretexts.org/Courses/Cerritos_College/Introduction_to_Statistics_with_R/02%3A_Introduction_to_R/2.01%3A_Why_Programming_Is_Hard_to_LearnA large amount of psychological research has shown that practice needs to be deliberate, meaning that it focuses on developing the specific skills that one needs to perform the skill, at a level that ...A large amount of psychological research has shown that practice needs to be deliberate, meaning that it focuses on developing the specific skills that one needs to perform the skill, at a level that is always pushing one’s ability. Whenever I experience an error that I don’t understand, the first thing that I do is to copy and paste the error message into a search engine Often this will provide several pages discussing the problem and the ways that people have solved it.
- https://stats.libretexts.org/Courses/Cerritos_College/Introduction_to_Statistics_with_R/01%3A_Basics/1.01%3A_Introduction/1.1.02%3A_Dealing_with_Statistics_AnxietyAnxiety feels uncomfortable, but psychology tells us that this kind of emotional arousal can actually help us perform better on many tasks, by focusing our attention So if you start to feel anxious ab...Anxiety feels uncomfortable, but psychology tells us that this kind of emotional arousal can actually help us perform better on many tasks, by focusing our attention So if you start to feel anxious about the material in this course, remind yourself that many others in the class are feeling similarly, and that the arousal could actually help you perform better (even if it doesn’t seem like it!).
- https://stats.libretexts.org/Courses/Cerritos_College/Introduction_to_Statistics_with_R/02%3A_Introduction_to_R/2.09%3A_Math_with_VectorsYou can apply mathematical operations to the elements of a vector just as you would with a single number: We can also apply logical operations across vectors; again, this will return a vector with the...You can apply mathematical operations to the elements of a vector just as you would with a single number: We can also apply logical operations across vectors; again, this will return a vector with the operation applied to the pairs of values at each position. Most functions will work with vectors just as they would with a single number. We could create a vector and pass it to the sin() function, which will return as many sine values as there are input values:
- https://stats.libretexts.org/Courses/Cerritos_College/Introduction_to_Statistics_with_R/02%3A_Introduction_to_R/2.04%3A_Getting_Started_with_RWhen we work with R, we often do this using a command line in which we type commands and it responds to those commands. We will return to variables in a little while, but if we want R to print out the...When we work with R, we often do this using a command line in which we type commands and it responds to those commands. We will return to variables in a little while, but if we want R to print out the word hello then we need to contain it in quotation marks, telling R that it is a character string. Another important one is real numbers, which are the most common kind of numbers that we will deal with in statistics, which span the entire number line including the spaces in between the integers.
- https://stats.libretexts.org/Courses/Cerritos_College/Introduction_to_Statistics_with_R/02%3A_Introduction_to_R/2.06%3A_FunctionsThis means that those values are the default settings, so that if you don’t do anything, then the function will return random numbers with a mean of 0 and a standard deviation of 1. Try typing in the ...This means that those values are the default settings, so that if you don’t do anything, then the function will return random numbers with a mean of 0 and a standard deviation of 1. Try typing in the function rnorm() with no arguments and see what happens — it will return an error telling you that the argument “n” is missing and does not have a default value.
- https://stats.libretexts.org/Courses/Cerritos_College/Introduction_to_Statistics_with_R/01%3A_Basics/1.02%3A_Working_with_Data/1.2.01%3A_What_Are_DataThe first important point about data is that data are - meaning that the word “data” is plural (though some people disagree with me on this). You might also wonder how to pronounce “data” – I say “day...The first important point about data is that data are - meaning that the word “data” is plural (though some people disagree with me on this). You might also wonder how to pronounce “data” – I say “day-tah” but I know many people who say “dah-tah” and I have been able to remain friends with them in spite of this. Now if I heard them say “the data is” then that would be bigger issue…
- https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Statistical_Thinking_for_the_21st_Century_(Poldrack)/30%3A_Practical_statistical_modeling/30.01%3A_The_Process_of_Statistical_ModelingThe significant F test shows us that there is a significant difference between diets, but we should also note that the model doesn’t actually account for much variance in the data; the R-squared value...The significant F test shows us that there is a significant difference between diets, but we should also note that the model doesn’t actually account for much variance in the data; the R-squared value is only 0.03, showing that the model is only accounting for a few percent of the variance in weight loss.
- https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Statistical_Thinking_for_the_21st_Century_(Poldrack)/06%3A__Data_Visualization/6.02%3A_Principles_of_Good_Visualization“In general, in a time-series, use a baseline that shows the data not the zero point; don’t spend a lot of empty vertical space trying to reach down to the zero point at the cost of hiding what is goi...“In general, in a time-series, use a baseline that shows the data not the zero point; don’t spend a lot of empty vertical space trying to reach down to the zero point at the cost of hiding what is going on in the data line itself.” (from https://qz.com/418083/its-ok-not-to-start-your-y-axis-at-zero/)
- https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Statistical_Thinking_for_the_21st_Century_(Poldrack)/12%3A_Sampling/12.04%3A_The_Central_Limit_TheoremThe Central Limit Theorem tells us that as sample sizes get larger, the sampling distribution of the mean will become normally distributed, even if the data within each sample are not normally distrib...The Central Limit Theorem tells us that as sample sizes get larger, the sampling distribution of the mean will become normally distributed, even if the data within each sample are not normally distributed. Let’s work with the variable AlcoholYear in the NHANES distribution, which is highly skewed, as shown in the left panel of Figure ??. This distribution is, for lack of a better word, funky – and definitely not normally distributed.
- https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Statistical_Thinking_for_the_21st_Century_(Poldrack)/17%3A_Hypothesis_Testing_in_R/17.01%3A_Simple_Example-_Coin-flipping_(Section_16.3.5.1)We use such a large number because it turns out that it’s very rare to get 70 heads, so we need many attempts in order to get a reliable estimate of these probabilties. # simulate tossing of 100,000 f...We use such a large number because it turns out that it’s very rare to get 70 heads, so we need many attempts in order to get a reliable estimate of these probabilties. # simulate tossing of 100,000 flips of 100 coins to identify # empirical probability of 70 or more heads out of 100 flips For comparison, we can also compute the p-value for 70 or more heads based on a null hypothesis of P h e a d s = 0.5 P_{heads}=0.5 , using the binomial distribution.
- https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Statistical_Thinking_for_the_21st_Century_(Poldrack)/26%3A_The_General_Linear_Model/26.08%3A_AppendixThe rules of matrix multiplication tell us that the dimensions of the matrices have to match with one another; in this case, the design matrix has dimensions of 8 (rows) X 2 (columns) and the Y variab...The rules of matrix multiplication tell us that the dimensions of the matrices have to match with one another; in this case, the design matrix has dimensions of 8 (rows) X 2 (columns) and the Y variable has dimensions of 8 X 1. The challenge here is that X X and β \beta are now matrices, not single numbers – but the rules of linear algebra tell us how to divide by a matrix, which is the same as multiplying by the inverse of the matrix (referred to as X − 1 X^{-1} ).
