Please enable JavaScript.

Coggle requires JavaScript to display documents.

Swirl: Data Analysis (Dispersion (Box and Whisker plot (IQR = inter…

- - - - the range is equal to Q3 - Q1
- - - - therefore: Power = 1- beta
    - - i am correctly proving what i want to prove about my claim by correctly rejecting my null hypothesis
    - - knowing how to do this will ensure that sample sizes for experiments are large enough to ensure a powerful result
      - Note: assuming a known sigma allows me to use the standard normal distribution instead of the t-distribution for the sake of the swirl lesson. (sigma wouldn't me known in real life)
      - What's needed for the calculation
        
        1) population st. dev (sigma)
        
        2) the difference in means I'd like to be able to detect (delta)
        
        3) the z critical value for my chosen level of significance(alpha)
        
        4)z critical value for my chosen level of power
    - - use the pwr package
        
        pwr.norm.test()
        
        this function will automatically generate the sample size required for 80% power once I specify the necessary information
        
        needed arguments
        
        1) effect size (which is the difference I wish to detect divided by sigma
        
        2) chosen significance level
        
        3) chosen power
        
        4)whether I'm conducting a one or two sided test
        
        pwr.norm.test(d = effectsize, sig.level = 0.05, power = 0.8, alternative = "greater")
        
        in this example of how to use the function, the effect size is an R object that stores the difference I want to see between the posted speed limit and how much people are speeding a certain zone
        
        the significance level is 5% in this example. the power was chosen to be 80%, meaning that I want a sample size that will ensure I will correctly reject my null hyp when the null is false 80% of the time
        
        the alternative could by "two.sided", "less", "greater"
        
        in this case, I'm looking for a difference that is at my specified difference or above that. because of that, it's a one sided test.
        
        pwr.t.test()
        
        this function can automatically determine the sample size needed to obtain a desired level of power given that the population standard deviation is not known
        
        the inputs to the function are identical to the power function for the normal distribution except that I must specify either a one-sample, two-sample or pair t-test under the argument "type"
        
        Note: the required sample size for a given power is larger under the pwr.t.test() function than the pwr.norm.test(). this is because the standard deviation is estimated instead of assuming a known quantity . this assumption introduces more uncertainty into the process so the t-test provides a more conservative estimate of the sample size needed
- - - - 1)sample mean
      - 2) assumed population mean
      - 3)variance
      - 4) sample size
      - t-stat= xbar - mu / s/sqrt(n)
        
        t-stat= sample mean - population mean / sample st. dev. / sample size
        
        pt()
        
        this function computes the area under the curve to the right of the t test statistic. p stands for probability and t stands for t-distribution
        
        pValue <- pt(tStat, degrees of freedom = , lower.tail = false)
        
        this is an example of use the pt function in practice. the tStat is an R object that holds the computed t test statistic, degrees of freedom and lower tail are arguments. the lower tail false will specify that you want the area under the curve for the upper tail or the tail to the right of the distribution a
      - R has a built in function for calculating a t test p value
        
        t.test(dataset, mu = some assumed #, alternative = "two.sided")
        
        the alternative can also be one sided depending on the question being asked