Statistics Features

Use the search box (command + f on macs or control + f on windows) to search for whichever function you're looking for (try "1-prop-z-test")

Statistics functions can be accessed in one of two ways:

1. You can type them directly in the input bar, using either the function name (ex: geometricdist) or its shortcut (ex: gdist)
2. You can use the buttons found under the "stats" category button, as seen below, which has 4 subcategories: 1) Basic (basic stats functions), 2) Advanced (regressions and more), 3) Distributions and 4) Tests (Hypothesis Testing)

Webapp:

 Mobile:

Below is a list of all ClassCalc statistics functions and how to use them:

Lists

• • To input a list, you can either:
    1. type in "[]" or "list"
    2. click "add" > list
       • 
       • 
  • input: comma-separated values
  • output: list (can be stored as a constant, like a or b, and then used in other functions)
  • example:
    1. using lists to compute multiple equations at once: 
       •  
    2. using lists to plot multiple functions at once: 
       
       • 

Tables

• to input a table you can either:
  
  1. type "table"
  2. click "add" > table
     
     • 
     • 
  3. transform a function into a table:
     1. enter your function
        • 
     2. hold press the color menu and press "table convert"
        
        • 
     3. enjoy your table
        
        •  
• input: rows and columns of values
• output: points plotted on the graph
  
  • 
• extra options:
  1. regress any column against the first column
     
     • 
  2. connect points into a line (or create a Frequency Polygon)
     • 
  3. change table headers
     • table headers are constants that represent each column. Constants can be  defined in the table header (column 1 below) or they can be defined elsewhere (in another column or another input entirely). Table headers are smart, so you can manipulate them like so:
       • 
  4. use table columns as lists
     • 

Basic Statistics

• mean
  
  • input: comma-separated values
  • output: mean
  • 
• median
  • input: comma-separated values
  • output: median
  • 
• mode
  • input: comma-separated values
  • output: mode
  • 
• min
  • input: comma-separated values
  • output: minimum of the inputted values
  • 
• max
  • input: comma-separated values
  • output: maximum of the inputted values
  • 
• range
  • input: comma-separated values
  • output: largest value inputed minus the smallest
  • 
• combination (nCr)
  • input: 
    • n - total number of items in the given set
    • r - number of items required in the subset created from the main set
  • output: combination of the two inputted values
  • 
• permutation (nPr)
  • input:
    • n - total number of items in the given set
    • r - number of items required in the subset created from the main set
  • output: permutation of the two inputted values
  • 
• factorial (!)
  • input: value
  • output: factorial
  • 
• standard deviation (stdev)
  
  • input: comma-separated values 
  • output:
    • σ - population standard deviation
    • s - sample standard deviation
  • 
• variance
  • input: comma-separated values
  • output:
    • σ² - population variance 
    • s² - sample variance
  • 
• sort
  • input: comma-separated values
  • output: inputted values, in ascending order
  • 

Advanced Statistics

• linear regression (lin-reg) [Shortcut: "lin"]
  • input:
    • list1
    • list2 
  • output:
    • the line of best fit - regressed against a linear model, y=mx+b
    • r - correlation coefficient
    • r² - correlation of determination 
  • extra options: plot residuals
  •   or 
• polynomial regression (poly-reg) [Shortcut: "poly"]
  • input:
    • list1
    • list2
    • degree of polynomial ("2" for quadratic, "3" for cubic, etc)
  • output:
    • the curve of best fit - regressed against the polynomial model specified by the input
  • extra options: plot residuals
  • 
• exponential regression (exp-reg) [Shortcut: "exp"]
  • input:
    • list1
    • list2
  • output:
    • the exponential curve of best fit - regressed against an exponential model, y=ab^x
  • extra options:
    • plot residuals
• logarithmic regression (lg-reg) [Shortcut: "lg"]
  • input:
    • list1
    • list2
  • output:
    • the logarithmic curve of best fit - regressed against a logarithmic model, y=a+b*ln(x))
  • extra options: plot residuals
• random integer (rand-int) [Shortcut: "rint"]
  • input:
    • min
    • max
    • n - number of random integers to generate
  • output:
    • array of random integers within the bounds set by min and max
• random number (rand-num) [Shortcut: "rnum"]
  • input:
    • min
    • max
    • n - number of random numbers to generate
  • output:
    • array of random numbers within the bounds set by min and max
• random binomial (rand-binomial) [Shortcut: "rbin"]
  • input:
    • p - probability of success
    • t - trials
    • n -number of random binomial values to generate
  • output:
    • array of random values from binomial distribution
• random normal (rand-norm) [Shortcut: "rnorm"]
  • input:
    • µ - mean
    • σ - standard deviation
    • n - number of random normal values to generate
  • output:
    • array of random values from normal distribution
• 1-variable-statistics (1-var-stats) [Shortcut: "1varstats", "onevarstats", "ovs" or "1vs"]
  • input: list
  • output:
    • x̅  - average
    • Σx - sum
    • Σx² - sum of the squares
    • Sx - sample standard deviation
    • σx - population standard deviation
    • n - number of elements in the list
    • Xmin - minimum value
    • Q1 - first quartile
    • Med - median
    • Q3 - third quartile
    • Xmax - max value
    • SSx - Sum of squared deviations
• 2-variable-statistics (2-var-stats) [Shortcut: "2varstats", "twovarstats", "tvs" or "2vs"]
  • input: listX, listY
  • output:
    
    • Σx - sum of first list
    • Σx² - sum of the squares of first list
    • x̅  - average of first list
    • Sx - sample standard deviation of first list
    • σx - population standard deviation of first list
    • Xmin - minimum value of first list
    • Xmax - maximum value of first list
    • Σy - sum of second list
    • Σy² - sum of the squares of second list
    • ȳ - average of second list
    • Sy - sample standard deviation of second list
    • σy - population standard deviation of second list
    • Ymin - minimum value of second list
    • Ymax - maximum value of second list
    • Σxy - sum of both lists
    • n - number of elements in both lists
    • r -  Pearson’s product-moment correlation coefficient
    • Q1x - First quartile of first list 
    • Medx - Median of first list
    • Q3x - Third quartile of first list 
    • Q1y - First quartile of second list 
    • Medy - Median of second list
    • Q3y - Third quartile of second list 
    • SSx - Sum of squared deviations for first list
    • SSy - Sum of squared deviations for second list
• frequency list
  
  • Input:
    • L1 - List of values
    • L2 - List of Frequencies
  • Output:
    • A new frequency list which takes each value in L1, duplicates it as many times as is specified by its corresponding frequency in L2.

• Note: If the new list is stored under a constant (like "a" in the above example), it can then be used in other functions, like so: 

Distributions & Plots

• Note: All distributions have the following extra options:
  1. Using the magnifying glass to auto-scale the axes to focus the distribution
     1.            
  2. finding the area under a curve using the CDF sub-field 
     1.    
  3. appending a ".cdf", ".pdf" or ".inversecdf"
• normal distribution (normal-dist) [Shortcut: "ndist"]
  • input:
    • µ - population mean
    • σ - population standard deviation
  • output: normal distribution
• t-distribution (t-dist) [Shortcut: "tdist"]
  • input:
    • DoF - Degrees of Freedom
  • output: t-distribution
• binomial distribution (binomial-dist) [Shortcut: "bdist"]
  • input:
    • n - # of trials
    • p - probability of success
  • output: binomial distribution
• geometric distribution (geometric-dist) [Shortcut: "gdist"]
  • input:
    • p - probability of success
  • output: geometric distribution
• poisson-distribution (poisson-dist) [Shortcut: "pdist"]
  • input:
    • µ - population mean
  • output: poisson distribution
• chi-square-distribution (χ²-dist) [Shortcut: "cdist"]
  • input:
    • DoF - Degrees of Freedom
  • output: chi-squared distribution
• cumulative distribution function (.cdf)
  • input:
    • lower bound
    • upper bound
  • output:
    • the area under the curve between the two inputted values under the given distribution 
• probability density function (.pdf)
  • input: x value
  • output: the associated y value (probability) on the given distribution
• inverse cumulative distribution function (.inversecdf) (Also known as "invNorm" or "inverseNorm")
  • input: p - probability of outcome
  • output: z-score with that tail probability
• histogram
  • input: list
  • output: histogram

• options:
  • Change Bind Width
  • Change Alignment

• boxplot
  • input: list
  • output: boxplot

• Options:
  • trim outliers

• normal probability plot (NPP or QQ Plot)
  • input: list of values
  • output:
    • normal probability plot
    • line of best fit
    • r - correlation coefficient
  • option:
    • Switch axis of Normal Quantile

Statistical Tests (Hypothesis Testing)

• ZTest
  
  • input:
    •  stats:
      • µ - population mean
      • σ - population standard deviation
      • x̅ - sample mean
      • n - sample size
    • data: 
      • µ - population mean
      • σ - population standard deviation
      • list
  • output: 
    • z-score
    • p-values:
      • <
      • >
      • ≠
    • Example:
      • 
    • If you inputed data, as opposed to stats, you'll also get:
      • x̅ - sample mean
      • n - sample size 
      • Sx - sample standard deviation
• 1PropZTest [Shortcut: "1pzt" or "opzt"]
  • input: 
    • P0 - value of null hypothesis
    • x - success count in sample
    • n - total sample size
  • output:
    • z score
    • p-values:
      • <
      • >
      • ≠
    • p̂  - sample proportion calculated as x/n
  • Example:
    • 
• 2PropZTest [Shortcut: "2pzt" or "tpzt"]
  • input:
    • x₁ - success count in the first sample
    • n₁ - size of the first sample
    • x₂ - success count in the second sample
    • n₂ - size of the second sample
  • output:
    • z-score
    • p-values:
      • <
      • >
      • ≠
    • p̂ 1 - first sample proportion calculated as x1/n1
    • p̂ 2 - second sample proportion calculated as x2/n2
    • p̂  - total sample proportion
• 2SampleZTest [Shortcut: "2szt" or "tszt"]
  • input:
    • stats:
      
      • σ1 - first population standard deviation
      • σ2 - second population standard deviation
      • x̅1 - first sample mean
      • n1 - first sample size
      • x̅2 - second sample mean
      • n2 - second sample size
    • data: 
      • σ1 - first population standard deviation
      • σ2 - second population standard deviation
      • list1
      • list2
  • output:
    • z-score
    • p-values:
      • <
      • >
      • ≠
    • If you inputed as data, you'll also get:
      • x̅1 - first sample mean
      • x̅2 - second sample mean
      • Sx1 (sample standard deviation of first list)
      • Sx2 (sample standard deviation of second list)
      • n1 - first sample size
      • n2 - second sample size
• ZInterval [Shortcut: "zint"]
  • input:
    • stats
      • σ - population standard deviation
      • x̅ - sample mean
      • n - sample size
      • c-level - confidence level
    • data
      • σ - population standard deviation
      • list
      • c-level - confidence level
  • output:
    
    • z-interval
    • If you inputted data (as opposed to stats) you also get:
      
      • x̅ - sample mean
      • n - sample size
      • Sx - sample standard deviation
• 1PropZInterval [Shortcut: "1pzi" or "opzi"]
  • input:
    • x - number of positive outcomes
    • n - total sample size
    • c-level - confidence level
  • output:
    • z-interval
    • p̂  - sample proportion calculated as x/n
    • ME - margin of error
• 2PropZInterval [Shortcut: "2pzi" or "tpzi"]
  • input:
    • x̅1 - first sample mean
    • n1 - first sample size
    • x̅2 - second sample mean
    • n2 - second sample size
    • c-level - confidence level
  • output:
    • z-interval
    • p̂ 1 - first sample proportion calculated as x1/n1
    • p̂ 2 - second sample proportion calculated as x2/n2
    • p̂ Diff:  p̂ 1 –  p̂ 2
    • ME - margin of error
• 2SampleZInterval [Shortcut: "2szi" or "tszi"]
  • input:
    • stats:
      • σ1 - population standard deviation of first list
      • σ2 - population standard deviation of second list
      • x̅1 - first sample mean
      • n1 - first sample size
      • x̅2 - second sample mean
      • n2 - second sample size
      • c-level - confidence level
    •  data:
      • σ1 - population standard deviation of first list
      • σ2 - population standard deviation of second list
      • list1
      • list2
      • c-level - confidence level
  • output:
    • z-interval 
    • x̄ Diff - Difference between the two sample means (x̅1 - x̅2)
    • ME - Margin of Error
    • If you inputted data (as opposed to stats) you also get:
      
      • x̅1 - first sample mean
      • x̅2 - second sample mean
      • Sx1 - sample standard deviation of first list
      • Sx2 - sample standard deviation of second list
      • n1 - first sample size
      • n2 - second sample size
• TTest
  • input:
    • Stats
      • µ - population mean
      • x̅ - sample mean
      • Sx - sample standard deviation
      • n - sample size
    •  Data
      • µ - population mean
      • list
  • output:
    • Data:
      • t-statistic
      • p-values:
        • <
        • >
        • ≠
      • DoF - Degrees of Freedom
    • If you inputted data (as opposed to stats) you also get:
      
      • x̅ - sample mean
      • Sx - sample standard deviation
      • n - sample size
• 2SampleTTest[Shortcut: "2stt" or "tstt"]
  • input:
    • Stats:
      • x̅1 - first sample mean
      • Sx1 - sample standard deviation of first list
      • n1 - first sample size
      • x̅2 - second sample mean
      • Sx2 - sample standard deviation of second list
      • n2 - second sample size
      • pooled (yes/no)
    •  Data:
      • list1
      • list2
      • pooled (yes/no)
  • output:
    • t-statistic
    • p-values:
      • <
      • >
      • ≠
    • DoF - Degrees of Freedom
    • If you inputted data (as opposed to stats) you also get:
      • x̅1 - first sample mean
      • x̅2 - second sample mean
      • Sx1 - sample standard deviation of first list
      • Sx2 - sample standard deviation of second list
      • n1 - first sample size
      • n2 - second sample size
• TInterval[Shortcut: "tint"]
  • input:
    • stats:
      • x̅ - sample mean
      • Sx - sample standard deviation
      • n - sample size
      • c-level - confidence level
    • data:
      
      • list
      • c-level - confidence level
  • output:
    
    • t-interval
    • DoF - Degrees of Freedom
    • If you inputted data (as opposed to stats) you also get:
      • x̅ - sample mean
      • Sx - sample standard deviation
      • n - sample size
• 2SampleTInterval[Shortcut: "2sti" or "tsti"]
  • input:
    • Stats:
      • x̅1 - first sample mean
      • Sx1 - sample standard deviation of first list
      • n1 - first sample size
      • x̅2 - second sample mean
      • Sx2 - sample standard deviation of second list
      • n2 - second sample size
      • c-level - confidence level
      • pooled (yes/no)
    • Data:
      
      • list1
      • list2
      • c-level - confidence level
      • pooled (yes/no)
  • output:
    
    • t-interval
    • DoF - Degrees of Freedom
    • x̄ Diff - Difference between the two sample means (x̅1 - x̅2)
    • ME - Margin of Error
    • If you inputted data (as opposed to stats) you also get:
      • x̅1 - first sample mean
      • x̅2 - second sample mean
      • Sx1 - sample standard deviation of first list
      • Sx2 - sample standard deviation of second list
      • n1 - first sample size
      • n2 - second sample size
• LinRegTTest [Shortcut: "lrt"]
  • input:
    • list1
    • list2
  • output:
    
    • t-statistic
    • p-values:
      • <
      • >
      • ≠
    • DoF - Degrees of Freedom
    • a - constant from y=ax+b
    • b - constant from y=ax+b
    • s - standard error
    • r - correlation coefficient
    • r² - correlation of determination
    • SES - standard error of the slope
    • Residuals
• LinRegTIntervalShortcut: "lri"]
  • input:
    • list1
    • list2
    • c-level - confidence level
  • output:
    
    • t-interval
    • DoF - Degrees of Freedom
    • a - constant from y=ax+b
    • b - constant from y=ax+b
    • s - standard error
    • r - correlation coefficient
    • r² - correlation of determination
    • SES - standard error of the slope
    • Residuals
    • ME- Margin of Error
• ChiSquareTest (χ² test) [Shortcut: "cst" or "ctest"] 
  • input:
    • Observed Matrix (inputted as an array of lists)**
  • output:
    • Expected Matrix (displayed as an array of lists)**
    • χ²-value
    • p-value
    • DoF - Degrees of Freedom
    • **This 3 X 3 matrix   would be inputted/outputted as this array of lists [[1,2,3],[4,5,6],[7,8,9]]
• ChiSquareGoodnessOfFitTest (χ²-gof-test) [Shortcut: "gof"]
  • input:
    • Observed List
    • Expected List
    • DoF - Degrees of Freedom
  • output:
    • χ²-value
    • p-value
• ANOVA [Shortcut: "anv" or "ano"]
  
  • input:
    • list1
    • list2
    • list3
    • ect... 
  • output:
    • F-statistic
    • p-value
    • Factor (Numerator):
      • DoF - Degrees of Freedom
      • SS - Sum of Squares
      • MS - Mean Square
    • Error (Denominator)
      • DoF - Degrees of Freedom
      • SS - Sum of Squares
      • MS - Mean Square
    • CLower - Lower limit of 95% confidence intervals for the mean of each input list
    • CUpper - Upper limit of 95% confidence intervals for the mean of each input list
    • X̅list - Outputs a list of means for each inputted list: [mean(L1), mean(L2)]
  •