The Caffeine and Endurance dataset

#r "nuget: FSharp.Data"
#r "nuget: Deedle"

open FSharp.Data
open Deedle
open System.Text.RegularExpressions

let rawDataCaffeine = Http.RequestString @"https://raw.githubusercontent.com/fslaborg/datasets/main/data/CaffeineAndEndurance(wide).dat"
// This data format features a char column-wise structure. To transform it into a seperator-delimited format, we have to replace the multiple spaces via Regex:
let regexCaffeine = [Regex("[ ]{2,}1"), "1"; Regex("[ ]{2,}"), "\t"; Regex("\n\t"), "\n"]
let rawDataCaffeineAdapted = 
    regexCaffeine
    |> List.fold (fun acc (reg,rep) -> reg.Replace(acc, rep)) rawDataCaffeine

let df = Frame.ReadCsvString(rawDataCaffeineAdapted, hasHeaders = false, separators = "\t", schema = "Subject ID, no Dose, 5 mg, 9 mg, 13 mg")

// Otherwise, the following already adapted dataset can be used:
let rawData2 = Http.RequestString @"https://raw.githubusercontent.com/fslaborg/datasets/main/data/CaffeineAndEndurance(wide)_adapted.tsv"

let df2 = Frame.ReadCsvString(rawData2, hasHeaders = false, separators = "\t", schema = "Subject ID, no Dose, 5 mg, 9 mg, 13 mg")

df2.Print()

Subject ID no Dose 5 mg  9 mg  13 mg 
0 -> 1          36.05   42.47 51.5  37.55 
1 -> 2          52.47   85.15 65    59.3  
2 -> 3          56.55   63.2  73.1  79.12 
3 -> 4          45.2    52.1  64.4  58.33 
4 -> 5          35.25   66.2  57.45 70.54 
5 -> 6          66.38   73.25 76.49 69.47 
6 -> 7          40.57   44.5  40.55 46.48 
7 -> 8          57.15   57.17 66.47 66.35 
8 -> 9          28.34   35.05 33.17 36.2

#r "nuget: FSharp.Stats, 0.4.2"
#r "nuget: Plotly.NET, 2.0.0-preview.6"

open FSharp.Stats
open FSharp.Stats.Testing
open Plotly.NET

// We want to compare the subjects' performances under the influence of 13 mg caffeine and in the control situation.
let dataCaffeineNoDose, dataCaffeine13mg =
    let getVectorFromCol col = 
        df2
        |> Frame.getCol col
        |> Series.values
        |> vector
    getVectorFromCol "no Dose", getVectorFromCol "13 mg"

// Transforming our data into a chart.
let visualizePairedData = 
    Seq.zip dataCaffeineNoDose dataCaffeine13mg
    |> Seq.mapi (fun i (control,treatment) -> 
        let participant = "Person " + string (i + 1)
        Chart.Line(["no dose", control; "13 mg", treatment], Name = participant)
        )
    |> Chart.Combine
    |> Chart.withX_AxisStyle ""
    |> Chart.withY_AxisStyle("endurance performance", MinMax = (0.,100.))

let twoSamplePairedResult = TTest.twoSamplePaired dataCaffeineNoDose dataCaffeine13mg

{ Statistic = 3.252507672
  DegreesOfFreedom = 8.0
  PValueLeft = 0.9941713794
  PValueRight = 0.005828620625
  PValue = 0.01165724125 }

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namespace FSharp

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namespace Microsoft.FSharp

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namespace FSharp.Data

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namespace Microsoft.FSharp.Data

namespace Deedle

namespace System

namespace System.Text

namespace System.Text.RegularExpressions

val rawDataCaffeine : string

type Http = private new : unit -> Http static member private AppendQueryToUrl : url:string * query:(string * string) list -> string static member AsyncRequest : url:string * ?query:(string * string) list * ?headers:seq<string * string> * ?httpMethod:string * ?body:HttpRequestBody * ?cookies:seq<string * string> * ?cookieContainer:CookieContainer * ?silentHttpErrors:bool * ?silentCookieErrors:bool * ?responseEncodingOverride:string * ?customizeHttpRequest:(HttpWebRequest -> HttpWebRequest) * ?timeout:int -> Async<HttpResponse> static member AsyncRequestStream : url:string * ?query:(string * string) list * ?headers:seq<string * string> * ?httpMethod:string * ?body:HttpRequestBody * ?cookies:seq<string * string> * ?cookieContainer:CookieContainer * ?silentHttpErrors:bool * ?silentCookieErrors:bool * ?customizeHttpRequest:(HttpWebRequest -> HttpWebRequest) * ?timeout:int -> Async<HttpResponseWithStream> static member AsyncRequestString : url:string * ?query:(string * string) list * ?headers:seq<string * string> * ?httpMethod:string * ?body:HttpRequestBody * ?cookies:seq<string * string> * ?cookieContainer:CookieContainer * ?silentHttpErrors:bool * ?silentCookieErrors:bool * ?responseEncodingOverride:string * ?customizeHttpRequest:(HttpWebRequest -> HttpWebRequest) * ?timeout:int -> Async<string> static member private EncodeFormData : query:string -> string static member private InnerRequest : url:string * toHttpResponse:(string -> int -> string -> string -> 'a0 option -> Map<string,string> -> Map<string,string> -> Stream -> Async<'a1>) * ?query:(string * string) list * ?headers:seq<string * string> * ?httpMethod:string * ?body:HttpRequestBody * ?cookies:seq<string * string> * ?cookieContainer:CookieContainer * ?silentHttpErrors:bool * ?silentCookieErrors:bool * ?responseEncodingOverride:'a0 * ?customizeHttpRequest:(HttpWebRequest -> HttpWebRequest) * ?timeout:int -> Async<'a1> static member Request : url:string * ?query:(string * string) list * ?headers:seq<string * string> * ?httpMethod:string * ?body:HttpRequestBody * ?cookies:seq<string * string> * ?cookieContainer:CookieContainer * ?silentHttpErrors:bool * ?silentCookieErrors:bool * ?responseEncodingOverride:string * ?customizeHttpRequest:(HttpWebRequest -> HttpWebRequest) * ?timeout:int -> HttpResponse static member RequestStream : url:string * ?query:(string * string) list * ?headers:seq<string * string> * ?httpMethod:string * ?body:HttpRequestBody * ?cookies:seq<string * string> * ?cookieContainer:CookieContainer * ?silentHttpErrors:bool * ?silentCookieErrors:bool * ?customizeHttpRequest:(HttpWebRequest -> HttpWebRequest) * ?timeout:int -> HttpResponseWithStream static member RequestString : url:string * ?query:(string * string) list * ?headers:seq<string * string> * ?httpMethod:string * ?body:HttpRequestBody * ?cookies:seq<string * string> * ?cookieContainer:CookieContainer * ?silentHttpErrors:bool * ?silentCookieErrors:bool * ?responseEncodingOverride:string * ?customizeHttpRequest:(HttpWebRequest -> HttpWebRequest) * ?timeout:int -> string
<summary> Utilities for working with network via HTTP. Includes methods for downloading resources with specified headers, query parameters and HTTP body </summary>

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static member Http.RequestString : url:string * ?query:(string * string) list * ?headers:seq<string * string> * ?httpMethod:string * ?body:HttpRequestBody * ?cookies:seq<string * string> * ?cookieContainer:System.Net.CookieContainer * ?silentHttpErrors:bool * ?silentCookieErrors:bool * ?responseEncodingOverride:string * ?customizeHttpRequest:(System.Net.HttpWebRequest -> System.Net.HttpWebRequest) * ?timeout:int -> string

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static member Http.RequestString : url:string * ?query:(string * string) list * ?headers:seq<string * string> * ?httpMethod:string * ?body:HttpRequestBody * ?cookies:seq<string * string> * ?cookieContainer:System.Net.CookieContainer * ?silentHttpErrors:bool * ?silentCookieErrors:bool * ?responseEncodingOverride:string * ?customizeHttpRequest:(System.Net.HttpWebRequest -> System.Net.HttpWebRequest) * ?timeout:int -> string

val regexCaffeine : (Regex * string) list

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type Regex = interface ISerializable new : unit -> unit + 4 overloads member GetGroupNames : unit -> string [] member GetGroupNumbers : unit -> int [] member GroupNameFromNumber : i: int -> string member GroupNumberFromName : name: string -> int member InitializeReferences : unit -> unit member IsMatch : input: string -> bool + 4 overloads member Match : input: string -> Match + 5 overloads member Matches : input: string -> MatchCollection + 4 overloads ...
<summary>Represents an immutable regular expression.</summary>

--------------------
Regex(pattern: string) : Regex
Regex(pattern: string, options: RegexOptions) : Regex
Regex(pattern: string, options: RegexOptions, matchTimeout: System.TimeSpan) : Regex

val rawDataCaffeineAdapted : string

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module List from Microsoft.FSharp.Collections
<summary>Contains operations for working with values of type <see cref="T:Microsoft.FSharp.Collections.list`1" />.</summary>
<namespacedoc><summary>Operations for collections such as lists, arrays, sets, maps and sequences. See also <a href="https://docs.microsoft.com/dotnet/fsharp/language-reference/fsharp-collection-types">F# Collection Types</a> in the F# Language Guide. </summary></namespacedoc>

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type List<'T> = | ( [] ) | ( :: ) of Head: 'T * Tail: 'T list interface IReadOnlyList<'T> interface IReadOnlyCollection<'T> interface IEnumerable interface IEnumerable<'T> member GetReverseIndex : rank:int * offset:int -> int member GetSlice : startIndex:int option * endIndex:int option -> 'T list static member Cons : head:'T * tail:'T list -> 'T list member Head : 'T member IsEmpty : bool member Item : index:int -> 'T with get ...
<summary>The type of immutable singly-linked lists.</summary>
<remarks>Use the constructors <c>[]</c> and <c>::</c> (infix) to create values of this type, or the notation <c>[1;2;3]</c>. Use the values in the <c>List</c> module to manipulate values of this type, or pattern match against the values directly. </remarks>
<exclude />

val fold : folder:('State -> 'T -> 'State) -> state:'State -> list:'T list -> 'State
<summary>Applies a function to each element of the collection, threading an accumulator argument through the computation. Take the second argument, and apply the function to it and the first element of the list. Then feed this result into the function along with the second element and so on. Return the final result. If the input function is <c>f</c> and the elements are <c>i0...iN</c> then computes <c>f (... (f s i0) i1 ...) iN</c>.</summary>
<param name="folder">The function to update the state given the input elements.</param>
<param name="state">The initial state.</param>
<param name="list">The input list.</param>
<returns>The final state value.</returns>

val acc : string

val reg : Regex

val rep : string

Regex.Replace(input: string, evaluator: MatchEvaluator) : string
Regex.Replace(input: string, replacement: string) : string
Regex.Replace(input: string, evaluator: MatchEvaluator, count: int) : string
Regex.Replace(input: string, replacement: string, count: int) : string
Regex.Replace(input: string, evaluator: MatchEvaluator, count: int, startat: int) : string
Regex.Replace(input: string, replacement: string, count: int, startat: int) : string

val df : Frame<int,string>

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module Frame from Deedle

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type Frame = static member ReadCsv : location:string * hasHeaders:Nullable<bool> * inferTypes:Nullable<bool> * inferRows:Nullable<int> * schema:string * separators:string * culture:string * maxRows:Nullable<int> * missingValues:string [] * preferOptions:bool -> Frame<int,string> + 1 overload static member ReadReader : reader:IDataReader -> Frame<int,string> static member CustomExpanders : Dictionary<Type,Func<obj,seq<string * Type * obj>>> static member NonExpandableInterfaces : ResizeArray<Type> static member NonExpandableTypes : HashSet<Type>

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type Frame<'TRowKey,'TColumnKey (requires equality and equality)> = interface IDynamicMetaObjectProvider interface INotifyCollectionChanged interface IFsiFormattable interface IFrame new : rowIndex:IIndex<'TRowKey> * columnIndex:IIndex<'TColumnKey> * data:IVector<IVector> * indexBuilder:IIndexBuilder * vectorBuilder:IVectorBuilder -> Frame<'TRowKey,'TColumnKey> + 1 overload member AddColumn : column:'TColumnKey * series:seq<'V> -> unit + 3 overloads member AggregateRowsBy : groupBy:seq<'TColumnKey> * aggBy:seq<'TColumnKey> * aggFunc:Func<Series<'TRowKey,'a>,'b> -> Frame<int,'TColumnKey> member Clone : unit -> Frame<'TRowKey,'TColumnKey> member ColumnApply : f:Func<Series<'TRowKey,'T>,ISeries<'TRowKey>> -> Frame<'TRowKey,'TColumnKey> + 1 overload member DropColumn : column:'TColumnKey -> unit ...

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new : names:seq<'TColumnKey> * columns:seq<ISeries<'TRowKey>> -> Frame<'TRowKey,'TColumnKey>
new : rowIndex:Indices.IIndex<'TRowKey> * columnIndex:Indices.IIndex<'TColumnKey> * data:IVector<IVector> * indexBuilder:Indices.IIndexBuilder * vectorBuilder:Vectors.IVectorBuilder -> Frame<'TRowKey,'TColumnKey>

static member Frame.ReadCsvString : csvString:string * ?hasHeaders:bool * ?inferTypes:bool * ?inferRows:int * ?schema:string * ?separators:string * ?culture:string * ?maxRows:int * ?missingValues:string [] * ?preferOptions:bool -> Frame<int,string>

val rawData2 : string

val df2 : Frame<int,string>

static member FrameExtensions.Print : frame:Frame<'K,'V> -> unit (requires equality and equality)
static member FrameExtensions.Print : frame:Frame<'K,'V> * printTypes:bool -> unit (requires equality and equality)

namespace FSharp.Stats

namespace FSharp.Stats.Testing

namespace Plotly

namespace Plotly.NET

val dataCaffeineNoDose : Vector<float>

val dataCaffeine13mg : Vector<float>

val getVectorFromCol : (string -> Vector<float>)

val col : string

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module Frame from Deedle

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type Frame = inherit DynamicObj new : unit -> Frame

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type Frame<'TRowKey,'TColumnKey (requires equality and equality)> = interface IDynamicMetaObjectProvider interface INotifyCollectionChanged interface IFsiFormattable interface IFrame new : rowIndex:IIndex<'TRowKey> * columnIndex:IIndex<'TColumnKey> * data:IVector<IVector> * indexBuilder:IIndexBuilder * vectorBuilder:IVectorBuilder -> Frame<'TRowKey,'TColumnKey> + 1 overload member AddColumn : column:'TColumnKey * series:seq<'V> -> unit + 3 overloads member AggregateRowsBy : groupBy:seq<'TColumnKey> * aggBy:seq<'TColumnKey> * aggFunc:Func<Series<'TRowKey,'a>,'b> -> Frame<int,'TColumnKey> member Clone : unit -> Frame<'TRowKey,'TColumnKey> member ColumnApply : f:Func<Series<'TRowKey,'T>,ISeries<'TRowKey>> -> Frame<'TRowKey,'TColumnKey> + 1 overload member DropColumn : column:'TColumnKey -> unit ...

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new : unit -> Frame

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new : names:seq<'TColumnKey> * columns:seq<ISeries<'TRowKey>> -> Frame<'TRowKey,'TColumnKey>
new : rowIndex:Indices.IIndex<'TRowKey> * columnIndex:Indices.IIndex<'TColumnKey> * data:IVector<IVector> * indexBuilder:Indices.IIndexBuilder * vectorBuilder:Vectors.IVectorBuilder -> Frame<'TRowKey,'TColumnKey>

val getCol : column:'C -> frame:Frame<'R,'C> -> Series<'R,'V> (requires equality and equality)

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module Series from Deedle

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type Series = static member ofNullables : values:seq<Nullable<'a0>> -> Series<int,'a0> (requires default constructor and value type and 'a0 :> ValueType) static member ofObservations : observations:seq<'c * 'd> -> Series<'c,'d> (requires equality) static member ofOptionalObservations : observations:seq<'K * 'a1 option> -> Series<'K,'a1> (requires equality) static member ofValues : values:seq<'a> -> Series<int,'a>

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type Series<'K,'V (requires equality)> = interface IFsiFormattable interface ISeries<'K> new : index:IIndex<'K> * vector:IVector<'V> * vectorBuilder:IVectorBuilder * indexBuilder:IIndexBuilder -> Series<'K,'V> + 3 overloads member After : lowerExclusive:'K -> Series<'K,'V> member Aggregate : aggregation:Aggregation<'K> * keySelector:Func<DataSegment<Series<'K,'V>>,'TNewKey> * valueSelector:Func<DataSegment<Series<'K,'V>>,OptionalValue<'R>> -> Series<'TNewKey,'R> (requires equality) + 1 overload member AsyncMaterialize : unit -> Async<Series<'K,'V>> member Before : upperExclusive:'K -> Series<'K,'V> member Between : lowerInclusive:'K * upperInclusive:'K -> Series<'K,'V> member Compare : another:Series<'K,'V> -> Series<'K,Diff<'V>> member Convert : forward:Func<'V,'R> * backward:Func<'R,'V> -> Series<'K,'R> ...

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new : pairs:seq<System.Collections.Generic.KeyValuePair<'K,'V>> -> Series<'K,'V>
new : keys:seq<'K> * values:seq<'V> -> Series<'K,'V>
new : keys:'K [] * values:'V [] -> Series<'K,'V>
new : index:Indices.IIndex<'K> * vector:IVector<'V> * vectorBuilder:Vectors.IVectorBuilder * indexBuilder:Indices.IIndexBuilder -> Series<'K,'V>

val values : series:Series<'K,'T> -> seq<'T> (requires equality)

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val vector : l:seq<float> -> Vector<float>

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type vector = Vector<float>

val visualizePairedData : GenericChart.GenericChart

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module Seq from Plotly.NET

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module Seq from FSharp.Stats
<summary> Module to compute common statistical measure </summary>

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module Seq from Microsoft.FSharp.Collections
<summary>Contains operations for working with values of type <see cref="T:Microsoft.FSharp.Collections.seq`1" />.</summary>

val zip : source1:seq<'T1> -> source2:seq<'T2> -> seq<'T1 * 'T2>
<summary>Combines the two sequences into a list of pairs. The two sequences need not have equal lengths: when one sequence is exhausted any remaining elements in the other sequence are ignored.</summary>
<param name="source1">The first input sequence.</param>
<param name="source2">The second input sequence.</param>
<returns>The result sequence.</returns>
<exception cref="T:System.ArgumentNullException">Thrown when either of the input sequences is null.</exception>

val mapi : mapping:(int -> 'T -> 'U) -> source:seq<'T> -> seq<'U>
<summary>Builds a new collection whose elements are the results of applying the given function to each of the elements of the collection. The integer index passed to the function indicates the index (from 0) of element being transformed.</summary>
<param name="mapping">A function to transform items from the input sequence that also supplies the current index.</param>
<param name="source">The input sequence.</param>
<returns>The result sequence.</returns>
<exception cref="T:System.ArgumentNullException">Thrown when the input sequence is null.</exception>

val i : int

val control : float

val treatment : float

val participant : string

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val string : value:'T -> string
<summary>Converts the argument to a string using <c>ToString</c>.</summary>
<remarks>For standard integer and floating point values the and any type that implements <c>IFormattable</c><c>ToString</c> conversion uses <c>CultureInfo.InvariantCulture</c>. </remarks>
<param name="value">The input value.</param>
<returns>The converted string.</returns>

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type string = System.String
<summary>An abbreviation for the CLI type <see cref="T:System.String" />.</summary>
<category>Basic Types</category>

type Chart = static member Area : x:seq<#IConvertible> * y:seq<#IConvertible> * ?Name:string * ?ShowMarkers:bool * ?Showlegend:bool * ?MarkerSymbol:Symbol * ?Color:string * ?Opacity:float * ?Labels:seq<#IConvertible> * ?TextPosition:TextPosition * ?TextFont:Font * ?Dash:DrawingStyle * ?Width:float -> GenericChart + 1 overload static member Bar : keys:seq<#IConvertible> * values:seq<#IConvertible> * ?Name:string * ?Showlegend:bool * ?Color:string * ?Opacity:float * ?Labels:seq<#IConvertible> * ?TextPosition:TextPosition * ?TextFont:Font * ?Marker:Marker -> GenericChart + 1 overload static member BoxPlot : ?x:'a0 * ?y:'a1 * ?Name:string * ?Showlegend:bool * ?Color:string * ?Fillcolor:'a2 * ?Opacity:float * ?Whiskerwidth:'a3 * ?Boxpoints:Boxpoints * ?Boxmean:BoxMean * ?Jitter:'a4 * ?Pointpos:'a5 * ?Orientation:Orientation * ?Marker:Marker * ?Line:Line * ?Alignmentgroup:'a6 * ?Offsetgroup:'a7 * ?Notched:bool * ?NotchWidth:float * ?QuartileMethod:QuartileMethod -> GenericChart + 1 overload static member Bubble : x:seq<#IConvertible> * y:seq<#IConvertible> * sizes:seq<#IConvertible> * ?Name:string * ?Showlegend:bool * ?MarkerSymbol:Symbol * ?Color:string * ?Opacity:float * ?Labels:seq<#IConvertible> * ?TextPosition:TextPosition * ?TextFont:Font * ?StackGroup:string * ?Orientation:Orientation * ?GroupNorm:GroupNorm * ?UseWebGL:bool -> GenericChart + 1 overload static member Candlestick : open:seq<#IConvertible> * high:seq<#IConvertible> * low:seq<#IConvertible> * close:seq<#IConvertible> * x:seq<#IConvertible> * ?Increasing:Line * ?Decreasing:Line * ?WhiskerWidth:float * ?Line:Line * ?XCalendar:Calendar -> GenericChart + 1 overload static member ChoroplethMap : locations:seq<string> * z:seq<#IConvertible> * ?Text:seq<#IConvertible> * ?Locationmode:LocationFormat * ?Autocolorscale:bool * ?Colorscale:Colorscale * ?Colorbar:Colorbar * ?Marker:Marker * ?GeoJson:'a2 * ?FeatureIdKey:string * ?Zmin:float * ?Zmax:float -> GenericChart static member ChoroplethMapbox : locations:seq<#IConvertible> * z:seq<#IConvertible> * geoJson:'a2 * ?FeatureIdKey:string * ?Text:seq<#IConvertible> * ?Below:string * ?Colorscale:Colorscale * ?Colorbar:Colorbar * ?ZAuto:bool * ?ZMin:float * ?ZMid:float * ?ZMax:float -> GenericChart static member Column : keys:seq<#IConvertible> * values:seq<#IConvertible> * ?Name:string * ?Showlegend:bool * ?Color:string * ?Opacity:float * ?Labels:seq<#IConvertible> * ?TextPosition:TextPosition * ?TextFont:Font * ?Marker:Marker -> GenericChart + 1 overload static member Contour : data:seq<#seq<'a1>> * ?X:seq<#IConvertible> * ?Y:seq<#IConvertible> * ?Name:string * ?Showlegend:bool * ?Opacity:float * ?Colorscale:Colorscale * ?Showscale:'a4 * ?zSmooth:SmoothAlg * ?Colorbar:'a5 -> GenericChart (requires 'a1 :> IConvertible) static member DensityMapbox : lon:seq<#IConvertible> * lat:seq<#IConvertible> * ?Z:seq<#IConvertible> * ?Radius:float * ?Opacity:float * ?Text:seq<#IConvertible> * ?Below:string * ?Colorscale:Colorscale * ?Colorbar:Colorbar * ?Showscale:bool * ?ZAuto:bool * ?ZMin:float * ?ZMid:float * ?ZMax:float -> GenericChart + 1 overload ...
<summary> Provides a set of static methods for creating charts. </summary>

static member Chart.Line : xy:seq<#System.IConvertible * #System.IConvertible> * ?Name:string * ?ShowMarkers:bool * ?Showlegend:bool * ?MarkerSymbol:StyleParam.Symbol * ?Color:string * ?Opacity:float * ?Labels:seq<#System.IConvertible> * ?TextPosition:StyleParam.TextPosition * ?TextFont:Font * ?Dash:StyleParam.DrawingStyle * ?Width:float * ?StackGroup:string * ?Orientation:StyleParam.Orientation * ?GroupNorm:StyleParam.GroupNorm * ?UseWebGL:bool -> GenericChart.GenericChart
static member Chart.Line : x:seq<#System.IConvertible> * y:seq<#System.IConvertible> * ?Name:string * ?ShowMarkers:bool * ?Showlegend:bool * ?MarkerSymbol:StyleParam.Symbol * ?Color:string * ?Opacity:float * ?Labels:seq<#System.IConvertible> * ?TextPosition:StyleParam.TextPosition * ?TextFont:Font * ?Dash:StyleParam.DrawingStyle * ?Width:float * ?StackGroup:string * ?Orientation:StyleParam.Orientation * ?GroupNorm:StyleParam.GroupNorm * ?UseWebGL:bool -> GenericChart.GenericChart

static member Chart.Combine : gCharts:seq<GenericChart.GenericChart> -> GenericChart.GenericChart

static member Chart.withX_AxisStyle : title:string * ?MinMax:(float * float) * ?Showgrid:bool * ?Showline:bool * ?Side:StyleParam.Side * ?Overlaying:StyleParam.AxisAnchorId * ?Id:int * ?Domain:(float * float) * ?Position:float * ?Zeroline:bool * ?Anchor:StyleParam.AxisAnchorId -> (GenericChart.GenericChart -> GenericChart.GenericChart)

static member Chart.withY_AxisStyle : title:string * ?MinMax:(float * float) * ?Showgrid:bool * ?Showline:bool * ?Side:StyleParam.Side * ?Overlaying:StyleParam.AxisAnchorId * ?Id:int * ?Domain:(float * float) * ?Position:float * ?Zeroline:bool * ?Anchor:StyleParam.AxisAnchorId -> (GenericChart.GenericChart -> GenericChart.GenericChart)

module GenericChart from Plotly.NET
<summary> Module to represent a GenericChart </summary>

val toChartHTML : gChart:GenericChart.GenericChart -> string
<summary> Converts a GenericChart to it HTML representation. The div layer has a default size of 600 if not specified otherwise. </summary>

val twoSamplePairedResult : TestStatistics.TTestStatistics

module TTest from FSharp.Stats.Testing

val twoSamplePaired : sample1:Vector<float> -> sample2:Vector<float> -> TestStatistics.TTestStatistics
<summary> which observations in one sample can be paired with observations in the other sample. </summary>