{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Reliability Scale analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Analysis 2015-06-04 13:31:06 +0530\n",
      "= Statsample::Reliability\n",
      "  == Reliability Analysis\n",
      "    Summary for Reliability Analysis\n",
      "+------------------------------+--------------------+\n",
      "| Valid Items                  | 20                 |\n",
      "| Valid cases                  | 100                |\n",
      "| Sum mean                     | -0.6359            |\n",
      "| Sum sd                       | 17.7154            |\n",
      "| Sum median                   | -2.054407295286337 |\n",
      "+------------------------------+--------------------+\n",
      "| Item mean                    | -0.0318            |\n",
      "| Item sd                      | 0.8858             |\n",
      "+------------------------------+--------------------+\n",
      "| Skewness                     | 0.2122             |\n",
      "| Kurtosis                     | 0.4319             |\n",
      "+------------------------------+--------------------+\n",
      "| Cronbach's alpha             | 0.9975             |\n",
      "| Standarized Cronbach's alpha | 0.9975             |\n",
      "| Mean rpb                     | 0.9750             |\n",
      "| Variances mean               | 0.821453           |\n",
      "| Covariances mean             | 0.782646           |\n",
      "+------------------------------+--------------------+\n",
      "\n",
      "    Items for obtain alpha(0.8) : 0\n",
      "    Items for obtain alpha(0.9) : 0\n",
      "    Items report for Reliability Analysis\n",
      "+----------+----------+---------+-----------------+----------------+---------------+---------------------+------------------+\n",
      "|   item   |   mean   |   sd    | mean if deleted | var if deleted | sd if deleted |  item-total correl. | alpha if deleted |\n",
      "+----------+----------+---------+-----------------+----------------+---------------+---------------------+------------------+\n",
      "| v0(v0)   | -0.01939 | 0.91391 | -0.61649        | 282.86748      | 16.81866      | 0.98017             | 0.99737          |\n",
      "| v1(v1)   | -0.01105 | 0.90391 | -0.62483        | 283.35031      | 16.83301      | 0.97490             | 0.99740          |\n",
      "| v2(v2)   | -0.04160 | 0.89147 | -0.59428        | 283.80743      | 16.84659      | 0.97324             | 0.99741          |\n",
      "| v3(v3)   | 0.00590  | 0.89465 | -0.64177        | 283.75704      | 16.84509      | 0.97134             | 0.99742          |\n",
      "| v4(v4)   | -0.03419 | 0.91352 | -0.60169        | 283.12127      | 16.82621      | 0.97192             | 0.99741          |\n",
      "| v5(v5)   | -0.00990 | 0.90108 | -0.62598        | 283.35560      | 16.83317      | 0.97795             | 0.99738          |\n",
      "| v6(v6)   | -0.06509 | 0.91126 | -0.57079        | 282.94896      | 16.82109      | 0.98039             | 0.99736          |\n",
      "| v7(v7)   | -0.03301 | 0.91149 | -0.60287        | 283.23276      | 16.82952      | 0.97038             | 0.99742          |\n",
      "| v8(v8)   | -0.05375 | 0.89613 | -0.58213        | 283.64726      | 16.84183      | 0.97348             | 0.99741          |\n",
      "| v9(v9)   | -0.07195 | 0.90778 | -0.56392        | 283.21608      | 16.82902      | 0.97514             | 0.99740          |\n",
      "| v10(v10) | -0.02870 | 0.91018 | -0.60718        | 283.07772      | 16.82491      | 0.97718             | 0.99738          |\n",
      "| v11(v11) | -0.02767 | 0.92831 | -0.60821        | 282.42700      | 16.80556      | 0.97899             | 0.99737          |\n",
      "| v12(v12) | -0.03720 | 0.87348 | -0.59868        | 284.31081      | 16.86152      | 0.97639             | 0.99739          |\n",
      "| v13(v13) | -0.05193 | 0.94256 | -0.58395        | 282.20356      | 16.79892      | 0.97078             | 0.99743          |\n",
      "| v14(v14) | -0.00975 | 0.91671 | -0.62613        | 282.89654      | 16.81953      | 0.97602             | 0.99739          |\n",
      "| v15(v15) | -0.03857 | 0.86246 | -0.59731        | 284.93006      | 16.87987      | 0.96718             | 0.99745          |\n",
      "| v16(v16) | -0.01798 | 0.92181 | -0.61790        | 282.57388      | 16.80993      | 0.98128             | 0.99736          |\n",
      "| v17(v17) | -0.07719 | 0.90038 | -0.55869        | 283.47451      | 16.83670      | 0.97463             | 0.99740          |\n",
      "| v18(v18) | -0.02076 | 0.89879 | -0.61511        | 283.40454      | 16.83462      | 0.97888             | 0.99737          |\n",
      "| v19(v19) | 0.00792  | 0.92351 | -0.64380        | 282.85021      | 16.81815      | 0.97000             | 0.99743          |\n",
      "+----------+----------+---------+-----------------+----------------+---------------+---------------------+------------------+\n",
      "\n",
      "    -50.00 : *\n",
      "    -39.00 : ******\n",
      "    -28.00 : *********\n",
      "    -17.00 : *********************\n",
      "    -6.00 : ***************************\n",
      "     5.00 : ********************\n",
      "    16.00 : **********\n",
      "    27.00 : *****\n",
      "    38.00 : \n",
      "    49.00 : *\n",
      "  == Multi Scale analyss\n",
      "    === Reliability analysis of scales\n",
      "      ==== Scale Scale 1\n",
      "        Summary for Scale Scale 1\n",
      "+------------------------------+---------------------+\n",
      "| Valid Items                  | 10                  |\n",
      "| Valid cases                  | 100                 |\n",
      "| Sum mean                     | -0.3434             |\n",
      "| Sum sd                       | 8.8514              |\n",
      "| Sum median                   | -1.0470435648512906 |\n",
      "+------------------------------+---------------------+\n",
      "| Item mean                    | -0.0343             |\n",
      "| Item sd                      | 0.8851              |\n",
      "+------------------------------+---------------------+\n",
      "| Skewness                     | 0.1727              |\n",
      "| Kurtosis                     | 0.5424              |\n",
      "+------------------------------+---------------------+\n",
      "| Cronbach's alpha             | 0.9952              |\n",
      "| Standarized Cronbach's alpha | 0.9952              |\n",
      "| Mean rpb                     | 0.9740              |\n",
      "| Variances mean               | 0.817537            |\n",
      "| Covariances mean             | 0.779684            |\n",
      "+------------------------------+---------------------+\n",
      "\n",
      "        Items for obtain alpha(0.8) : 0\n",
      "        Items for obtain alpha(0.9) : 0\n",
      "        Items report for Scale Scale 1\n",
      "+----------+----------+---------+-----------------+----------------+---------------+---------------------+------------------+\n",
      "|   item   |   mean   |   sd    | mean if deleted | var if deleted | sd if deleted |  item-total correl. | alpha if deleted |\n",
      "+----------+----------+---------+-----------------+----------------+---------------+---------------------+------------------+\n",
      "| v1(v1)   | -0.01105 | 0.90391 | -0.33231        | 63.52256       | 7.97010       | 0.97215             | 0.99468          |\n",
      "| v10(v10) | -0.04160 | 0.89147 | -0.30176        | 63.70750       | 7.98170       | 0.97287             | 0.99467          |\n",
      "| v2(v2)   | 0.00590  | 0.89465 | -0.34926        | 63.67059       | 7.97939       | 0.97187             | 0.99469          |\n",
      "| v3(v3)   | -0.03419 | 0.91352 | -0.30917        | 63.36891       | 7.96046       | 0.97246             | 0.99468          |\n",
      "| v4(v4)   | -0.00990 | 0.90108 | -0.33347        | 63.49721       | 7.96851       | 0.97753             | 0.99454          |\n",
      "| v5(v5)   | -0.06509 | 0.91126 | -0.27828        | 63.31355       | 7.95698       | 0.97941             | 0.99449          |\n",
      "| v6(v6)   | -0.03301 | 0.91149 | -0.31036        | 63.40747       | 7.96288       | 0.97193             | 0.99469          |\n",
      "| v7(v7)   | -0.05375 | 0.89613 | -0.28961        | 63.61415       | 7.97585       | 0.97446             | 0.99462          |\n",
      "| v8(v8)   | -0.07195 | 0.90778 | -0.27141        | 63.46304       | 7.96637       | 0.97209             | 0.99468          |\n",
      "| v9(v9)   | -0.02870 | 0.91018 | -0.31466        | 63.38617       | 7.96154       | 0.97513             | 0.99460          |\n",
      "+----------+----------+---------+-----------------+----------------+---------------+---------------------+------------------+\n",
      "\n",
      "        -30.00 : *\n",
      "        -24.00 : \n",
      "        -18.00 : *******\n",
      "        -12.00 : ****************\n",
      "        -6.00 : ******************************\n",
      "         0.00 : *************************\n",
      "         6.00 : ************\n",
      "        12.00 : *******\n",
      "        18.00 : *\n",
      "        24.00 : *\n",
      "      ==== Scale Scale 2\n",
      "        Summary for Scale Scale 2\n",
      "+------------------------------+--------------------+\n",
      "| Valid Items                  | 9                  |\n",
      "| Valid cases                  | 100                |\n",
      "| Sum mean                     | -0.2731            |\n",
      "| Sum sd                       | 8.0002             |\n",
      "| Sum median                   | -0.508167259967186 |\n",
      "+------------------------------+--------------------+\n",
      "| Item mean                    | -0.0303            |\n",
      "| Item sd                      | 0.8889             |\n",
      "+------------------------------+--------------------+\n",
      "| Skewness                     | 0.2502             |\n",
      "| Kurtosis                     | 0.3290             |\n",
      "+------------------------------+--------------------+\n",
      "| Cronbach's alpha             | 0.9946             |\n",
      "| Standarized Cronbach's alpha | 0.9947             |\n",
      "| Mean rpb                     | 0.9739             |\n",
      "| Variances mean               | 0.824273           |\n",
      "| Covariances mean             | 0.785909           |\n",
      "+------------------------------+--------------------+\n",
      "\n",
      "        Items for obtain alpha(0.8) : 0\n",
      "        Items for obtain alpha(0.9) : 0\n",
      "        Items report for Scale Scale 2\n",
      "+----------+----------+---------+-----------------+----------------+---------------+---------------------+------------------+\n",
      "|   item   |   mean   |   sd    | mean if deleted | var if deleted | sd if deleted |  item-total correl. | alpha if deleted |\n",
      "+----------+----------+---------+-----------------+----------------+---------------+---------------------+------------------+\n",
      "| v11(v11) | -0.02767 | 0.92831 | -0.24546        | 50.23527       | 7.08768       | 0.98083             | 0.99369          |\n",
      "| v12(v12) | -0.03720 | 0.87348 | -0.23593        | 51.06596       | 7.14604       | 0.97526             | 0.99391          |\n",
      "| v13(v13) | -0.05193 | 0.94256 | -0.22120        | 50.16754       | 7.08290       | 0.96972             | 0.99410          |\n",
      "| v14(v14) | -0.00975 | 0.91671 | -0.26337        | 50.48105       | 7.10500       | 0.97360             | 0.99393          |\n",
      "| v15(v15) | -0.03857 | 0.86246 | -0.23455        | 51.29881       | 7.16232       | 0.96818             | 0.99416          |\n",
      "| v16(v16) | -0.01798 | 0.92181 | -0.25515        | 50.30906       | 7.09289       | 0.98229             | 0.99364          |\n",
      "| v17(v17) | -0.07719 | 0.90038 | -0.19593        | 50.72663       | 7.12226       | 0.97202             | 0.99399          |\n",
      "| v18(v18) | -0.02076 | 0.89879 | -0.25236        | 50.69197       | 7.11983       | 0.97700             | 0.99382          |\n",
      "| v19(v19) | 0.00792  | 0.92351 | -0.28104        | 50.46942       | 7.10418       | 0.96647             | 0.99418          |\n",
      "+----------+----------+---------+-----------------+----------------+---------------+---------------------+------------------+\n",
      "\n",
      "        -30.00 : \n",
      "        -24.00 : *\n",
      "        -18.00 : *******\n",
      "        -12.00 : **************\n",
      "        -6.00 : *****************************\n",
      "         0.00 : ****************************\n",
      "         6.00 : ****************\n",
      "        12.00 : ****\n",
      "        18.00 : \n",
      "        24.00 : *\n",
      "\n"
     ]
    }
   ],
   "source": [
    "require 'statsample'\n",
    "\n",
    "Statsample::Analysis.store(Statsample::Reliability) do \n",
    "  Daru.lazy_update = true\n",
    "  samples=100\n",
    "  a=rnorm(samples)\n",
    "  \n",
    "  ds = Daru::DataFrame.new({})\n",
    "  \n",
    "  20.times do |i|\n",
    "    ds[\"v#{i}\".to_sym]= a + rnorm(samples,0,0.2)\n",
    "  end  \n",
    "  ds.update\n",
    "  \n",
    "  rel=Statsample::Reliability::ScaleAnalysis.new(ds)\n",
    "  summary rel\n",
    "  \n",
    "  ms=Statsample::Reliability::MultiScaleAnalysis.new(:name=>\"Multi Scale analyss\") do |m|\n",
    "    m.scale \"Scale 1\", ds.clone([:v1, :v2, :v3, :v4, :v5, :v6, :v7, :v8, :v9, :v10])\n",
    "    m.scale \"Scale 2\", ds.clone([:v11, :v12, :v13, :v14, :v15, :v16, :v17, :v18, :v19])\n",
    "  end\n",
    "  \n",
    "  summary ms\n",
    "  \n",
    "  Daru.lazy_update = false\n",
    "end\n",
    "\n",
    "Statsample::Analysis.run_batch"
   ]
  }
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