t-test: variance

Discussion in 'Homework Help' started by zulfi100, Jan 6, 2015.

  1. zulfi100

    Thread Starter Member

    Jun 7, 2012
    320
    0
  2. Shagas

    Active Member

    May 13, 2013
    802
    74
    I suggest you find a different site to study from. They don't mention many important details and the explanations is confusing.
    Basically what you do in this sort of thing is the following:
    1)Assume that your sample is large enough that you can safely assume that you are working with values that are normally distributed (look up central limit theorem).
    2) If the variance is given as a population parameter (basically , if we know the variance) then you use a test statistic T = [(Xaverage-(population mean that you are testing against)) / (sqrt(variance))]
    and this is approximately drawn from the Normalized normal distribution N(0,1)
    3)If the variance is unknown then we estimate it by: (1/(n-1)) * Sum( Xi-Xaverage)^2 and the test statistic T = [(Xaverage-(population mean that you are testing against)) / (sqrt(Estimated variance))]
    is now equal to t(n-1)
    4) Depending on your hypothesis and a value you will reject your hypothesis if the test statistic has a smaller or bigger (depending on the hypothesis that you are testing) value than the value found in the appropriate distribution tables.
    You can look up on how that is done.
     
    zulfi100 likes this.
  3. zulfi100

    Thread Starter Member

    Jun 7, 2012
    320
    0
    Hi,
    Thanks for your reply. I have found another site. Based upon your 3rd suggestion, I have found t-test formula from a site.This is based upon unequal sample size(n1=60 & n2 =120).
    http://en.wikipedia.org/wiki/Student's_t-test#Equal_or_unequal_sample_sizes.2C_unequal_variances

    I have t=0.8145 but i dont know whether it rejects my hypotheses or not.
    I dont know how to use the table given at:
    http://www.fgse.nova.edu/edl/secure/stats/lesson4.htm

    I am not able to attach the excel file, so i am pasting my work. Some body please check if its correct or not:
    Code (Text):
    1.  
    2. Pupil :    Grade points GP    : Difference of GP from Mean (x_k-m):    sqr(x_k-m)
    3. 1    30    -2.45    6.0025
    4. 2    35.5    3.05    9.3025
    5. 3    34.5    2.05    4.2025
    6. 4    45    12.55    157.5025
    7. 5    55    22.55    508.5025
    8. 6    56    23.55    554.6025
    9. 7    45    12.55    157.5025
    10. 8    15    -17.45    304.5025
    11. 9    14.5    -17.95    322.2025
    12. 10    5    -27.45    753.5025
    13. 11    35    2.55    6.5025
    14. 12    42.5    10.05    101.0025
    15. 13    24.5    -7.95    63.2025
    16. 14    35.5    3.05    9.3025
    17. 15    24    -8.45    71.4025
    18. 16    11    -21.45    460.1025
    19. 17    12    -20.45    418.2025
    20. 18    16    -16.45    270.6025
    21. 19    54.5    22.05    486.2025
    22. 20    55.5    23.05    531.3025
    23. 21    40    7.55    57.0025
    24. 22    29    -3.45    11.9025
    25. 23    22    -10.45    109.2025
    26. 24    36    3.55    12.6025
    27. 25    31    -1.45    2.1025
    28. 26    27    -5.45    29.7025
    29. 27    28    -4.45    19.8025
    30. 28    54    21.55    464.4025
    31. 29    51    18.55    344.1025
    32. 30    54    21.55    464.4025
    33. 31    13    -19.45    378.3025
    34. 32    8    -24.45    597.8025
    35. 33    9    -23.45    549.9025
    36. 34    37    4.55    20.7025
    37. 35    43    10.55    111.3025
    38. 36    55    22.55    508.5025
    39. 37    44    11.55    133.4025
    40. 38    33    0.55    0.3025
    41. 39    22    -10.45    109.2025
    42. 40    11    -21.45    460.1025
    43. 41    1    -31.45    989.1025
    44. 42    7    -25.45    647.7025
    45. 43    8    -24.45    597.8025
    46. 44    4    -28.45    809.4025
    47. 45    24    -8.45    71.4025
    48. 46    57    24.55    602.7025
    49. 47    58    25.55    652.8025
    50. 48    39    6.55    42.9025
    51. 49    23    -9.45    89.3025
    52. 50    28    -4.45    19.8025
    53. 51    39    6.55    42.9025
    54. 52    47    14.55    211.7025
    55. 53    45    12.55    157.5025
    56. 54    41    8.55    73.1025
    57. 55    40    7.55    57.0025
    58. 56    56    23.55    554.6025
    59. 57    57    24.55    602.7025
    60. 58    60    27.55    759.0025
    61. 59    56    23.55    554.6025
    62. 60    9    -23.45    549.9025
    63. 1    30    -2.45    6.0025
    64. 2    35.5    3.05    9.3025
    65. 3    34.5    2.05    4.2025
    66. 4    45    12.55    157.5025
    67. 5    55    22.55    508.5025
    68. 6    56    23.55    554.6025
    69. 7    45    12.55    157.5025
    70. 8    15    -17.45    304.5025
    71. 9    14.5    -17.95    322.2025
    72. 10    5    -27.45    753.5025
    73. 11    35    2.55    6.5025
    74. 12    42.5    10.05    101.0025
    75. 13    24.5    -7.95    63.2025
    76. 14    35.5    3.05    9.3025
    77. 15    24    -8.45    71.4025
    78. 16    11    -21.45    460.1025
    79. 17    12    -20.45    418.2025
    80. 18    16    -16.45    270.6025
    81. 19    54.5    22.05    486.2025
    82. 20    55.5    23.05    531.3025
    83. 21    40    7.55    57.0025
    84. 22    29    -3.45    11.9025
    85. 23    22    -10.45    109.2025
    86. 24    36    3.55    12.6025
    87. 25    31    -1.45    2.1025
    88. 26    27    -5.45    29.7025
    89. 27    28    -4.45    19.8025
    90. 28    54    21.55    464.4025
    91. 29    51    18.55    344.1025
    92. 30    54    21.55    464.4025
    93. 31    13    -19.45    378.3025
    94. 32    8    -24.45    597.8025
    95. 33    9    -23.45    549.9025
    96. 34    37    4.55    20.7025
    97. 35    43    10.55    111.3025
    98. 36    55    22.55    508.5025
    99. 37    44    11.55    133.4025
    100. 38    33    0.55    0.3025
    101. 39    22    -10.45    109.2025
    102. 40    11    -21.45    460.1025
    103. 41    1    -31.45    989.1025
    104. 42    7    -25.45    647.7025
    105. 43    8    -24.45    597.8025
    106. 44    4    -28.45    809.4025
    107. 45    24    -8.45    71.4025
    108. 46    23    -9.45    89.3025
    109. 47    58    25.55    652.8025
    110. 48    39    6.55    42.9025
    111. 49    17    -15.45    238.7025
    112. 50    28    -4.45    19.8025
    113. 51    39    6.55    42.9025
    114. 52    27    -5.45    29.7025
    115. 53    45    12.55    157.5025
    116. 54    41    8.55    73.1025
    117. 55    40    7.55    57.0025
    118. 56    56    23.55    554.6025
    119. 57    57    24.55    602.7025
    120. 58    30    -2.45    6.0025
    121. 59    56    23.55    554.6025
    122. 60    9    -23.45    549.9025
    123. Mean    32.45    Sum of sqr of diff    34033.7000
    124. Variance2            283.6141667
    125. Variance2/n2            2.363451389
    126.          
    127.          
    128.          
    129.          
    130. Pupil    Grade Point GP    Diff of GP with Mean (xk-m)    sqr(xk-m)
    131. 1    27    -7.4    54.76
    132. 2    28    -6.4    40.96
    133. 3    54    19.6    384.16
    134. 4    51    16.6    275.56
    135. 5    54    19.6    384.16
    136. 6    13    -21.4    457.96
    137. 7    8    -26.4    696.96
    138. 8    9    -25.4    645.16
    139. 9    37    2.6    6.76
    140. 10    43    8.6    73.96
    141. 11    23    -11.4    129.96
    142. 12    43    8.6    73.96
    143. 13    33    -1.4    1.96
    144. 14    22    -12.4    153.76
    145. 15    19    -15.4    237.16
    146. 16    35    0.6    0.36
    147. 17    45    10.6    112.36
    148. 18    26    -8.4    70.56
    149. 19    57    22.6    510.76
    150. 20    55    20.6    424.36
    151. 21    52    17.6    309.76
    152. 22    12    -22.4    501.76
    153. 23    11    -23.4    547.56
    154. 24    23    -11.4    129.96
    155. 25    13    -21.4    457.96
    156. 26    16    -18.4    338.56
    157. 27    43    8.6    73.96
    158. 28    41    6.6    43.56
    159. 29    26    -8.4    70.56
    160. 30    59    24.6    605.16
    161. 31    40    5.6    31.36
    162. 32    43    8.6    73.96
    163. 33    44    9.6    92.16
    164. 34    55    20.6    424.36
    165. 35    53    18.6    345.96
    166. 36    51    16.6    275.56
    167. 37    27    -7.4    54.76
    168. 38    28    -6.4    40.96
    169. 39    29    -5.4    29.16
    170. 40    30    -4.4    19.36
    171. 41    31    -3.4    11.56
    172. 42    32    -2.4    5.76
    173. 43    33    -1.4    1.96
    174. 44    27    -7.4    54.76
    175. 45    34    -0.4    0.16
    176. 46    21    -13.4    179.56
    177. 47    35    0.6    0.36
    178. 48    45    10.6    112.36
    179. 49    56    21.6    466.56
    180. 50    59    24.6    605.16
    181. 51    32    -2.4    5.76
    182. 52    21    -13.4    179.56
    183. 53    40    5.6    31.36
    184. 54    14    -20.4    416.16
    185. 55    29    -5.4    29.16
    186. 56    39    4.6    21.16
    187. 57    44    9.6    92.16
    188. 58    36    1.6    2.56
    189. 59    47    12.6    158.76
    190. 60    11    -23.4    547.56
    191. Mean    34.4    Sum of sqr of diff    12124.4
    192. Variance            202.0733333
    193. Variance1/n1            3.367888889
    194. Variance1/n1+Variance2/n2            5.731340278
    195. sqrt(var1/n1 + var2/n2)            2.394021779
    196. Mean1-Mean2            1.95
    197. t            0.814528931
     
  4. zulfi100

    Thread Starter Member

    Jun 7, 2012
    320
    0
    Hi,
    I have used an online calculator. I obtained following p-value:
    Code (Text):
    1. P Value from T Score Calculator
    2.  
    3. This should be self-explanatory, but just in case it's not: your T Score goes in the T Score box, you stick your degrees of freedom in the DF box (N - 1 for single sample and dependent pairs, (N1 - 1) + (N2 - 1) for independent samples), select your significance level and whether you're testing a one or two-tailed hypothesis (if you're not sure, go with the defaults), then press the button!
    4.  
    5. If you need to derive a T Score from raw data, then you can find t test calculators here.
    6.  
    7. T Score:  
    8. DF:  
    9. Significance Level:
    10. 0.01
    11. 0.05
    12. 0.10
    13. One-tailed or two-tailed hypothesis?:
    14. One-tailed
    15. Two-tailed
    16. The P-Value is 0.416447. The result is not significant at p < 0.05.
    17.  
    The calculator is available at:
    http://www.socscistatistics.com/pvalues/tdistribution.aspx

    Kindly guide me how to improve on this.

    Zulf.
     
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