# t-test: variance

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

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.