Hi,
I am trying to understand the concept of t-test. I have got an example form the following site:
http://www.brightstat.com/index.php...ask=view&id=40&Itemid=60&limit=1&limitstart=1

I cant understand the how the value of variance is obtained. Somebody please guide me.

Zulfi.

 

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.

 

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:

Pupil :    Grade points GP    : Difference of GP from Mean (x_k-m):    sqr(x_k-m)
1    30    -2.45    6.0025
2    35.5    3.05    9.3025
3    34.5    2.05    4.2025
4    45    12.55    157.5025
5    55    22.55    508.5025
6    56    23.55    554.6025
7    45    12.55    157.5025
8    15    -17.45    304.5025
9    14.5    -17.95    322.2025
10    5    -27.45    753.5025
11    35    2.55    6.5025
12    42.5    10.05    101.0025
13    24.5    -7.95    63.2025
14    35.5    3.05    9.3025
15    24    -8.45    71.4025
16    11    -21.45    460.1025
17    12    -20.45    418.2025
18    16    -16.45    270.6025
19    54.5    22.05    486.2025
20    55.5    23.05    531.3025
21    40    7.55    57.0025
22    29    -3.45    11.9025
23    22    -10.45    109.2025
24    36    3.55    12.6025
25    31    -1.45    2.1025
26    27    -5.45    29.7025
27    28    -4.45    19.8025
28    54    21.55    464.4025
29    51    18.55    344.1025
30    54    21.55    464.4025
31    13    -19.45    378.3025
32    8    -24.45    597.8025
33    9    -23.45    549.9025
34    37    4.55    20.7025
35    43    10.55    111.3025
36    55    22.55    508.5025
37    44    11.55    133.4025
38    33    0.55    0.3025
39    22    -10.45    109.2025
40    11    -21.45    460.1025
41    1    -31.45    989.1025
42    7    -25.45    647.7025
43    8    -24.45    597.8025
44    4    -28.45    809.4025
45    24    -8.45    71.4025
46    57    24.55    602.7025
47    58    25.55    652.8025
48    39    6.55    42.9025
49    23    -9.45    89.3025
50    28    -4.45    19.8025
51    39    6.55    42.9025
52    47    14.55    211.7025
53    45    12.55    157.5025
54    41    8.55    73.1025
55    40    7.55    57.0025
56    56    23.55    554.6025
57    57    24.55    602.7025
58    60    27.55    759.0025
59    56    23.55    554.6025
60    9    -23.45    549.9025
1    30    -2.45    6.0025
2    35.5    3.05    9.3025
3    34.5    2.05    4.2025
4    45    12.55    157.5025
5    55    22.55    508.5025
6    56    23.55    554.6025
7    45    12.55    157.5025
8    15    -17.45    304.5025
9    14.5    -17.95    322.2025
10    5    -27.45    753.5025
11    35    2.55    6.5025
12    42.5    10.05    101.0025
13    24.5    -7.95    63.2025
14    35.5    3.05    9.3025
15    24    -8.45    71.4025
16    11    -21.45    460.1025
17    12    -20.45    418.2025
18    16    -16.45    270.6025
19    54.5    22.05    486.2025
20    55.5    23.05    531.3025
21    40    7.55    57.0025
22    29    -3.45    11.9025
23    22    -10.45    109.2025
24    36    3.55    12.6025
25    31    -1.45    2.1025
26    27    -5.45    29.7025
27    28    -4.45    19.8025
28    54    21.55    464.4025
29    51    18.55    344.1025
30    54    21.55    464.4025
31    13    -19.45    378.3025
32    8    -24.45    597.8025
33    9    -23.45    549.9025
34    37    4.55    20.7025
35    43    10.55    111.3025
36    55    22.55    508.5025
37    44    11.55    133.4025
38    33    0.55    0.3025
39    22    -10.45    109.2025
40    11    -21.45    460.1025
41    1    -31.45    989.1025
42    7    -25.45    647.7025
43    8    -24.45    597.8025
44    4    -28.45    809.4025
45    24    -8.45    71.4025
46    23    -9.45    89.3025
47    58    25.55    652.8025
48    39    6.55    42.9025
49    17    -15.45    238.7025
50    28    -4.45    19.8025
51    39    6.55    42.9025
52    27    -5.45    29.7025
53    45    12.55    157.5025
54    41    8.55    73.1025
55    40    7.55    57.0025
56    56    23.55    554.6025
57    57    24.55    602.7025
58    30    -2.45    6.0025
59    56    23.55    554.6025
60    9    -23.45    549.9025
Mean    32.45    Sum of sqr of diff    34033.7000
Variance2            283.6141667
Variance2/n2            2.363451389
         
         
         
         
Pupil    Grade Point GP    Diff of GP with Mean (xk-m)    sqr(xk-m)
1    27    -7.4    54.76
2    28    -6.4    40.96
3    54    19.6    384.16
4    51    16.6    275.56
5    54    19.6    384.16
6    13    -21.4    457.96
7    8    -26.4    696.96
8    9    -25.4    645.16
9    37    2.6    6.76
10    43    8.6    73.96
11    23    -11.4    129.96
12    43    8.6    73.96
13    33    -1.4    1.96
14    22    -12.4    153.76
15    19    -15.4    237.16
16    35    0.6    0.36
17    45    10.6    112.36
18    26    -8.4    70.56
19    57    22.6    510.76
20    55    20.6    424.36
21    52    17.6    309.76
22    12    -22.4    501.76
23    11    -23.4    547.56
24    23    -11.4    129.96
25    13    -21.4    457.96
26    16    -18.4    338.56
27    43    8.6    73.96
28    41    6.6    43.56
29    26    -8.4    70.56
30    59    24.6    605.16
31    40    5.6    31.36
32    43    8.6    73.96
33    44    9.6    92.16
34    55    20.6    424.36
35    53    18.6    345.96
36    51    16.6    275.56
37    27    -7.4    54.76
38    28    -6.4    40.96
39    29    -5.4    29.16
40    30    -4.4    19.36
41    31    -3.4    11.56
42    32    -2.4    5.76
43    33    -1.4    1.96
44    27    -7.4    54.76
45    34    -0.4    0.16
46    21    -13.4    179.56
47    35    0.6    0.36
48    45    10.6    112.36
49    56    21.6    466.56
50    59    24.6    605.16
51    32    -2.4    5.76
52    21    -13.4    179.56
53    40    5.6    31.36
54    14    -20.4    416.16
55    29    -5.4    29.16
56    39    4.6    21.16
57    44    9.6    92.16
58    36    1.6    2.56
59    47    12.6    158.76
60    11    -23.4    547.56
Mean    34.4    Sum of sqr of diff    12124.4
Variance            202.0733333
Variance1/n1            3.367888889
Variance1/n1+Variance2/n2            5.731340278
sqrt(var1/n1 + var2/n2)            2.394021779
Mean1-Mean2            1.95
t            0.814528931

 

Hi,
I have used an online calculator. I obtained following p-value:

P Value from T Score Calculator

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!

If you need to derive a T Score from raw data, then you can find t test calculators here.

T Score:   
DF:   
Significance Level:
0.01
0.05
0.10
One-tailed or two-tailed hypothesis?:
One-tailed
Two-tailed
The P-Value is 0.416447. The result is not significant at p < 0.05.

The calculator is available at:
http://www.socscistatistics.com/pvalues/tdistribution.aspx

Kindly guide me how to improve on this.

Zulf.