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Homework Help: T-test and effect size

  1. Nov 21, 2008 #1
    Hello! I hope it's okay to ask stats questions...
    I think the calculations are correct, but I would appreciate it if someone could check for me!
    These are the results from the exp. using repeated measures. My hypothesis is that the reuslts in condition 2 should be less than condition 1.
    Cond 1
    49
    41
    42
    44
    44
    42
    66
    57
    44
    66
    66
    59
    Cond 2
    43
    39
    36
    42
    48
    41
    38
    44
    34
    40
    32
    43

    I know working out the standard deviation is tedious, but I checked with excel and it matched (I used n-1, so I got the population, not just the sample).
    So, for condition 1:
    mean=51.66666667
    s.d.= 10.36895132
    standard error= 2.99325842
    and condition 2:
    mean= 40
    s.d.= 4.51260859854
    standard error= 1.30267789
    These (I think) are correct, its the t-test, p value and effect size I would greatly appreciate some feedback for.
    For the t-test I used the realted t-test, since its repeated measures (same participant in both):
    ttestaudio.jpg
    I got t= 3.346118674
    are the units sd?
    and DoF would be 11, and since I specified a direction, I got p=0.003261139 (one-tailed); which is significant? since P is less than 0.05?
    and for effect size:
    effectsizeaudio.jpg
    I got (d)= 1.567935986
    Can somone verify the t-test, effect size and p value for me? Please! I used fractions at some points where I could quickly get the data (I wrote it down), in ideal circumstances should I use fractions for all the 'inputs' (e.g. stand. dev of difference, etc.), if possible, since its more 'accurate'?
    Thanks! I now it's a lot to ask, but I would geratly appreciate it! I realise the formuale are slightly different depending on the narue of the experiment, I think I chose the right ones!
     
  2. jcsd
  3. Nov 22, 2008 #2

    Mark44

    Staff: Mentor

    It's been a while since I've done anything with statistics, but I think you might not be using the right form for t. The form I've included is for a two-sample t test, which seems to me the right one for your problem.

    Instead of the standard error, I think you might need to use a pooled standard deviation.

    [tex]t = \frac{X - Y}{S_p\sqrt{\frac{1}{12} + \frac{1}{12}}}[/tex]
    where X and Y are the sample means for the two conditions, and [tex]S_p[/tex] is the pooled s.d., which is given as
    [tex]\sqrt{\frac{(n - 1)s_x^2 + (m - 1)s_y^2}{n + m - 2}}[/tex]
    For your problem, n = m = 12.

    Your use of fractions and decimal values probably won't affect your values, since you apparently used quite a few decimal places in your calculations.

    The t distribution is close to a normal distribution with mean 0 and s.d. 1. For n around 30 there's no difference between the two distributions. That should answer your question about units of s.d.s.

    Hope this is helpful.
     
  4. Nov 25, 2008 #3
    Thanks for the response!
    I've got to do some reading... I haven't come across (or I don't think I have) the pooled s.d. yet.
    I kow the related and independent t-tests. The latter being the (mean 1 - mean 2)/sqrt{(variance 1/n1)+(variance 2/n2)}.
     
    Last edited: Nov 25, 2008
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