ttest 2 Independent Samples

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t-test 2 Independent Samples

• HED 489 Biostatistics

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• t-test 2 compares the means of two samples to
  see if they differ. This is often done to see if
  some dependent variable differs between human
  characteristics, such as women vs. men, between
  two races, or between two age groups. It is not
  necessary that you have the same number of people
  in both groups in order to use t-test 2, but you
  would certainly want to try to have the same
  number in the beginning of the study. Some may
  drop out.
• If you'll look at the slide, what you'll see,
  essentially, are two standard deviations under
  the square root sign. This is, obviously, the
  scariest part of the formula.

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Step 1

• The example in the excel file tests whether there
  is a statistically-significant difference in IQ
  test scores between boys and girls. Here are the
  two hypotheses
• H0 There is no difference in IQ test scores
  between boys and girls.
• H1 There is a difference in IQ test scores
  between boys and girls.
• Step 1 is, again, to put your data in two
  columns. It doesn't make any difference what
  order you use as long as you get Group 1 in one
  column and Group 2 in the other.

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Step 2

• Step 2 is to simply sum the scores in Group 1
  males).

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Step 3

• In Step 3, you square each score in Group and sum
  these values. Just like in t-test 1, this is
  "square, then sum."

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Step 4

• Step 4 has two parts. The first is to square the
  summed valued. You summed the values in Step 2.
  This is "sum first, then square." Then, divide by
  the number of scores in Group 1.

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Step 5

• Step 5 completes the calculations for the portion
  of Group 1 under the square root sign. To do it,
  subtract the square of the summed values divided
  by n, from the sum of the squared values.
• Or, subtract Step 4 from Step 3.

121,318-119,2012,117
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Step 6

• Step 6 begins a repeat of Steps 1 - 5 for Group 2
  (Females). Step 6 simply sums the scores in Group
  2.

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Step 7

• Step 7 is square first, then sum for Group 2.

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Step 8

• Step 8 has two steps first, square the value you
  summed in Step 6. Then, divide by n for Group 2.

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Step 9

• Step 9 completes the calculations for Group 2
  data under the square root sing subtract the
  square of the summed values divided by n, from
  the sum of the squared values.
• This is, subtract Step 8 from Step 7.

148,202-145,656 2,546
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Step 10

• In Step 10, you add the value you calculated in
  Steps 2 through 5 to the value you calculated in
  Steps 6 through 9. This is where you sum the two
  variance-looking things. To actually do this, you
  add Step 5 to Step 9.

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Step 10
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• Step 11 takes care of the division under the
  square root sign. To do this, you divide
  everything above the line, represented now by
  Step 10, by the number of values in Group 1 plus
  the number of values in Group 2, minus two.
  That's where the 24 in Step 11 comes from.

4,66326-2
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Step 12
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• Step 12 apply a correction factor for unequal
  group sizes, if they exist, to the rest of the
  formula under the square root sign. You sum the
  reciprocals of the group sizes, and multiply it
  times the result of Step 11.

194 .155
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Step 13
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• Step 13, finally, calculates the square root of
  everything under it. All you really have to do is
  calculate the square root of Step 12.

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Step 14a
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• Step 14 deals with the top of the formula
  everything above the division line. All you do is
  calculate the mean of both groups. You know how
  to do that by now!

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Step 14b
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Step 15
99.67 102.00

• In Step 15, you simply subtract the mean of Group
  2 from the mean of Group 1. The only think that
  matters is the absolute value, so if you get a
  negative number, ignore the minus sign.

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Or 2.33
We just use absolutes
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Step 16
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• Step 16 calculates t by dividing the stuff under
  the line, Step 13, into the stuff above the line,
  Step 15.

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Step 17

• Step 17 is interpretation time. In this case, the
  t-value you calculated is greater than the tabled
  value, so you conclude that there is no
  difference in IQ test scores between boys and
  girls and it is not statistically significant. As
  a result you accept as true the null hypothesis
  that there is no difference and reject the
  alternative hypothesis that there is a difference

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Assignment

• calculate t-test 2 for the following two groups
  of twenty cholesterol scores. But this time,
  lets use Excel to do it.
• follow this tutorial...