t-Test: Follow Up Questions

Your goals for this section are:

1) To comprehend subtle aspects of the analyses

2) To explain the data and analysis to someone else (i.e. your goal is to teach the information)

3) To assess your understanding of the analyses.

This section is open ended in nature.  Your professor may choose to use this information and grade you on it.

Another researcher, Bumble Beasley, working on the same problem, has come up with a slightly different answer to the same question. He comes to you looking to figure out where he went wrong.  Bumble tells you the following: “After I got the data, I stated my hypotheses and did my t-test.” Below are the results of the 2 analyses.

Bumble’s Results Your Results
t(46)=-1.69 t(46)-2.46
Critical t(df=46)=1.684 Critical t(df=46)=1.684
Mean Belize = 1142 Mean Belize = 1142
SD Belize = 1885 SD Belize = 1185
Mean Samoa = 10005 Mean Samoa = 4824
SD Samoa = 25612 SD Samoa = 7096

Why is your analysis different from Bumble’s? Try to explain to Bumble what he did wrong and teach him the correct steps.

Bumble’s Data and Procedure

Bumble used the exact same computational procedures you did and made no mathematical errors. Given his data, the t-value was calculated correctly.

Note Culture 2 = Belize, 3 = Samoa.

BUMBLE’S DATA YOUR DATA
CULTURE Distance CULTURE Distance
2.00 966.39 2.00 966.39
2.00 322.66 2.00 322.66
2.00 415.00 2.00 415.00
2.00 238.21 2.00 238.21
2.00 335.93 2.00 335.93
2.00 102.06 2.00 102.06
2.00 508.10 2.00 508.10
2.00 1286.00 2.00 1286.00
2.00 1048.21 2.00 1048.21
2.00 96.21 2.00 96.21
2.00 465.75 2.00 465.75
2.00 1698.99 2.00 1698.99
2.00 3686.00 2.00 3686.00
2.00 388.82 2.00 388.82
2.00 137.29 2.00 137.29
2.00 937.97 2.00 937.97
2.00 9246.30 2.00 9246.30
2.00 1374.00 2.00 1374.00
2.00 1219.62 2.00 1219.62
2.00 645.51 2.00 645.51
2.00 108.05 2.00 108.05
2.00 639.66 2.00 639.66
2.00 878.33 2.00 878.33
2.00 663.57 2.00 663.57
3.00 1811.24 3.00 1811.24
3.00 441.22 3.00 441.22
3.00 1081.04 3.00 1081.04
3.00 706.33 3.00 706.33
3.00 730.00 3.00 730.00
3.00 444.34 3.00 444.34
3.00 714.80 3.00 714.80
3.00 1968.17 3.00 1968.17
3.00 19898.00 3.00 19898.00
3.00 420.00 3.00 420.00
3.00 526.40 3.00 526.40
3.00 669.24 3.00 669.24
3.00 683.97 3.00 683.97
3.00 12502.79 3.00 12502.79
3.00 2684.76 3.00 2684.76
3.00 1632.26 3.00 1632.26
3.00 5985.72 3.00 5985.72
3.00 602.11 3.00 602.11
3.00 125600.00 3.00 1256.00
3.00 3733.70 3.00 3733.70
3.00 640.00 3.00 640.00
3.00 15212.00 3.00 15212.00
3.00 20121.00 3.00 20121.00
3.00 21331.00 3.00 21331.00

Some Questions to Guide You:

1. What did Bumble do wrong?

2. What effect did Bumble’s error have on the t-test value?  The following information is provided for convenience:T-Formula

3.  Bumble may say ” I don’t see how your t-test can have a value that attains significance whereas in my analysis I can’t draw this conclusion. Look at my data! The difference between distance in Belize and Samoa is much larger than yours. In my analysis the differences between the Belize and Samoa is much larger, children in Belize are much closer to their mothers in my analysis relative to yours. You must have made a mistake, if I can’t reject my null hypothesis when the groups are so dissimilar, then surely, you shouldn’t be able to either.”  Explain to Bumble why his logic is flawed

Ask the Expert

This is an interesting problem. I think the key here is to examine what you both did similarly and what you did differently. Recall all the steps you went through and be sure that Bumble has done the same.

An important point here is examination of the raw data. Remember that errors in data entry can lead to errors in hypothesis testing.  The issue here is that Bumble may be paying attention to the raw differences between means while ignoring another aspect of the relationship that creates the t-value. Why would a large raw difference not be statistically significant in this case?  Ask yourself these questions:

1. What effect do differences in the data have on the values that go into the t- test?

2. What effect does this have on the numerator (Mean for Samoa minus Mean for Belize).

3. What effect does this have on the denominator (Standard error of the difference between the means?)

4. What did this do to the t value?

It can be the case that incorrectly entered scores can raise or lower means and variance estimates, producing results that are not indicative of relationships in the data but, rather the effect of scores that are extreme. Examination of the t and standard error of the difference between means formulae can shed light on this issue as well.

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