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There may be similar questions posted earlier but I am a novice for statistics and cannot discern them from mine, so I am posting my question as it is.

What statistics can I use and how to use it (need some guidance, if possible) to calculate the following hypothetical scenario -

4 12y/o males, average height 164cm, se = 2cm
5 12y/o females, average height 163cm, se = 3cm
6 18y/o males, average height 175cm, se = 2cm
7 18y/o females, average height 165cm, se = 3cm

Question to answer: If the difference in height ( 1 v 10 cm) between males and females differs statistically (p <0.05) between 12 y/o and 18 y/o group.

Any help will be appreciated.

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    $\begingroup$ Seems to me that in that scenario there is no sensible hypothesis that would say that the difference between male and female heights should be unaffected by age, so why do a test? Just characterise the heights or the differences and you are done. (I suggest confidence intervals.) $\endgroup$ Mar 29, 2018 at 20:43
  • $\begingroup$ Thanks but the example was stated as hypothetical, so clearly it did not represent the real-world scenario. $\endgroup$
    – B Chen
    Mar 29, 2018 at 21:22

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You can use a two way analysis of variance. Deciding if there is a "difference in differences" is just testing if interaction between age and sex is significant.

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  • $\begingroup$ thank you ! I did some google search and found that two way ANOVA is applicable when the sample numbers are the same. Is this correct? As in the provided example, we have different numbers of members in each group? Is any adjustment on two-way ANOVA needed ?? A great many thanks. $\endgroup$
    – B Chen
    Mar 29, 2018 at 19:38
  • $\begingroup$ You are looking for an unbalanced two way ANOVA. It can be done, although balanced ANOVA has some advantages (easier to interpret, more power with little overall sample...). $\endgroup$
    – Pere
    Mar 29, 2018 at 19:46
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If you have a randomly sampled cross-section of children, you just have a linear combination of 4 means, which are themselves uncorrelated random variables. You can use the formula for the variance of uncorrelated weighted random variables to calculate the standard error of the difference in differences. This will allow you to determine if it is significantly different from zero. In this case, the two-sided p-value is ~0.03.

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