Hello r/statistics!

This is my first post here, so I apologize if I’m not following proper etiquette specific to this subreddit.

To the matter at hand: I’m currently working on a paper which I’m writing sheerly out of curiosity at the moment. I’ve gathered data on four primary countries , as well as 31 other countries, regarding the proportion of total imports and total exports which is taken up by the imports and exports of capital goods respectively from the world bank. I’ve gathered this data for two periods, 2008 and 2018, and have found the percent change in these proportions in that time period for the countries mentioned. The method of I have used is as follows:

Thailand, 2008:

Proportion of total exports expressed in capital goods: 35.88%

Proportion of total imports expressed in capital goods: 31.76%

Thailand, 2018:

Proportion of total exports expressed in capital goods: 38.3%

Proportion of imports expressed in capital goods: 33.96%

Percent change

Exports: /35.88) x 100 = 6.744% change

Imports: /31.76) x 100 = 6.92%

change

I’ve repeated this for the other three countries. My question is, can I prove the significance of these data, and if so, how? Using the same source, I have the proportion of exports and imports expressed in the flow of capital goods for the time periods mentioned, and have calculated their percent change, as provided below:

World, 2008

Proportion of total exports expressed in capital goods: 30.89%

Proportion of total imports expressed in capital goods: 29.11%

World, 2018

Proportion of total exports expressed in capital goods: 32.58%

Proportion of total imports expressed in capital goods: 32.75%

Percent change:

Exports: /30.89) x 100 = 5.47% change

Imports: /29.11) x 100 = 12.50% change

I wanted to use this as a parameter for a one sample z test, however these four countries are not randomly selected, nor large enough, and inclusion of these into the sample of the other 31 countries would be testing the significance of the whole sample, and not the results of these four countries. Do you know of anyway around this dilemma, wherein which I could actually test the significance of the data from the four primary countries specified?

P.S I’ve also been confused on another matter. The percent change of exports and imports expressed in the flow of capital goods is important. However, the change in exports and imports may not be independent, and in fact may act on one another.I figured a test for independence would be in order, however I’ve already proceeded with another course of action, should they not be independent, in a separate document. What I did was express the proportions of exports and imports expressed in the flow of capital goods as a proportion. An example would be:

Thailand, 2008

35.88/31.76 = 1.129

Thailand, 2018

38.3/33.96 = 1.127

Percent change

/1.129) x 100 = -0.17% change

I figured this would observe a change in the general direction of a country’s economy regarding whether they are importing or exporting more capital. For instance, given the data available, Vietnam over the last decade has seen a 180% change in favor of exporting capital goods, following this math. Would any of this be worthwhile to pursue, or have I fudged the math on this?

I know this is a lot to read. To those of you who have taken the time to read my question, thank you sincerely. I apologize in advance if my replies or short or sparse. That being said, I intent earnestly to reply to the answers provided.

EDIT: user u/Fabulous-Nobody- kindly commented asking for clarification on the meaning of “can I prove this significance of this data”. I realized that I forgot to state my hypotheses and properly define my terms. My sincere apologies.

For the purposes of this problem: a significance test is a test which serves to demonstrate whether or not data falls along the normal distribution provided by a stated parameter. In this case, our data suggests the percent change in the proportion of world exports and imports expressed in the flow of capital goods is 5.47% and 12.5% respectively. I am seeking to find out whether the normal distribution of these figures accurately predicts the percent change in the proportion of exports and imports expressed in the flow of capital goods for Thailand, Vietnam, India, and The Philippines.

For the purposes of this test, let us set our hypotheses as the following:

Null: the normal distribution of the stated parameters accurately predicts the percent change in the proportion of exports and imports expressed by the flow of capital goods in the four countries stated.

Alternative: the normal distribution of the stated parameters does NOT accurately predict the percent change in the proportion of exports and imports expressed by the flow of capital goods in the four countries stated.