Note: I have read Finding an appropriate trend test but unfortunately this post does not apply for me

Suppose I have a small sample of data for 2 numeric variables $T$ and $Y$ where $T$ represents some measure of time, such as years ('small sample' in this context refers to less than 10 data points).

I would like to determine whether there is a trend between $T$ and $Y$. I have considered the following:

1. Simple linear regression (Test whether $\beta_1 = 0$ vs $\beta_1 \neq 0$).
2. Kendall's Tau (also called Kendall's rank correlation test or the Mann-Kendall test).
3. Bootstrapped confidence interval for a LOESS estimator.
4. The Jonckheere-Terpstra Trend Test.
5. Sieve-bootstrap Student's t-test for a linear trend of a time series.
6. Lyubchich et al. (2013) non-parametric test for trend
7. kolmogorov-Smirnov test (compare whether data follows a discrete uniform distribution)

This issue is that regression assumes normally distributed error terms (which may not be appropriate for my data as we believe the residuals would be skewed), and the other tests appear inappropriate for small sample size.

Can someone advise on an appropriate test I could use in this situation, or whether there is something that I may be overlooking in the tests I have considered please?

I believe that the Jonckheere Terpstra Test might be the most appropriate, however the only information I could find in the R documentation is that the sample size should be less than 100 (https://rdrr.io/cran/DescTools/man/JonckheereTerpstraTest.html), however the documentation doesn't specify the minimum size.

Note: I have read Finding an appropriate trend test but unfortunately this post does not apply for me

Suppose I have a small sample of data for 2 numeric variables $T$ and $Y$ where $T$ represents some measure of time, such as years ('small sample' in this context refers to less than 10 data points).

I would like to determine whether there is a trend between $T$ and $Y$. I have considered the following:

1. Simple linear regression (Test whether $\beta_1 = 0$ vs $\beta_1 \neq 0$).
2. Kendall's Tau (also called Kendall's rank correlation test or the Mann-Kendall test).
3. Spearman's rho (Spearman's rank correlation coefficient).
4. Bootstrapped confidence interval for a LOESS estimator.
5. The Jonckheere-Terpstra Trend Test.
6. Sieve-bootstrap Student's t-test for a linear trend of a time series.
7. Lyubchich et al. (2013) non-parametric test for trend
8. kolmogorov-Smirnov test (compare whether data follows a discrete uniform distribution)

This issue is that regression assumes normally distributed error terms (which may not be appropriate for my data as we believe the residuals would be skewed), and the other tests appear inappropriate for small sample size, with most small sample tests requiring about 10-12 observations.

Can someone advise on an appropriate test I could use in this situation, or whether there is something that I may be overlooking in the tests I have considered please?

Note: I have read Finding an appropriate trend test but unfortunately this post does not apply for me

Suppose I have a small sample of data for 2 numeric variables $T$ and $Y$ where $T$ represents some measure of time, such as years ('small sample' in this context refers to less than 10 data points).

I would like to determine whether there is a trend between $T$ and $Y$. I have considered the following:

1. Simple linear regression (Test whether $\beta_1 = 0$ vs $\beta_1 \neq 0$).
2. Kendall's Tau (also called Kendall's rank correlation test or the Mann-Kendall test).
3. Bootstrapped confidence interval for a LOESS estimator.
4. Sieve-bootstrap Student's t-test for a linear trend of a time series.
5. Lyubchich et al. (2013) non-parametric test for trend
6. kolmogorov-Smirnov test (compare whether data follows a discrete uniform distribution)

This issue is that regression assumes normally distributed error terms (which may not be appropriate for my data as we believe the residuals would be skewed), and the other tests appear inappropriate for small sample size.

Can someone advise on an appropriate test I could use in this situation, or whether there is something that I may be overlooking in the tests I have considered please?

Note: I have read Finding an appropriate trend test but unfortunately this post does not apply for me

Suppose I have a small sample of data for 2 numeric variables $T$ and $Y$ where $T$ represents some measure of time, such as years ('small sample' in this context refers to less than 10 data points).

I would like to determine whether there is a trend between $T$ and $Y$. I have considered the following:

1. Simple linear regression (Test whether $\beta_1 = 0$ vs $\beta_1 \neq 0$).
2. Kendall's Tau (also called Kendall's rank correlation test or the Mann-Kendall test).
3. Bootstrapped confidence interval for a LOESS estimator.
4. The Jonckheere-Terpstra Trend Test.
5. Sieve-bootstrap Student's t-test for a linear trend of a time series.
6. Lyubchich et al. (2013) non-parametric test for trend
7. kolmogorov-Smirnov test (compare whether data follows a discrete uniform distribution)

This issue is that regression assumes normally distributed error terms (which may not be appropriate for my data as we believe the residuals would be skewed), and the other tests appear inappropriate for small sample size.

Can someone advise on an appropriate test I could use in this situation, or whether there is something that I may be overlooking in the tests I have considered please?

I believe that the Jonckheere Terpstra Test might be the most appropriate, however the only information I could find in the R documentation is that the sample size should be less than 100 (https://rdrr.io/cran/DescTools/man/JonckheereTerpstraTest.html), however the documentation doesn't specify the minimum size.