Testing for statistical significance of trends in proportion over time

[Ronald Smith]

Hello,

I have a simple question about testing for trends in proportion over time. I have data on how proportions of a variable: STRENGTH (coded as Low, Medium, and High) changed from years 1990-2000 (coded as variable YEAR). For example: In 1990, Low was 20%, Middle was 40%, High was 40%; in 1991, Low was 25%, Mid was 45%, High was 30%, etc for the subsequent years up to 2000 (with Low/Med rising and High falling throughout).

How do I test whether this trend over time is statistically significant? I am not sure what statistical test to use, nor am I sure how to run it in Stata.

Thanks for your help.

[Carlo Lazzaro]

Ronald:
welcome to this forum.
My jerk-knee reaction would be to take a look at -ologit-.

[Joseph Coveney]

In addition to Carlo's suggestion, you could try one of the several brand-name nonparametric tests for trend that are available in Stata.

version 15.1

clear *
set seed `=strreverse("1430084")'

quietly set obs `=2000 - 1990 + 1'
generate int year = _n + 1989

generate byte strength = runiformint(1, 3)

ologit strength c.year, nolog

// Cuzick
nptrend strength, by(year)

// Daniels
spearman strength year

// Mann-Kendall
ktau strength year

// Jonckheere-Terpstra [available from SSC: search jonter]
jonter strength, by(year) continuity

// Cox-Stuart
sort year
quietly drop if _n == (_N + 1) / 2
generate byte half = _n > _N / 2
quietly bysort half (year): replace year = _n
quietly reshape wide strength, i(year) j(half)
signtest strength0 = strength1

exit

See also this FAQ on StataCorp's website.

[Ayub UOM]

Joseph Coveney
hello sir,
sir i want to test trend analysis year by year (for 10 years ) in my data .i want to use Mann–Kendall non-parametric test for trend analysis and to get Z-value ( p- value),
sir i am using stata13, and i run the following codes to

xtset code year, yearly
ktau  var1 var2 var3 var4 year

i just got the correlation matrix,but i cant get z-value and (p-value),
but when i am just runing this command for one variable then i get this result and z-value but no p-value

 ktau  change_BS year

  Number of obs =    6993
Kendall's tau-a =      -0.0046
Kendall's tau-b =      -0.0072
Kendall's score = -113194
    SE of score =  152938.017   (corrected for ties)

Test of Ho: change_BS and year are independent
     Prob > |z| =       0.4592  (continuity corrected)

sir could you please guide me that how can i run correct command for Mann–Kendall non-parametric test so that i can get both z-value and p-value for my 4 variables
thank you in advance.
Ayub

[Carlo Lazzaro]

Ayub:
as far as -ktau- is concerned, you can get what you're interested via -ktau- -stats-, as you can see from the following toy-example:

. use "http://www.stata-press.com/data/r15/auto.dta"
(1978 Automobile Data)

. ktau price mpg, stats(taua taub score se obs p)

  Number of obs =      74
Kendall's tau-a =      -0.3895
Kendall's tau-b =      -0.4002
Kendall's score =   -1052
    SE of score =     213.627   (corrected for ties)

Test of Ho: price and mpg are independent
     Prob > |z| =       0.0000  (continuity corrected)

.

[Ayub UOM]

Carlo Lazzaro
thank you so much sir for your very quick reply and kindness.sir i read a paper and they reported z-value as well as p-values in the last row in the following format in his descriptive statistic table for different trend varaiables.
.

Mann–Kendall test: Year-to-year variation in the number of board directors
Z-value (p-value):
0.34 (p = .735)

sir if you don't mind could you please let me know how can i report yours above test values on this pattern for p-value and z-value?

and i also tried this command and i get z-value as well as p-values but its not Mann-kendall test command

nptrend change_BS , by( year )

          z  = -0.83
  Prob > |z| = 0.404

as the authors mentioned in the paper that

We carried out the Mann–Kendall non-parametric test for trend analysis. The null hypothesis is not rejected for the time series and no trends can be inferred from our data on year-to-year variation

.
OR
sir could you please guide me that how can i get the correct command for getting the right result just like my base paper?
Best regards sir

[Carlo Lazzaro]

Ayub:
I do not think that Mann-Kendall test is available in Stata.
I would stick with -ktau- as per Joseph Coveney excellent reply #3:

 
 // Mann-Kendall ktau strength year

[Rich Goldstein]

also, see the following FAQ: https://www.stata.com/support/faqs/s...end/index.html

[Ayub UOM]

Rich Goldstein Rich Goldstein
Thank you so much for your time, nice suggestions and guidance.I will follow it accordingly .
Best regards