In statistics, the terms up and down are normally reserved for trends. Trends have a specific definition, which are based not on a cherry-picked or manipulative start/stop period, statistical method or interpretation. [1]
The only way for someone to report the opposite trend from what the data supports is either lying or hiding the actual data. [2]
If i tell you crime is down, and I'm using only the comparison between yesterday and today, that's an absolute lie. A trend is not defined by a 24 hour period. if that's what's being used, then it's reqired that the trend be reported with "over the past 24 hours" in the report. [3]
So, while statistics can be, and are, manipulated to provide a desired answer, that answer needs to be within the realm of accepted statistical standards. [4]
Trends are based on direct data evidence, not some statistical method that changes from another method. [5]
Trend analysis can use statistical methods to filter, smooth or isolate trends that are hidden or not well defined in a "noisy" dataset, but the trend still exists if the data supports it. The direction doesn't change with those methods. It's either up, down, or not present, it can't be altered unless the analyst is manipulating the data or the results. [6]
There are at least 3 basic weaknesses in trend analysis:
1. All data is subject to sampling errors. That's not the case with HPD using actual numbers the department gathered from official reports. Unless the reporting process is error prone, the datat used is as close to correct as you could expect. [7]
2. Data is subject to sampling errors. Again, since HPD has ALL the data, there's nothing to be gained by even using a sampling method. The amount of data over a few years is not so massive that samples should be used. It's always best to use ALL available data, which given the totals HPD often reports publcly, is not a problem for them. [8]
3. "Phantom" trends can crop up in short term data points. That's why trends should be studied as far back as possible. To pick a short term in which a given trend is reported tells me they are cherry-picking the data if the data isn't being labeled "short term" with the specific period also labeled. i.e. if reporting the number of gun sales year over year, it would be inaccurate to report 2020 sales versus 2024. So much about 2020 was unique that comparing that with 3 years later would be considered cherry-picking unless the numbers are being used to illustrate a specific point being made -- not to report a trend. [9]
Up, down or flat -- it can't be more than one if the data is being used correctly and reported honestly. [10]
1) A "trend" is just something observed in a Time Series Analysis. There are many different types of Time Series Analyses and some of them in fact do in fact use "manipulative start/stop methods" see: "Interrupted Time Series Analysis". "Cherry Picking" could be used to skew results, but technically all samples within a population are cherry-picked, and without a sample you cannot perform a statistical analysis.
2) Maybe. Most people cannot be bothered trying to understand the comprehensive statistical method(s) of the stats they are receiving, the same way most people cannot be bothered calculating friction coefficients but trust its safe to be on airplanes and drive cars anyway.
3) False. Trends can absolutely be reported using 24 hour denominations (see: "day-to-day trend"). Additionally, in some cases, data from preceding/proceeding days/months/years may be unavailable. In these cases, you can employ other statistical methods to determine if the "true mean" lies within your sample, especially if the qualitative and quantitative nature of your population is unknown (ex: we know human height is evenly distributed, even if we cannot and did not measure everyone on the planets height to reach this conclusion).
4) Agree.
5) False. The "trend" from every conceivable statistical model may or may not be congruent. This is why in an academic study the author must demonstrate why a particular model was used over the alternatives. In the news, they can report whatever they want.
6) Trend analysis is a particularly useful benefit of stats, however, analysts can absolutely change the observable trend. You can add or remove "noise" from a dataset by changing the sample within a population. For this reason, "outliers" are usually identified and accompanied with an explanation as to why they were omitted--and the opposite may also occur (Think about the HPD Major(?) who said rape was not included in the crime statistics because rape is an indoor crime and Waikiki is "outdoors", and therefore "crime in District 6 is down").
7) As ChangeMyOil666 reports, sometimes crimes occur without the documentation of a police report. Interestingly enough, a proper and comprehensive statistical analysis can account for this (see: point estimation)

Samples are used for many reasons, especially when using a population of data is costly, inaccurate, or ineffective. Generally speaking, the smaller the sample, the more accurate the analysis.
9) Agree, especially since we should know how many "non-private sales" occurred within the state. In a statistical analysis, years such as 2020 may possibly be excluded, but in such an event, there should be an explanation.
10) Agree, but not many people want the real "facts and data", and would prefer to receive the 'analysis' according to the narrative they subscribe (left or right).
I've been told harsh prison conditions don't deter crime [1]. Only a support network which can embarrass the offender into not wanting to go back to prison can prevent that person from breaking the law in the future. [2]
Or something like that....
Curious if you would ever factor in those prison conditions should you ever be tempted to fracture a law again?
1) There is significant scientific evidence that demonstrates incarceration is ineffective as a deterrent and actually has a dramatic effect on furthering reoffence (see: School to Prison Pipeline). There is also 'collateral damage' when it comes to harsh penalties as well. I remember SCOTUS case involving a juvenile who was expelled from school under a "Zero Tolerance Policy" for bringing a small pocket knife to school that she forgot in her backpack. The knife was discovered in her bag during a random locker search. The student explained she was using it to cut open haybales on the farm and had forgotten to remove it from her purse before the next school day.
2) Not exactly. Strong social bonds prevent people from committing crime to begin with, in addition to the shame someone will experience in those social circles if they are arrested; found guilty; and spends time in jail for a crime. Think of it this way... some people may be more afraid of their parents beating their ass for stealing even if retail theft is decriminalized, whereas others may have friends and family who are joining them in retail theft because they are entitled to self-help "reparations".