Covid-19 - (3) A World-Wide Test of the Mask Law Hypothesis - Detailed Statistics 3, Kenya to Portugal

 Covid-19  - (3) A World-Wide Test of the Mask Law Hypothesis - Detailed Statistics, Kenya to Portugal

Introduction

(note that if you have previously read the introduction to Part 1 and/or Part 2, this is essentially the same text, so you can skip right to the graphs and results)

The use of masks and mask-laws to prevent Covid-19 infections is obviously a huge, multi-faceted, complex and controversial subject. There are a lot of lines of evidence, sometimes contradictory, ranging from detailed medical studies (e.g. hospital ICU studies), to engineering studies (e.g. viral aerosol particle hang-time indoors),  to ecological studies (how did mask-laws seem to affect infection rates in various situation).

So, intrepidly and perhaps foolishly, I thought I would add to the discussion via looking at how mask-laws seemed to have actually worked around the world, on a national level.  I used publicly available data sources (as outlined below) and relied on primarily graphical evidence, supplemented by simple curve-fitting, to examine and judge the evidence as objectively as I possibly could. I also state the methods that I used and the overall hypothesis that the data will be used to test.

The evidence and my judgments are shown below, and in three more blogs, on a case-by-case basis.  I broke the data in to 4 blogs, as there are some 123 countries that had mask-laws in the data, and I didn't want to overwhelm the reader with that much data all at once. 

An accompanying blog will give my analysis of the overall conclusions, taking into account the evidence of the 123 countries as a whole.  However, by presenting the evidence in this way, it is my intention that anyone (statistician or interested layperson) can look at the data and draw their own conclusions.

As for my own qualifications, I am a statistician (or data scientist, a popular new term) who does operational research for a large Canadian university.  Covid-19 isn't my area of expertise but data analysis of this sort (practical observational studies of the effect of targeted interventions on a population) is a fairly broad area, one with which I am familiar. But, as I say, interested readers should scan through the graphs and narratives and form their own conclusions.

Statement of Hypothesis and Description of Method of Evaluation

For my purposes the Mask-Law Hypothesis can be stated as: "A national mask-law will result in the number of new Covid-19 cases coming down within the one month period after the mask-law date, relative to the trend in the one month period before that date".  It has often expressed in more informal terms as "a mask-law will help bend the curve downwards".

Since observational studies of this sort have many potential confounders, the hypothesis can be restated in a form that attempts to control for these confounders, by analyzing a large number of cases, on the assumption that the effects of these confounding variables will tend to cancel out as the number of cases increases.   The restated form of the hypothesis is then: "National mask-laws will result in new Covid-19 cases coming down within the one month period after the mask-law date, relative to the trend in the one month period before that date, in the vast majority of countries in which the mask-law is implemented".

Below are the detailed, country-by-country statistics for Covid-19 cases by days before and after that particular country's mask-law, as indicated on the source Masks4All website (which provided the mask-law date) and the GitHub repository of Covid-19 statistics (which provided the aggregate number of cases during the study period, by day).

The graphs show:

• Line graphs of aggregate case counts in the 4 week periods before and after the law, to obtain an overall sense of how the numbers evolved during the study period.  Linear and quadratic functions are fit to the data, to give a visual and mathematical basis for determining whether the general trend was up, flat or down in that country during the 8 week period.
• Line graphs with forecasts of cases for the four weeks after the mask-law, based on the trend during the four weeks before the law, along with the actual results during that succeeding four weeks.  This enables a comparison of forecasts and actuals,  to determine whether or not the pre-law trend in cases appeared to be affected by the mask-law.  Generally speaking, the two best fitting functions  of the linear, quadratic, exponential and logarithmic cases are shown (determined by R-square, a conventional measure of model fitness, where the best forms have R-square closest to 1.00).
• A bar graph with the number of new cases each week during that time, as well as the functional form that best fits that data.  This gives a visual and mathematical picture of how new cases varied on a weekly basis.

I use this data to judge how well the evidence supports the mask-law's apparent effectiveness for each country.  Readers may sometimes dispute my opinion, though I think the majority of cases are not too difficult to categorize.  However, although  the evidence for or against the mask-law hypothesis is sometimes quite clear-cut, at other times it is only somewhat persuasive and sometimes it is too inconclusive to render any sort of judgment.

The upper left hand corner graphs, giving the functional forms (visually and mathematically) for the aggregate data are measures of how well the mask-laws seem to be doing in their expected roles (i.e. bending the curve downwards).

• Concave Down -The second order polynomial fit to the data (the yellow line) tends to bend downwards.  This is generally supportive of the mask-laws (positive evidence), though in some cases this could just be the continuation of a trend that began before the law was passed.
• Linear - The second order polynomial and the linear function nearly overlie each other, indicating that the number of new cases was essentially steady during the period.  This would not be supportive of the mask-law's effectiveness (neutral evidence), though it could be argued that the mask-law prevented an exponential increase.
• Concave Up - The second order polynomial fit to the data (the yellow line) tends to bend upwards.  This is generally not supportive of the mask-laws (negative evidence).  Indeed, it could be argued that in these cases the mask-law not only didn't work, but actually contributed to making the situation worse (perhaps by creating a false sense of security).

The upper right hand corner graphs show the forecast of cases, based on the four weeks of data before the mask-law date.  As noted, some alternative trend lines are given, those which best fit the pre-law data (based on their R-square, a statistical measure of goodness-of-fit).

I should note that forecasts of this sort, based on limited data, can be misleading, so you have to use your common sense as well as the statistical R-square measure, when deciding whether they are appropriate.  For example, exponential functions don't generally apply over a very long range of data in the real world (resources eventually run out), so care has to be taken when utilizing them.  Also, a quadratic function can predict a decline in aggregate cases, which is physically impossible, so care must be taken to not rely on this form in these instances.

The actual case counts during the four weeks after the mask-law are also shown.  Again, there are three main possibilities:

• Actuals Below the Trend - If the number of cases are below the forecasts, that indicates that the mask-law appears to have slowed or reversed the trend.  This is generally supportive of the mask law's effectiveness (positive evidence for the mask-law hypothesis).
• Actuals Mirror Trend - If the number of cases are very close to the forecast, that indicates that the mask-law had no observable effect on the trend.  This would not be supportive of the mask- law's effectiveness, but wouldn't indicate that the mask-law was counter-productive (neutral evidence as regards the mask-law hypothesis).
• Actuals Above the Trend - If the number of cases exceeds the forecasts, that indicates that cases grew faster than the pre-existing trend and that the the mask-law did not slow the trend, it may have even sped it up.  This is generally not supportive of the mask-law's effectiveness (negative evidence against the mask-law hypothesis).

The lower left hand bar graphs give the number of new cases, on a week-by-week basis, before and after the mask-law.  It also has as best-fit function for the new cases data, to aid the visual interpretation.  There are three main ideal-type cases, as well as many intermediate possibilities:

• The graph has a hump-like shape, with new cases rising before the mask-law date, peaking shortly after the mask-law, then falling.  This is generally supportive of the mask-law's effectiveness (positive evidence for the mask-law hypothesis).
• The graph is more or less flat, with no strong pattern of growth or shrinkage over the course of the eight week period.  This would not be supportive of the mask-law's effectiveness, but wouldn't indicate that the mask-law was counter-productive (neutral evidence as regards the mask-law hypothesis).
• The graph shows steady, often exponential, growth after the mask-law date, compared to before that date.  This is generally not supportive of the mask-law's effectiveness (negative evidence against the mask-law hypothesis).

The three lines of evidence are then considered and an overall evaluation is given, via a five-level categorization.   The categories are given below: 

• Category 2: Strong positive evidence.  The aggregate case graph is generally downward, actual cases are below the pre-law forecasts and new cases clearly fall after the mask-law date.
• Category 1: Weak positive evidence.  The majority of the lines of evidence favour the mask-law, but the evidence is relatively weak and/or has some contrary indications. 
• Category 0: Neutral evidence.  None of the lines of evidence show very persuasive evidence, one way or the other.
• Category -1: Weak negative evidence.  The majority of the lines of evidence do not favour the mask-law, but the evidence is relatively weak and/or has some contrary indications.
• Category -2: Strong negative evidence.  The aggregate case graph is generally upward, actual cases are above the pre-law forecasts and new cases clearly rise (often exponentially) after the mask-law date.

Since there are 123 countries in the study, I will  have to break the data into several blogs, just to avoid overloading blogger with graphs.   This is Part 3, with countries from Kenya to Portugal (alphabetically ordered).  Note that not all countries passed mandatory mask laws and therefore not all countries could be included in this study.

Part 1, with countries from Algeria to Cuba is in the link below:

https://dodecahedronbooks.blogspot.com/2021/09/covid-19-1-world-wide-test-of-mask-law.html

Part 2, with countries from Czechia to Kazakhstan is in the link below:

https://dodecahedronbooks.blogspot.com/2021/09/covid-19-2-world-wide-test-of-mask-law.html

Kenya

Mask Law Date: 05/04/2020

Aggregate Cases Functional Form: Concave Up

Forecasts vs Actuals:  Actuals lower than forecasts.

New Cases Bar Graph: New cases higher after mask-law date than before. 

Categorization: 1 (Weak Positive Evidence) 

Comment: The yellow quadratic function in the line graph is trending upwards, indicating rising Covid rates. New cases did fall during the first week after the mask law, though they quickly resumed their exponential rise.  However, post-law actuals are well under the best-fit pre-law forecast.  So, this data will be considered weak positive evidence for for mask law hypothesis.

 

Kuwait

Mask Law Date: 12/05/2020

Aggregate Cases Functional Form: Concave Up

Forecasts vs Actuals:  Actuals less than forecasts.

New Cases Bar Graph: New cases lower after mask-law date than before.  

Categorization: 2 (Strong Positive Evidence) 

Comment: The quadratic function is slightly concave up, but the bar graph shows that new cases tended to fall after the mask law date.  Actuals were under the best-fit forecast line. Finally, the hump-like appearance of the new cases bar graph indicates that this can be categorized as strong positive evidence for the mask law hypothesis.

 

 

Kyrgyzstan

Mask Law Date: 11/05/2020

Aggregate Cases Functional Form: Concave Up

Forecasts vs Actuals:  Actuals higher than best-fit forecasts.

New Cases Bar Graph: New cases higher after mask-law date than before.  

Categorization: -1 (Weak Negative Evidence) 

Comment: The quadratic function is slightly concave up and the bar graph shows that new cases tended to rise after the mask law date.  That said, the rise was rather small and could be interpreted as a continuation of the previous trend.  However, the actuals were higher than the best-fit forecast line (the yellow quadratic).  So, this is categorized as weak negative evidence.

 

Latvia

Mask Law Date: 08/05/2020

Aggregate Cases Functional Form: Concave Down

Forecasts vs Actuals:  Actuals lower than forecasts.

New Cases Bar Graph: New cases lower after mask-law date than before.  

Categorization: 1 (Weak Positive) 

Comment: The quadratic is slightly concave down and the new cases bar graph shows a generally declining trend for most of the period of the study.  However, the post-law actuals are below the best-fit pre-law forecast.  So, while the drop in cases after the mask law date can be considered as the continuation of an existing trend, it may have brought that trend down somewhat. This conflicting and uncertain evidence therefore leads the case to be classed as neutral evidence.

 

Lebanon

Mask Law Date: 08/05/2020

Aggregate Cases Functional Form: Concave Up

Forecasts vs Actuals:  Actuals about the same as best-fit forecast.

New Cases Bar Graph: New cases higher after mask-law date than before.  

Categorization: -2 (Strong Negative Evidence) 

Comment: The quadratic is concave up and the bar graph shows a general tendency for cases to rise after the mask law date.  Actuals are about the same or a bit above the best-fit forecast line.  Finally, the bar graph of new cases has the saddle shape characteristic of strong negative evidence against the mask-law hypothesis.

 

 

Liberia

Mask Law Date: 19/04/2020 

Aggregate Cases Functional Form: Concave Up

Forecasts vs Actuals:  Actuals less than than forecasts.

New Cases Bar Graph: New cases about the same after mask-law date than before.  

Categorization: 0 (Neutral Evidence)

Comment: The quadratic function is slightly concave up, but the weekly new case counts in the bar graph show little detectable change between the period before the mask law data and after.  Having said that, it is possible that the mask-law did bring down new cases, as the actuals are less than the best-fit forecast.  However, given the conflicting trends, this is classed as neutral evidence.

 

Lithuania

Mask Law Date: 10/04/2020 

Aggregate Cases Functional Form: Concave Up

Forecasts vs Actuals:  Actuals less than forecasts.

New Cases Bar Graph: New cases less than after mask-law date than before.  

Categorization: 1 (Weak Positive Evidence) 

Comment: The quadratic function is slightly concave down and new cases are mostly falling after the mask law date.  However, as the bar graph shows, that could be interpreted as the continuation of an existing trend.  On the other hand, the actuals are less than what the pre-law best fit trend predicts.  Given these somewhat contradictory indications, this is categorized as weak positive evidence. 

 

Luxembourg

Mask Law Date: 20/04/2020 

Aggregate Cases  Functional Form: Concave Down

Forecasts vs Actuals:  Actuals about the same as best-fit forecasts.

New Cases Bar Graph: New cases lower after mask-law date than before.  

Categorization: 0 (Neutral Evidence) 

Comment: The quadratic fit to the data is distinctly concave down, but the bar graph of new case shows clearly that the drop-off in the case counts was ongoing throughout the duration of the analysis period.  In addition, the post-law actuals are about the same or higher than what was predicted by the best-fit forecasts.  Therefore, this evidence is weak negative evidence, as concerns the mask-law hypothesis.

 

Malaysia

Mask Law Date: 01/08/2020 

Aggregate Cases Functional Form: Close to Linear

Forecasts vs Actuals:  Actuals less than than forecasts.

New Cases Bar Graph: New cases lower after mask-law date than before.  

Categorization: 1 (Weak Positive Evidence) 

Comment: The quadratic fit to to the data overlies the linear fit.  In addition, the week by week bar graph of new case counts shows a hump-like rise and fall before and after the mask-law, though with several inconsistencies.  Actuals are lower than the best-fit forecast.  So, this is weak positive evidence for the mask law hypothesis.

 

 

Maldives

Mask Law Date: 12/06/2020 

Aggregate Cases Functional Form: Concave Down

Forecasts vs Actuals:  Actuals       than forecasts.

New Cases Bar Graph: New cases     after mask-law date than before. 

Categorization: -1 (Weak Negative Evidence) 

Comment: The quadratic is concave down, but the bar graph of weekly new case counts shows that the drop in cases occurs in the week before the mask law date.  After that, cases plateau but eventually rise again.  Also, post-law actuals are at the level predicted by the best-fit forecast.  So this instance is classed as weak negative evidence.

 

 

Mali

Mask Law Date: 20/05/2020 

Aggregate Cases Functional Form: Concave Up

Forecasts vs Actuals:  Actuals are greater than forecasts.

New Cases Bar Graph: New cases higher after mask-law date than before. 

Categorization: -2 (Strong Negative Evidence) 

Comment: The quadratic is concave up and the weekly case count of new cases rises after the mask law date.  Post-law actuals are higher than predicted by pre-law forecasts.  Thus this is categorized as strong negative evidence.

 

 

Malta

Mask Law Date: 20/05/2020 

Aggregate Cases Functional Form: Concave Down

Forecasts vs Actuals:  Actuals higher than best-fit forecasts.

New Cases Bar Graph: New cases higher after mask-law date than before. 

Categorization: -2 (Strong Negative Evidence) 

Comment: The quadratic is concave down, but the bar graph of new cases shows a drop-off in cases up until the mask law date, followed by a rise afterwards and finally a fall to pre-law numbers by the final week (overall, a saddle shape).  Actuals are above the best-fit pre-law forecasts.  So, this is classed as strong negative evidence against the mask-law hypothesis.

 

 

Mauritania

Mask Law Date: 06/05/2020 

Aggregate Cases Functional Form: Concave Up

Forecasts vs Actuals:  Actuals (n/a) than forecasts.

New Cases Bar Graph: New cases higher after mask-law date than before. 

Categorization: -2 (Strong Negative Evidence) 

Comment: The quadratic is strongly concave up.  The weekly case counts are very low, until shortly after the mask-law date, after which they increase sharply.  There is insufficient data to produce pre-law forecasts.  So, this is strong negative evidence against the mask law hypothesis.

Mauritius

Mask Law Date: 24/04/2020 

Aggregate Cases Functional Form: Concave Up

Forecasts vs Actuals:  Actuals lower than forecasts.

New Cases Bar Graph: New cases lower after mask-law date than before. 

Categorization: 0 (Neutral Evidence) 

Comment: The quadratic function is strongly concave down, but the bar graph of new case counts shows that the dramatic fall-off in cases began well before the mask law date.  Actuals are slightly below.  However, given that new cases fell to near zero well before the mask-law date, then carried on at a low rate, this is classed as neutral evidence, neither for or against the mask-law hypothesis.

Mexico

Mask Law Date: 20/05/2020 

Aggregate Cases Functional Form: Concave Up

Forecasts vs Actuals:  Actuals a bit higher than forecasts.

New Cases Bar Graph: New cases higher after mask-law date than before. 

Categorization: -2 (Strong Negative Evidence) 

Comment: The quadratic is concave up, while the bar graph shows exponentially rising new case counts throughout the interval of the study.  Actuals are somewhat higher than pre-law best-fit forecast.  Thus, this is strong negative evidence against the mask law hypothesis.

 

 

Moldova

Mask Law Date: 07/05/2020 

Aggregate Cases Functional Form: Concave Up

Forecasts vs Actuals:  Actuals higher than forecasts.

New Cases Bar Graph: New cases higher after mask-law date than before. 

Categorization: -2 (Strong Negative Evidence) 

Aggregate Cases Comment: The quadratic is only slightly concave up and the bar graph of new case counts rises after the mask law date (though this could be considered the continuation of an existing trend).  Actuals are somewhat higher than forecasts.  So, this is classed as strong negative evidence against the mask law hypothesis.

 

 

Monaco

Mask Law Date: 07/05/2020 

Aggregate Cases Functional Form: Concave Down

Forecasts vs Actuals:  Actuals       than forecasts.

New Cases Bar Graph: New cases     after mask-law date than before. 

Categorization: 0 (Neutral Evidence) 

Comment: The quadratic is strongly concave down, but the bar graph of weekly case counts shows that cases dropped well before the mask law date and continued in this manner.  In addition, post-law actuals mirrored the pre-law forecasts.  Thus, this is classified as neutral evidence.

 

 

Mongolia

Mask Law Date: 14/03/2020 

Aggregate Cases Functional Form: Concave Up

Forecasts vs Actuals:  Actuals n/a than forecasts.

New Cases Bar Graph: New cases higher after mask-law date than before. 

Categorization: 0 (Neutral Evidence) 

Comment: The quadratic function is concave up and the weekly case count graph indicates that the numbers jumped at the time of the mask law, then fell back to numbers only slightly higher than the norm in the pre-law period.  There is insufficient data to produce pre-law forecasts.  So, this is best considered inconclusive, neutral evidence.

 

 

Montenegro

Mask Law Date: 30/04/2020 

Aggregate Cases Functional Form: Concave Down

Forecasts vs Actuals:  Actuals lower than forecasts.

New Cases Bar Graph: New cases lower after mask-law date than before. 

Categorization: 0 (Neutral Evidence) 

Comment: Although the quadratic function is concave down, the bar graph of new case counts shows that the low (nearly 0) level of new cases after the mask law was a continuation of an exponentially declining trend that had begun well before the mask-law date.  Though the actuals are somewhat below the forecasts, numbers are very low in either case. Thus, this is categorized as neutral evidence.

 

 

Morocco

Mask Law Date: 07/04/2020 

Aggregate Cases Functional Form: Concave Up

Forecasts vs Actuals:  Actuals about the same as forecasts.

New Cases Bar Graph: New cases higher after mask-law date than before. 

Categorization: -2 (Strong Negative Evidence) 

Comment: The quadratic function is concave up and the weekly case count graph shows strong growth in new cases after the mask law date.  Also, post-law actuals are about the same as was predicted by pre-law forecasts.  So this is classed as strong negative evidence.

 

Mozambique

Mask Law Date: 08/04/2020 

Aggregate Cases Functional Form: Concave Up

Forecasts vs Actuals:  Actuals higher than forecasts.

New Cases Bar Graph: New cases higher after mask-law date than before. 

Categorization: -2 (Strong Negative Evidence) 

Comment: The quadratic function is concave up and the weekly case counts are generally higher in the post mask-law era than previous to that, though case counts did fall back to pre-law levels by the last week.  Post-law actuals are generally higher than pre-law forecasts.  So this will be considered to be strong negative evidence.

 

 

Namibia

Mask Law Date: 02/05/2020 

Aggregate Cases Functional Form: Concave Up

Forecasts vs Actuals:  Actuals above forecasts.

New Cases Bar Graph: New cases higher after mask-law date than before. 

Categorization: -1 (Weak Negative Evidence) 

Comment: The quadratic function is concave up and new cases do rise after the mask-law date, though absolute numbers are low.  Actuals are above forecast.  However, since case counts are low, this is categorized as weak negative evidence.

 

 

Netherlands

Mask Law Date: 01/06/2020 

Aggregate Cases Functional Form: Close to linear

Forecasts vs Actuals:  Actuals higher than forecasts.

New Cases Bar Graph: New cases lower after mask-law date than before. 

Categorization: 1 (Weak Positive Evidence) 

Comment: The quadratic almost overlies the linear function.  The new weekly case count does fall after the mask-law date, but it takes several weeks and can be seen as a continuation of the pre-law trend, which was dropping.  Post-law actuals are somewhat below the best-fit line forecast.  So, this is categorized as neutral evidence.

 

Nigeria

Mask Law Date: 28/04/2020 

Aggregate Cases Functional Form: Concave Up

Forecasts vs Actuals:  Actuals lower than forecasts.

New Cases Bar Graph: New cases higher after mask-law date than before. 

Categorization: -1 (Weak Negative Evidence) 

Comment: The quadratic is strongly concave up and weekly case counts increase exponentially after the mask-law before stabilizing.  Actuals are above the quadratic forecast, but below the exponential (both have high R-squares).  The mixed evidence leads to a categorization as weak negative evidence, against the mask-law hypothesis.

 

 

Oman

Mask Law Date: 03/05/2020 

Aggregate Cases Functional Form: Concave Up

Forecasts vs Actuals:  Actuals higher than best-fit forecast.

New Cases Bar Graph: New cases higher after mask-law date than before. 

Categorization: -2 (Strong Negative Evidence) 

Comment: The quadratic function is strongly concave up and the weekly new cases bar graph shows exponential growth after the mask law date.  Post-law actuals are higher than the best-fit pre-law forecast (the yellow quadratic), so this is clearly negative evidence against the mask-law hypothesis.

 

 

Pakistan

Mask Law Date: 31/05/2020 

Aggregate Cases Functional Form: Concave Up

Forecasts vs Actuals:  Actuals higher than forecasts.

New Cases Bar Graph: New cases higher after mask-law date than before. 

Categorization: -1 (Weak Negative Evidence) 

Comment: The quadratic is concave up and the case count rises substantially after the mask-law date.  That said, it does fall off by the end of the period.  Post-law actuals are higher than the best-fit pre-law forecast (the yellow quadratic), and about the same as the next-best forecast (the exponential). However, due to the drop in cases in the final weeks, this is classed as weak negative evidence.

 

 

Panama

Mask Law Date: 07/04/2020 

Aggregate Cases Functional Form: Concave Up

Forecasts vs Actuals:  Actuals lower than forecasts.

New Cases Bar Graph: New cases higher after mask-law date than before. 

Categorization: 1 (Weak Positive Evidence) 

Comment: The quadratic function is concave up and the weekly new case count grows in a steady exponential fashion, but plateaus shortly after the mask-law date.  Actuals are somewhat lower than forecast.  Thus this instance is weak positive evidence for the mask-law hypothesis.

 

 

Paraguay

Mask Law Date: 20/04/2020 

Aggregate Cases Functional Form: Concave Up

Forecasts vs Actuals:  Actuals higher than forecasts.

New Cases Bar Graph: New cases higher after mask-law date than before. 

Categorization: -1 (Weak Negative Evidence) 

Comment: The quadratic function is concave up and the weekly case count jumps substantially after the mask-law date, before returning to approximately pre-law levels by the end of the period.  However, post-law actuals are still much higher than pre-law forecasts.  Thus, this is classified as weak negative evidence, against the mask-law hypothesis.

 

Peru

Mask Law Date: 07/04/2020 

Aggregate Cases Functional Form: Concave Up

Forecasts vs Actuals:  Actuals higher than forecasts.

New Cases Bar Graph: New cases higher after mask-law date than before. 

Categorization: -2 (Strong Negative Evidence) 

Comment: The quadratic function is strongly concave up and the weekly new case count rises in an exponential fashion.  Post-law actuals are much higher than forecast.  Thus this is strong negative evidence against the mask law hypothesis.

 

Philippines

Mask Law Date: 02/04/2020 

Aggregate Cases Functional Form: Concave Up

Forecasts vs Actuals:  Actuals lower than forecasts.

New Cases Bar Graph: New cases higher after mask-law date than before. 

Categorization: 1 (Weak Positive Evidence) 

Comment: The quadratic function function is strongly concave up and the weekly new case counts rise until the mask-law date, then drop and plateau after that date.  Actuals are lower than the pre-law forecasts.  Thus this is classed as weak positive evidence.

 

Poland

Mask Law Date: 16/04/2020 

Aggregate Cases Functional Form: Close to Linear

Forecasts vs Actuals:  Actuals lower than forecasts.

New Cases Bar Graph: New cases higher after mask-law date than before. 

Categorization: 1 (Weak Positive Evidence) 

Comment: The quadratic nearly overlies the linear function.  The weekly new case count essentially continues the trend that was set some two weeks before the mask-law date, neither rising nor falling.  However, the actuals are below the best pre-law forecast.  Thus, this is classed as weak positive evidence.

 

 

Portugal

Mask Law Date: 16/04/2020 

Aggregate Cases Functional Form: Concave Down

Forecasts vs Actuals:  Actuals lower than forecasts.

New Cases Bar Graph: New cases lower after mask-law date than before. 

Categorization: -1 (Weak Negative Evidence) 

Comment: The quadratic function is concave down, but the weekly new case count graph shows that the post-law data is basically a continuation of a trend set before the mask-law date, though rising by the final week.  Actuals are below the linear pre-law forecasts, but above the logarithmic forecast (the R-square values are close).  Thus, this is classed as weak negative evidence.

A Quick Summary of these 32 Cases

(+2) Strong Positive Evidence in favour of the mask-law hypothesis: 1 country

(+1) Weak Positive Evidence in favour of the mask-law hypothesis: 8 countries

 (0) Neutral Evidence, neither for or against the mask-law hypothesis: 6 countries

(-1) Weak Negative Evidence against the mask-law hypothesis: 7 countries

(-2) Strong Negative Evidence against the mask-law hypothesis: 10 countries