You may have read or heard that new Covid-19 cases are spiking. We used to think that a couple hundred of new cases were high, now thousands are the new normal. The Governor blames these new cases on increased testings. Obviously, more testing does reveal more Covid cases, but no one knows by how much.
So how can we tell if the virus is expanding? The Governor has cited new hospitalizations, as a better indicator of whether the virus is now spreading. In reality, that is not the case.
New hospitalizations reflect the severity of the virus cases and not the rate it is being spread. That is an important distinction, since many infected people have milder symptoms and never need to check into an ICU hospital room. Unfortunately , they can still spread the virus to more vulnerable people.
So let’s assume the Governor is right and new cases isn’t a good marker for tracking the virus and hospitalizations are.
The Chart above shows the daily number of new hospitalizations since March 27th. The average daily rate was 143, with the lowest daily hospitalization was 32 and the highest 265. The last few days it moved lower, but the pattern over time is up and down.
The question isn’t whether the state is in control of the virus, but more if is it capable of handling a significant spike in new hospitalizations, if it happens. Looking at the State’s five largest counties: Palm Beach, Miami-Dade, Broward, Hillsboro and Duval Counties, where most cases have occurred, we can see how prepared we are if faced by many life-threatening cases.
Below is a table with each county’s total ICU beds, ICU beds currently available and the percent of ICU beds available.
AVAILABLE ICU BEDS
% AVAILABLE ICU BEDS
As you can see, it wouldn’t take much of a spike to fill these remaining ICU beds. A bad traffic accident on I-95 could fill the remaining beds in Mami-Dade, and Hillsboro isn’t much better. Palm Beach County has only 59 beds and it’s averaging over 300 new Covid cases a day.
The chart below gives some perspective to the availability of ICU beds compared to the total number of ICU beds in each county. The tiny gray bars are the available ones.
The Governor maybe right and wrong at the same time. Hospitalizations are not, at this moment, significantly rising. But it won’t take much to overwhelm these large county hospitals in jut a few days. It’s his call and the results could determine his political future. Stay safe…
“Mr. Biden leads the President by around 10 percentage points in an average of recent of live-interview telephone surveys of registered voters.” The Upshot
I get the New York Times delivered everyday. It’s my morning coffee time and I look forward it. I’ve always considered the “Times” well researched and written. It does have a political slant, of course, but that doesn’t bother me. (I have my own biases.)
In yesterday’s paper, I noticed an article on how Trump’s numbers were “eroding” and that it was an indication of how the pandemic, economy and demonstrations were having a toll on his re-election chances.
The article contained a chart displaying six major polling firms and the increase in Biden’s percent lead against Trump from the same firm done earlier in the spring. Unfortunately, the article didn’t identify the earlier dates made in the comparison.
For instance, they cite a Monmouth poll showing a 7.5% increase in Biden’s lead, but the only two Monmouth polls listed in this time period had only a 1% percent difference.
The same was true of the ABC/Washington Post. They list Biden’s lead difference since the earlier survey was 7%. But the earlier poll had Biden with a 2% lead, and the later poll had him with a 5% lead, for a net difference of only 3%. And all the polls they identified are from the 538 website, the same site I used.
With differences this small it could easily be within the margin of error for both surveys. In other words, random error. So I decided to use a different method to decide if Biden’s lead is deteriorating.
As with the Times analysis, I collected polls from March 18 through June 3, a period which the Covid-19 virus was spreading, the economy collapsing and the killing of George Floyd and the ensuing protests. All polls were retrieved from the same 538 website.
To be sure I was comparing apples to apples, eighteen of the twenty polling firms were ranked by 538 as A or A+ and two a B+.These were national polls with the highest standards.
As in the Times article, all used live telephone interviews and national samples of 700 or more, the Gold Standard for surveys. Of the 20 firms, six were also included in the Times’ analysis.
With all 20 surveys, Biden had an lead of 5.1% over Trump. But this average difference does not tell us if Biden’s lead is expanding, declining or staying the same.
For comparison, I split the polls into two groups: Ten surveys were conducted from March 18 through April 15 and ten from April 29 through June 3. In the latter period, the killing of George Floyd took place, so we would expect Biden’s percent to increase. So my hypothesis is that the later surveys will show an increase in Biden’s numbers.
Biden’s early polls (March 15-April 15) his average lead over Trump was 4.9%. His later polls (April 29-June 3) averaged 5.4%, a 0.5% increase.
Below is a graph that visually represents Biden’s lead over Trump in all 20 surveys. The blue line represents the early polls and the red, the later ones.
As you can see, there is a degree of variability during this three month period. Considering these are America’s finest polling firms using the exact “gold standard” survey methods, it may seem unusual. For me, after conducting hundreds of surveys, it does not.
As I taught my students at the University of Florida, polls are estimates and not a precise representation of all voters. Even the gold standard surveys, produce errors beyond the margin of error, such as wording and question order effects.
An easier representation of the polling data, is a graph comparing both Biden’s and Trump’s percentage from each of these same surveys, as shown below.
The blue line represents Biden’s percent of the two person vote and the red, Trump’s percent. The dates are the same as the previous chart, but interpretation is clearer. As you see, the variation is quite narrow with no significant spike for either candidate. The total difference for all 20 surveys is 5%, but spread over all surveys the average per poll difference is only 0.25%.
But is this lead a statistically significant difference? The best way to test this is with a statistical measure of the means (averages) between the two groups, the early polls and the later polls. The null hypothesis is that there is no statistical difference between the two periods.
I’ll use a statistical method called a paired T-test, which compares the means of the two groups. When applied to the two groups above, the significance level is .140 (T=-1.69), which is not significant and, consequently, the null hypothesis prevails and the differences are not statistically different. In plain terms, this tells us that there no difference between the two time periods.
Using the same type of polling methodology, our analysis does not confirm the New York Times’ analysis that at this time period Biden’s lead is eroding. In fact, the two candidates’ polling is remarkably stable considering the current political and economic environment.
At the national level, the Trump numbers have been upside down almost from the moment he took the oath. For the Trump campaign, what really matters is at the state level. Their plan is to again capture the Electoral Vote and let the national popular vote go its own way. I’ll be watching those states…
You probably have read that Donald Trump has pulled the RNC Nomination Convention from Charlotte, North Carolina, because the the Governor would not guarantee that social distancing would not be required.
The RNC is now scrambling to find another location within three months. They are currently surveying seven cities as for a replacement site. One suggestion that is rumored to appeal to Trump, is a series of traveling rally-type conventions in different cities.
How or where the location or locations occur, there will be certain requirements that conventions will need to make the decision. You would think that at the top of the list, is how important that state is to winning the election, including the host state.
Most observers believe the Party wants a swing state that could make an electoral college difference. A state like Florida, with 29 electoral votes that has since 2000, chosen two Republicans and two Democrats (2000 was a tie) with an average popular vote difference of 0.5%.
Florida is certainly in the mix, and Florida Governor DeSantis is playing cheer leader for the state, with Orlando and Jacksonville as the primary cities for the event.
There are, of course, several other states that could meet the RNC’s need for a state win in addition to hotel rooms, a large convention center and a national airport, etc.. But I have a question, does holding the convention in a state actually help win that state?
As I was writing this post on Sunday, I saw on ABC a brief segment featuring the founder of the FiveThirtyEight website Nate Silver commenting that he didn’t believe the convention location had an effect on whether the party candidate won that state. He used an recent example of a Democratic Convention where the nominee lost the state in the general election (I can’t remember what state but I’m sure he was correct).
To confirm his statement, I looked at past conventions for both the Republicans and Democrats held from 1860 on. A somewhat arbitrary start, but one that eliminates the early conventions that were mostly held in the north east where travel was more difficult.
I split the convention locations into two categories: Republican and Democratic. My initial analysis was to measure how many of the Convention states the party nominee won.
For Republican Conventions, the party nominee won 73% of their convention states. The Democrats not so well, winning with 55% of their convention states.
From 1960 on however, the Republican nominee won the convention state some 67% of the time. The Democrats, on the other hand, won 53% of their convention states. I don’t know what data or time frame Mr. Silver used for his analysis but it wasn’t these two periods.
Where the Republicans and Democrats held their conventions since 1960, hints at what state’s the Republicans and the Democrats consider important. Below is a chart of where the Republican conventions were held since 1960.
REPUBLICAN CONVENTIONS SINCE 1960
# of CONVENTIONS
As the chart shows, Republicans put 5 of their conventions in Florida and Texas, which have a total of 67 electoral college votes. The Republicans won two of the three Florida elections (barely lost 2012) and both the Texas presidential elections.
Now let’s look at the Democrats choice for conventions since 1960 below.
DEMOCRATIC CONVENTIONS SINCE 1960
# of CONVENTIONS
PENNSYLVANIA /OHIO/ MINNESOTA
Like the Republicans, the Democrats put 5 of their conventions in Florida and Texas. Florida makes sense since 1992 they won 3 of the past 6 election cycles and lost the other three by less than 1%.
Texas, on the other hand, has been a safe Republican state since 1976. Perhaps the Democrats wanted to keep the Republicans from taking the state for granted. It didn’t work. Too long a long shot this year.
This year, the Democratic Convention was to be held in Milwaukee, Wisconsin, but may now be held “virtually.” Wisconsin was a good choice since it is a true battleground state that is presently leaning toward Biden. As for the virtual convention, it’s hard to get excited for an imaginary event. Success with virtual news conferences have been mixed at best.
The Republican Party are almost certain to hold a live, packed and boisterous convention. Good for TV and news coverage and of course, the Covid virus. A win-win so to speak.
My bet on where it will be held: Florida. I just looked up what “swing-state” means in the dictionary and it had Florida’s picture there…
“Tragedy is a tool for the living to gain wisdom, not a guide by which to live.” -Robert F. Kennedy.
After the horrific killing of George Floyd was broadcast on TV around the world along with the immediate protests throughout the country, I felt sick to my stomach.
But as the days past and I watched as both Black and White Americans mourning together for the first time in my lifetime, I realized that how this tragedy could have planted a seed that could change our nation for the better.
We are in the final months of what will probably become the most historic presidential race in the nation’s history, and I’m wondering what else could happen. My immediate reaction to all of these events, Covid-19, a wrongful death and protests by thousands of citizens standing in the bright light of the White House demanding change, is it will undoubtedly effect the election in November.
That impression starts with what effect the latest events, particularly the murder of George Floyd and the ensuing protests, will have for Donald Trump’s reelection. Specifically, will the fallout from all these events affect his immediate poll ratings.
In this quest, I gathered Trump Job Approval polls prior the death of Mr. Floyd and those polls following his death. My hypothesis is that the his death and the protests that followed will have a negative effect on these later polls. But to be clear, even if there is significant negative effect it doesn’t mean it won’t fade by the time we reach November.
I collected 24 public polls, 12 prior to Mr. Floyd’s death and 12 immediately following the May 25th killing. The dates of the prior surveys are from May 1st through May 23rd and after the killing, May 28th through June 4th.
The average job approval ratings for the prior event polls were 45 approve and 52 disapprove, a negative 7%. The average job approval ratings after Mr. Floyd’s death were 44% approve and 48% disapprove, a 4% difference.
Trump’s disapproval is four percent more and his approval is only one percent less after the killing. To determine if the differences are significant, I used Analysis of the Variance (ANOVA). This a statistical model to determine if two groups are statistically different.
The ANOVA comparison of both polling data prior and after the event is not significant, meaning that Trump’s job approval is statistically the same before and after the death of Mr. Floyd and the ensuing protests.
It is possible that as all of these events sinks in, voters will react more negatively, but for now, in the immediate aftermath of the murder and protests, it has changed no minds about Donald Trump as President.
Since his ratings were negative to begin with, it could have softened the impact of these latest events. In addition, I have found that the Trump’s base is unwavering about his performance regardless of what he does are says.
All of these recent events have made the upcoming election even more important. With or without the Covid virus, this country needs to turnout and cast their vote in November. Don’t complain about who was elected for the next four years, after the votes are cast, if your only participation was watching the vote count on TV. Be safe and vote…
Today is the day we matched our highest percentage change in Florida’s new Covid-19 cases.
Back on May 26, I published my new logarithmic model on the daily new cases in Florida (“The Canary in the Coal Mine is Beginning to Sing”).
Using a logarithmic transformation (natural log), I changed the daily new cases into a daily percentage of change and applied this data in a predictive cubic regression statistical technique.
Instead of trying to make sense of daily data that was going up and down like a yo-yo and making it impossible to interpret especially when using an linear bar graph even with a three or seven day average line though it. The percentage change growth is easy to understand, especially in graphs. Below is the latest model graph from data released today.
Using a cubic regression model with the natural log of new Covid cases we can predict the new path of the virus’s growth. The curved line is the model’s predicted path of Covid-19 growth rate in percentage changes over time. As you can see, the growth of new cases started out small but accelerated by the 20th day and peaked around the 40th day or around April 8th.
From that day, the growth of new cases slowly declined until about day 70 or around May 13th. From this point, the number of new cases slowly began to grow again. On May 18th, most of Florida was allowed to open their doors to the public. That was about 78 days into Florida’a pandemic. This is about when the curve started slowly upward. Probably a coincidence.
Remember that the daily data points are percent changes from each day, measuring the virus’s percentage growth and not the number of new cases. In other words, the Covid virus infections are increasing.
Will the Covid virus infections continue to grow? The model path says yes based on the current growth rate. It is important to note that this model is extremely sensitive and could easily change course. But it isn’t comforting to realize the gains the state made with social distancing and masks, is starting to evaporate. Keep tuned and wear your mask. Be safe…
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Conventional wisdom has always had Democrats benefiting from higher turnout. After all, Democrats have a larger proportion of lower income and less educated voters. Even the Republicans must believe this as well, since Republican legislatures often pass more restrictive rules to limit new registrants usually under the guise of preventing voter fraud.
Conventional wisdom, however, is not always right. In Florida, presidential election turnout in 2016 was 75% , which ranked 11th among all 50 states. Since 1954, the average presidential turnout was 74.5%.The average turnout consistency is remarkable considering the significant changes in population and demographics.
The question for me is, did the turnout help or hurt Clinton in the Florida 2016 election? In pursuit of this answer, I collected by each county’s turnout data the following four variables: Republican Percent, Democrat Percent, Turnout Percent, and Black Voter Percent. I have used a linear model and regressed these variables on Trump’s percent of the county vote.
Below are the model’s unstandardized coefficients and significance levels. All four variables are highly significant (Sig. column).
The unstandardized coefficients (in red) shows the effect of each variable, while holding all other variables constant. For instance, since the dependent variable is the percent of Trump’s vote, and the coefficient for Republican percent is positive (1.992), his percent of the vote (mean) increases as more Republicans vote.
Below is scatter plot of the regression model’s predicted Trump percent, with an Rsq.=.902.
In this case, for every one percent increase in Republicans who vote, his (Trump’s) mean percent of the total vote increases by 1.992%, while holding all other variables constant. This property of holding the other variables constant is crucial because it allows you to assess the effect of each variable in isolation from the others.
On the other hand, as the percent of Black voters increase, Trump’s percent of the total vote decreases since it has a negative sign. The same is true of turnout, since it is also negative. So in 2016, the common wisdom that higher turnout benefits the Democrats is true, at least in the 2016 election.
The -.310 means that a one percent increase in turnout reduces Trump’s percent by a negative .310%. So an increase in turnout by 10% reduces his vote by 3.1%. See how simple this is.
Now for the big surprise! An increase in the registered Democratic vote increases his percent of the total vote just like the Republican vote. In this case, a 10% increase in the Democratic vote increases his two party vote by 12.7%.
Now before you think I’m crazy or at least wrong, let me explain. First, this is Florida and the laws of physics or partisan voting don’t apply. In many counties, voters often vote for local Democratic candidates, but when it comes to statewide and national elections, they vote Republican.
Let’s look at a couple of counties as an example. In Calhoun County, the percent of registered Democrats is 52% but Hillary Clinton’s percent of the two party vote in 2016 election was only 20%. And how about Franklin County? Democratic registration is 47% and Republicans 38%. Clinton’s percent in the election was 28%. And so on..
All throughout the panhandle and central Florida rural counties, many registered Democrats voted for Donald J. Trump. And yes, larger urban counties did vote for Clinton. But in the end these small counties carried the day for Trump by a margin of 1.2%.
So does a higher turnout benefit the Democrats? The answer is yes when controlling for other variables. More importantly, the effect of higher turnout is dwarfed by the number of Democratic voters who voted for Trump, increasing his percent of the vote by over 12%.
With a difference of a only 1.2%, if you are a Democratic candidate it might be time to spend a little more time and money in these smaller counties. In 2012, Barack Obama beat Clinton’s total Florida vote by 4.4%, mainly on the small counties where he bested her vote by 5.3%.
So the road map for victory for Democrats is through the smaller counties. Start in Wakulla County and take the Swanee river south until you hit the Withlacoochee river. From there pick up the Kisssimmee to Lake Okeechobee and jump on the Ocklawaha River heading west. There aren’t many voters along there, but you when your finished the trip you’ll understand why Hillary Clinton lost Florida. Be safe…
Since January 1st, 1,131 national polls asked “Do you approve or disapprove of the way Donald Trump is handling his job as president?” The average percent of “Disapprove” for these 1131 surveys is 53.3%.
That virtually every national poll contains this question suggests that it has some significant importance that should effect voters’ political vote choice. But almost all studies suggest otherwise, that is until right before the election.
But I don’t find any academic studies on the effect that a President’s job approval has on their polling percent of the vote. You would expect a high degree of probability between the two variable.
To test this hypothesis, I obtained all 1,131 surveys conducted from January through May 26th, 2020 that contained both the standard job approval rating and the trial ballot question between Biden and Trump in the same survey.
In this time period, Trump had a net positive (approve less disapprove) rating in only four surveys, as shown in the chart below where the net positives are above the horizontal line.
His job rating has been underwater for most of his time in the White House. If Trump’s Job Approval rating were predictive at this point, I would recommend he put a reservation on a moving van for the fall. But as I have pointed out before, this variable has a short shelf-life and only predictive when measure close to the election.
In the Biden/Trump elections question, Trump has a 41.9% average against Biden’s 49.7%, an average lead of 7.8% for all 1,131 surveys.
His Biden/Trump polling is out performing his job approval rating by 1.7%. The chart below shows how his percent of the Biden/Trump poll changes as his disapproval rating changes.
This graph depicts what happens to Trump’s percent of the Biden match-up as more voters say they disapprove. That, of course, means that the people who are least likely to vote for Trump are those who disapprove his job performance.
This shouldn’t be a surprise since people who do not like someone will never vote for him or her, and people who do like him may or may not vote for him. What is surprising is that the “approval” rating is does not effect his polling percent.
I can now calculate the average reduction of Trump’s disapproval rating based on the regression model’s standardized coefficient estimate’s reduction of his percent of the two-party poll percent against Biden. The model coefficients are shown in the table below.
We can calculate Trump’poll percent of the vote against Biden’s with a simple equation: Y = -.547 (x) + Constant (68.95), where x is Trump’s disapproval rating and Y is the Trump’s percent of the vote against Biden. Notice that the significant (Sig.) level for “Approval” is .684, and non-significant at the <.05 standard.
Trump’s average disapproval rating in these surveys is 53%. So our equation is Y = -.547 (53) + 68.95 or Trump percent of vote =40%, 1% less than the actual average of all polls.
What is this analysis suggests is that Trump’s job disapproval rating is far more important than his approval rating in determining his percent of the vote. In fact, the approval rating in this analysis is not significant, meaning it has no impact on his percent of the vote.
Will this apply to the actual election in November? The honest answer is I don’t know. Normally, models that predict election outcomes use past election data (along with other exogenous variables, such the economy).
But the President’s “approval”rating has been shown to predict his re-election when polled near the election. No president since modern polling has won re-election with an approval less than 50% on election day.
Because of the inverse relationship, when the approval number is 50%, the disapproval rating is likely around 46% (excluding the “don’t knows”). As we get near the election, I will revisit this equation again to see if it does predict the winner.
In the mean time, when you see a 2020 poll, check out the disapproval rating. If it is more than 37%, he’s losing…
I’m sure that most of you have heard that President Trump wants to eliminate mail-in ballot voting, particularly in battleground states. His reasoning (I’m using that word in its broadest sense) that mail-in ballots are ripe for election fraud, even though most political scientists say the amount of election fraud is small, mail or otherwise.
I suspect his reasoning is more about his belief that mail-in ballots give Democrats an advantage. Others believe that the President is creating the idea of wide spread fraud as a potential excuse in case he loses the election. But none of this makes any sense to me because in all my campaign experiences, absentee voting has always benefited the Republican candidate.
In general, traditional Republican voters are better educated and consequently, more likely to use this less taxing method. This may not apply as much in the age of the Trump voter, where many are less educated than traditional Republicans and they may rely more on in-person voting. That’s speculative, of course.
So to satisfy my curiosity, I researched Florida’s past election data and found some mail-in ballot data with actual mail-in ballots cast by party affiliation in three general election cycles: 2014, 2016 and 2018. These election cycles include two non-presidential elections and one presidential one.
The data is broken down in to four categories, Republican, Democratic, No-Party Affiliation (NPA) and Other voters. Since my purpose is to find if one of the two major parties has some kind of partisan advantage, I have eliminated both NPA and other party mail votes from this analysis.
In 2016, the Republican state-wide mail vote total was 1,108,053 and the Democratic mail votes were 1,049,809, a 58,244 Republican vote advantage in the presidential election, graphically shown below.
In 2016, the Republican candidate (Trump) should have had a 2.8% vote advantage if both Democrats and Republicans voted the party line and NPA’s and other non-partisan voters split evenly between the two candidates. If you may recall, Trump beat Clinton by only 1.2% in Florida.
In the 2014 general election, the number of Republican mail ballots cast was 833,420, and by Democrats 705,752, a 127,668 more Republican mail votes, as shown below.
In this year, the Republican candidates could have had 8% more partisan support based on the Republican mail ballots. And finally, we have the 2018 general election when both the Florida Senate and House were on the ballot.
The Republican mail vote advantage here was the smallest of the three election cycles since it featured only state House and Senate races. Republican mail ballots cast were 1,080,808 versus 1,026,600 Democratic ballots, or 54,208 ballot difference, but still a 4% advantage.
This short analysis of three election cycles clearly demonstrates that Florida Democrats have no advantage when mail ballots are employed. Actually, the opposite is true. Republican candidates should benefit from an aggressive mail-in ballot campaign.
Florida maybe the most important state in the country. In fact since 1928, no Republican presidential candidate has won the presidency without winning Florida. Even Trump himself may have won Florida based on the partisan mail votes alone.
So why is he complaining about mail ballots when obviously the facts, at least in Florida, don’t support that Democrats benefit from this voting option?
It is possible his campaign found that mail ballots benefit the Democrats in other swing states. It is also possible the campaign hasn’t done any research on this subject at all. Or, that Donald Trump just believes this idea that Democrats benefit more from mail-in ballots and, God forbid, no one should contradict him.
If you have an idea, please post it in the comments section and I’ll share it with all readers. Be safe…
Regular viewers of this site may recall that one of my original posts was showing our Covid-19 model for both Florida and the US. The model was a non-linear (cubic) estimate of the direction of the virus that accurately predicted when the virus’s new cases began to decline in both Florida and the Nation.
Unfortunately, as the data points descended, they slowed down and eventually began backing up, causing a traffic jam of data points. New Covid-19 cases would on one day go down and the next go back up and so on and on. In addition, the up and down changes weren’t uniform.
To correct for this up and down pattern, I went to my old calculus tool box and applied a logarithmic data transformation called a natural log (ln). In this case, the transformation is from daily new cases to percentage change. So instead of watching cases move up an down we now plot the percent change from each data point. In addition, this log transformation makes the data far more interpretable.
Using a polynomial equation (cubic), I can now attempt to predict the direction of Florida’s new Covid cases by using the transformed (ln) data. I want to emphasize that this effort is experimental and could easily predict nothing except that I was wrong, but in theory it should work. The chart below plots the expected path.
The red line shows the predictive path of new cases. The small circles show the actual cases after transformed into percentage change. The blue lateral line shows the flattened ceiling of the data.
For example, the virus percentage change peaked around the 37th day and began to decline until about the 70th day when the cases (percentage change) began to rise again.
From that point, the red line bends upward. This is the model’s predicted path, which suggests a rise in new cases. In other words, the Florida Covid-19 pandemic is increasing and no longer stabilized! If this trend is correct, it strongly suggests that the loosening of restrictions has allowed the virus to expand.
I will post this graph on a regular basis or when significant changes occur. I have mixed emotions about the success of this experiment. Like all of us, I want this virus to disappear sooner than later. It is very possible that the prediction line will shift downward and show a decline in new cases. For me, that’s a win-win. Be safe in any case…
I don’t know about you, but I’m having trouble of whether Florida’s new virus cases are rising, declining or just plain stuck in second gear. On television, some news stations tell us that Florida’s new cases are stabilized, and another reports it’s declining and and some newspapers that they are rising.
The problem is that in Florida the pattern of new cases is not obvious. Some days the state health department reports 1,200 new cases and the next day 650.That’s, of course, not their fault because this virus can’t decide if it’s coming or going. So the data pattern is often up and down each day.
Contributing to the problem is how most media outlets and the Health Department display the daily counts using the linear format of the ubiquitous bar chart like the one below.
This bar chart tracks the actual daily number of cases since the first recorded cases in March. As you can see, the general pattern since the first peak around the 35th day, is downward until around the 40th day, when a series of up and down cases began to appear, interrupted only by occasional spikes.
Many times you will see a moving average line through the bars which is at least better than just the bars alone. The problem with moving averages, is how many days do you apply to make the average. Some use a seven-day average, or a three day or even a 30 day average. And besides smoothing the data, what does a moving average represent? How many days you apply effects the slope of the line and the more days used the flatter the line.
I have always opposed using linear graphs for data that isn’t linear. But the “up and down” pattern is hard for almost all graphic representations. The only way to solve this problem is to transform the data points into a form that moves in some systematic way and still accurately represents the data.
In calculus, log transformations are common in helping understand the data. In general, one of the main purposes of log transformations is to make the data better interpretable and graphs easier to understand.
Mathematicians, engineers and economists are the principal users of log transformations. For economists, the natural log (ln) is the preferred choice since it measures the percent change from data point to data point.
In other words, instead of raw data of new cases that go up and down, we can transform it into the percent change which can be graphed and understood. Below is a graph of the same data shown in the bar chart above, but with the data transformed into natural log (ln) values.
With the data transformed into percentage change, we can easily see that in the early days of the infections, the percentage change of new cases rose exponentially and then around the 30th day leveled off and has remained relatively flat since then.
You could interpret this chart as a good news-bad news story. The good news is that Florida’s new Covid cases have not continued to increase (as represented by percentage change). The bad news is that they haven’t declined yet either.
I will be using log transformations from time to time or when needed for you to understand graphs easier, without compromising the analysis. Some of my posts at times may be difficult to understand but feel free to ask me a question or leave me a comment and I will gladly reply. Be safe…