# How best to display a table of probabilities to a non-mathematical audience?

How would you best display this table of probabilities in an explanatory document? Basically they are the probibalbities of touching one of euipment, patient, hygiene products, etc given a type of care: Directcare etc. This table looks confusing to me, some sort of graph maybe?

$$\begin{array}{6*c} &\text{Equipment}&\text{Patient}&\text{Hygiene products}&\text{Near-bed objects}&\text{Far-bed objects}\\ \text{Direct Care}&\frac{49}{192}&\frac{170}{913}&\frac{18}{173}&\frac{79}{392}&\frac{21}{83}\\ \text{Housekeeping}&\frac{22}{89}&\frac{7}{89}&\frac{6}{89}&\frac{35}{89}&\frac{19}{89}\\ \text{Mealtimes}&0&\frac{6}{55}&\frac{2}{11}&\frac{31}{55}&\frac{8}{55}\\ \text{Medication round}&\frac{23}{429}&\frac{23}{143}&\frac{7}{39}&\frac{50}{143}&\frac{10}{39}\\ \text{Misc.}&\frac{4}{165}&\frac{19}{165}&\frac{8}{33}&\frac{10 }{33}&\frac{52}{165}\\ \text{Personal Care}&\frac{3}{89}&\frac{15}{89}&\frac{19}{89}&\frac{36}{89}&\frac{16}{89}\\ \text{Overall}&\frac{7}{233}&\frac{34}{233}&\frac{54}{233}&\frac{80}{233}&\frac{58}{233}\\ \end{array}$$

Use decimal fractions. First, it is easier to compare decimal fractions than standard fractions. Second, all data shown in this table are empirical, all listed probabilities are just approximations, so exact values don't make any sense.

You can also nicely summarize all data in pie charts (one chart for each activity).

• Yes you're absolutely correct about them being empirical data. I observed 500 nurses touching surfaces... Could you clarify why exact values make no sense, this is interesting?
– HCAI
Mar 25, 2013 at 18:58
• @user1134241: There is always some randomness when you observe empirical data. Even if you toss a coin 100 times most likely you will not see exactly 50 heads and 50 tails. Say, you can see 53 heads and 47 tails. It would be incorrect then to say that the probability of heads is 53/100. More generally, all empirical measurements have a certain accuracy, it doesn't make sense to specify their results with higher precision. (It would not make any sense to specify the distance between New York and Boston up to millimeters). So it's better to just write 15% instead of $34/233$.
– Yury
Mar 25, 2013 at 19:09
• Ah yes I understand your argument, than k you. This makes sense, In fact this data is used for creating a Markov Chain that represent the nurse's surface contacts based on these probabilities. Would you think these probabilities are a valid starting point? So perhaps showing a pie chart/bar graph is best...
– HCAI
Mar 25, 2013 at 19:14
• That might be a valid starting point but the answer depends on what your goal is. For some applications, you would want to compute confidence intervals, carefully check that there are no sampling biases etc.
– Yury
Mar 25, 2013 at 19:23