News stories are filled with numbers. Opinion polls, survey findings, and economic indicators such as stock market movements are often discussed with percentages and the upward or downward trend. For instance, a research unit in our university announces an approval rate of Hong Kong's top government officials in opinion polls twice a month, and the poll results often make headlines in the city. It's not uncommon to see news headlines that indicate one government official's popularity went down, while the public support for a politician from the opposition went up. But is it really true? When we come across news stories about opinion polls, we should be very careful because journalists often ignore some basic statistical concepts that are necessary to interpret the data correctly. The margin of error is one of those neglected factors that actually determine what the data shows. Let's say a news report claims a local politician's popularity went down 5 percentage points from 55% supportive to 50% supportive in the last 2 weeks. The report also implies that the public is unsatisfied with recent measures to create more jobs in the city as introduced by the politician. Before jumping to the conclusion that the politician's new measures are unpopular, what we need to evaluate is how much the poll results actually reflect the sentiment of the overall public. About 7 million people live in Hong Kong, but the sample size of opinion polls is normally about 1,000, if not less. So the question is, how representative the opinions of 1,000 people can be in relation to the overall population of the city. This process of statistical maneuver is called generalization. And that's where the margin of error comes in. Margin of error predicts the range that the poll results would actually fall into if everyone in the city could be polled. Suppose the margin of error in our scenario is plus or minus seven percentage points of both polls. 2 weeks ago, the opinion survey showed that 55% of the respondents supported the politician. 2 weeks later, it went down to 50%. Now, with the margin of error at plus or minus 7 percentage points, what the first poll indicates is that, when generalized to the entire population, his approval rate could be as low as 48%, and as high as 62%. The second poll tells us that the support among the respondents, this time, went down to 50%. This means, the proportion of the people who support the politician in the city can be anywhere from 43% to 57%. Now, what's wrong in the hypothetical news report? Yes, it's true that the support for the politician among the respondents went down when the two surveys are compared, but that does not mean his actual public support went down. In fact, we cannot really tell anything about an upward or downward trend from the two polls when considering the margin of error. The sampling method is another factor that's sometimes ignored by journalists. A sample is a very small portion of the entire population. Although there's a wide range of sampling methods, the most important thing is for the survey to be statistically valid for generalization, the sample must be truly representative of the demographics of the population. Online polls can never be generalized, because it only includes people who frequently use particular social media services or visit certain websites. The results of street interviews during the day time can almost never be generalized. Because such methods could include only those who are likely to be walking outside at particular locations, and those who can spend time talking to the pollsters in the middle of the day. Unfortunately there are many news reports out there that sound as if the results of such limited surveys could tell some overall trend about our society. You should dismiss such news reports as inconclusive or even baseless when you see one. As a news consumer, we don't need to have a sophisticated knowledge in statistics to make sense of the news. Just knowing the basic language and what each concept means can help us understand the numbers better. Sampling methods and margin of error are two such concepts you must always pay attention to when the news reports are about opinion polls or survey results.