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Appropriate statistical study example

Sal determines if a statistical study was a sample study, an experiment, or an observational study. Created by Sal Khan.

Video transcript

Voiceover:Alma has developed a new kind of antibiotic. For the antibiotic to be sufficiently effective, it has to kill at least 90% of bacteria when applied to a harmful bacteria culture. She applied her antibiotic to a petri dish full of harmful bacteria, waited for it to take effect, and then tried to estimate the percentage of dead bacteria in it. She took a random sample of 300 bacteria and found that 94% of them were dead. Then she calculated the margin of error and found that the true percentage of dead bacteria is most likely to be above 90%. So, what's happening over here, she's trying to figure out what percentage of the total population of bacteria died. Maybe there's something about this bacteria, maybe when you look at it from, you know, the naked eye, you can't tell whether the bacteria died or not. So, she decides to estimate the true percentage by sampling 300 individual bacterium, or by sampling ... I always forget the singular case. By sampling 300 bacteria, and then in her sample she found that 94% of them were dead. Then the margin of error tells us, because the margin of error says it's unlikely, or that it's very likely that the true percentage is above 90%. That means that given that you sample 300 bacteria, it's very unlikely that the true percentage is below 90%. So, she could feel reasonably confident that in her petri dish, more than 90% of the population did indeed die. Now, let's answer these questions. What type of statistical study did Alma use? Well, she used a ... she's trying to estimate a parameter for population, in this case, the parameter was the percentage of all of the bacteria that died. She couldn't observe that directly, so instead, she took a random sample of the bacteria in the petri dish, and she used ... she calculated the static for them, 94% of them were dead, and that's her estimate for the population parameter. The percentage of the population that died. So this is ... when you're using a ... when you're using a random sample to generate a statistic, which estimates a parameter for a population, that's a sample study. So, she ran a sample study. Now the next question is. Is the study appropriate for the statistical question it's supposed to answer? So what was the question that she's trying to answer? Well, at least the was it's written, it seems like she's trying to answer whether or not her antibiotic works, whether it's an effective antibiotic, whether it's capable of killing bacteria. You might be tempted to say, "Okay, well look. It looks like it killed ... it killed more than 90% of the bacteria, or very likely it killed more than 90% of the bacteria given ... given the sample size, and the margin error and all that." Even if it is indeed the case, that 95% of all the bacteria died, it doesn't necessarily mean that it was caused by the antibiotic, maybe it was caused by the plastic in the petri dish. Maybe the air in the petri dish was too cold or went bad, or maybe it was handled in a weird way. Or, maybe that bacteria was just a bad ... a bad culture, and it somehow it just spontaneously died on its own. She can't say with confidence that it was definitely ... it was definitely the antibiotic. In order for her to make that statement, she would have to run a proper experiment. She would have to have a control and a treatment group, where everything is equal except for the treatment group has the treatment. So if she had 2 petri dishes that were kept in the same conditions with the same lightning, the same air, the same material that the bacteria is growing on, everything the same, except for the treatment group, has the antibiotic applied to it. Then she saw that in the treatment group that most of the bacteria died while in the control group, most of the bacteria didn't die, then she could say, "Okay. It looks like the antibiotic caused the bacteria to die. That there was actual causality here." So, she would have had to run an experiment. The most appropriate statistical study, or the most appropriate study would have been a proper controlled experiment. Where you have a control group, where they don't have the antibiotic, and a treatment group, where they do have the antibiotic. Let's see what are the choices here. Where they say is the study appropriate? So, yes because she is appropriate study. No, I don't like that answer. No, because she can't know for certain that the true percentage of dead bacteria is above 90%. Well, I'm not going to click on that, because even if she knew for certain that the true percentage of the dead bacteria were 95%, she can't feel confident that it was due to the antibiotic. Once again, it could be caused by the air conditioner. It could have been caused by the petri dish. It could have been caused by the lighting in the room. So, no, because the study didn't have a treatment and a control group. Yeah, I would go with that one right over there. Yes, because she found that the antibiotic killed more than 90% of harmful bacteria. Once again, even if she knew for sure that more than 90% of the population had been killed, she doesn't know that it was caused by the antibiotic. It could have been caused by a whole bunch of things. If she had a controlled group that had the exact same conditions and the bacteria didn't die, then she could feel better that it was the bacteria death was due to the antibiotic.