3.1 Introducing Statistics: Do the Data We Collected Tell the Truth?

5 min read•june 18, 2024

Kanya Shah

Jed Quiaoit

Aly Moosa

AP Statistics 📊

265 resources

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📊 Data: Truth-Revealing or Deceiving?

Data (plural never singular) can represent a plethora of things. In many cases, it depends on perspective. As one completes this AP course, they will understand that one piece of data could mean something else. However, error can happen.

If data is misused to convince an audience to favor one side of a topic, then it’s likely that the conclusion is also flawed. 📍

The method chosen to present the data from a survey or experiment can be misleading if the creator has changed the visual representation of a graph or left the data in counts instead of percentiles. Being able to decipher whether the data is misleading is crucial because you catch falsities in arguments or issues presented. 🔍

Likewise, methods for data collection that do not rely on chance result in untrustworthy conclusions.

It's important to use random sampling or random assignment in data collection to ensure that the sample is representative of the population and to minimize bias. Otherwise, it's more likely that the sample will be biased and not representative of the population. This can lead to untrustworthy conclusions because the results may not be generalizable to the population.

Additionally, using methods that do not rely on chance can lead to omitted variable bias, where important variables are not included in the study. This can also lead to untrustworthy conclusions because the results may be influenced by factors that were not accounted for in the analysis. You'll learn more about the aspects revolving around bias throughout this unit. 💎

This graph is misleading; the axes are different.

Source: Youtube, Rebecca Mills

Examples of Unreliable Sampling

A political poll conducted by a particular news outlet may only survey individuals who subscribe to that outlet, leading to a biased sample that is not representative of the overall population. This type of bias, known as convenience sampling, can lead to inaccurate predictions about the outcome of an election.
A medical study that only includes participants who are willing to take a new medication may not accurately reflect the effectiveness of the medication for the general population. This type of bias, known as self-selection bias, can lead to incorrect conclusions about the safety and effectiveness of the medication.
A consumer survey that only includes individuals who have previously purchased a particular product may not accurately reflect the opinions of the general population about the product. This type of bias, known as voluntary response bias, can lead to incorrect conclusions about the overall satisfaction with the product.
A study on the effectiveness of a new teaching method may only include schools that are willing to implement the new method. This can lead to bias because the results may not be applicable to schools that are unwilling to try the new method.
A survey on consumer satisfaction with a particular brand of car may only include individuals who own that brand of car. This can lead to bias because the results may not be representative of the general population's opinion of the brand.
A study on the effects of a new exercise program may only include individuals who are already in good physical condition. This can lead to bias because the results may not be applicable to individuals who are not in good physical condition.
A study on the effectiveness of a new treatment for a particular medical condition may only include individuals who are willing to try the new treatment. This can lead to bias because the results may not be applicable to individuals who are unwilling to try the new treatment.

In each of these examples, the biased sample leads to untrustworthy conclusions because the results may not be generalizable to the population. It is important to use random sampling or random assignment in data collection to ensure that the sample is representative of the population and to minimize bias. 😔

Examples of Reliable Sampling

A national election poll conducted by a reputable polling organization may use random sampling techniques to select a representative sample of the population. This can lead to reliable conclusions about the outcome of the election because the sample is representative of the overall population.
A study on the effectiveness of a new medical treatment may use random assignment to allocate participants to either the treatment group or the control group. This can lead to reliable conclusions about the effectiveness of the treatment because the groups are similar, with any differences in outcomes being attributed to the treatment.
A consumer survey on the satisfaction with a particular brand of phone may use stratified sampling to ensure that the sample is representative of the overall population in terms of age, gender, and geographic location. This can lead to reliable conclusions about the overall satisfaction with the brand.
A study on the effects of a new exercise program may use cluster sampling to select a representative sample of gyms or fitness centers to participate in the study. This can lead to reliable conclusions about the effectiveness of the program because the sample is representative of the overall population of gyms and fitness centers.
A study on the effectiveness of a new teaching method may use systematic sampling to select a representative sample of schools to participate in the study. This can lead to reliable conclusions about the effectiveness of the method because the sample is representative of the overall population of schools.
A survey on consumer satisfaction with a particular brand of car may use multistage sampling to select a representative sample of the population. This can lead to reliable conclusions about the overall satisfaction with the brand because the sample is representative of the overall population.
A study on the effectiveness of a new treatment for a particular medical condition may use random sampling to select a representative sample of individuals to participate in the study. This can lead to reliable conclusions about the effectiveness of the treatment because the sample is representative of the overall population.

Notice the patterns and differences between the two groups? Again, don't worry about the specific terms (e.g., stratification, random sampling, etc.) for now and instead focus on the big idea. In summary, using methods that rely on chance in data collection is important to ensure the reliability and validity of the results and to minimize bias in the sample! 😁

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