randomly selected and properly designed, the sample statistic may deviate from the population parameter simply due to this inherent randomness. However, if the sample is representative of the population, the sample statistics should provide a reasonably accurate estimate of the population parameter.
Another reason for the difference between the sample statistic and the population parameter could be bias. Bias is a systematic error that occurs when the sampling or measurement process consistently produces results that are consistently different from the true population parameter. This can happen due to flaws in the study design, data collection methods, or measurement instruments. For example, if a survey is conducted via phone calls, only people with landline phones may introduce a bias towards older individuals. This bias can cause the sample statistic to substantially deviate from the true population parameter. Additionally, an inadequate sample size can result in a sample statistic that does not match the population parameter. When the sample size is small, there is a higher chance of getting extreme values or outliers, leading to a skewed sample statistic. With a larger sample size, the sample statistic is more likely to converge towards the true population parameter.
Non-random sampling methods can also contribute to a discrepancy between the sample statistic and the population parameter. Non-random sampling methods, such as convenience sampling or purposive sampling, may not provide a representative sample of the population and can introduce bias. This can lead to a sample statistic that does not accurately estimate the population parameter. Other factors, such as measurement error or external factors, can also impact the relationship between the sample statistic and the population parameter. Measurement error refers to inaccuracies or imprecisions in the measurement process. This can occur due to human error, faulty equipment, or inconsistent measurement procedures. External factors, such as a change in the environment or population characteristics, can also affect the relationship between the sample statistic and the population parameter.
Chapter 10
1. A researcher wants to test for a relationship between the number of citizen complaints that a police officer receives and whether or not that officer commits serious misconduct. He gathers a sample of officers and records the number of complaints lodged against them (0-2, 3-5, 6+) and whether they have ever been written up for misconduct (yes or no). Can he use a chi-square to test for a relationship between these two variables? Why or why not?
Yes, the researcher can use a chi-squared test to test for a relationship between the number of citizen complaints and whether or not the officer commits serious misconduct. The chi-squared test is appropriate for analyzing categorical data and examining the association or independence between two variables. In this case, the number of complaints (categorical variable with three groups) and the presence of misconduct (categorical variable with two groups) are both categorical variables, making the chi-squared test applicable. The test will compare the observed frequencies of officers falling into different combinations of these variables to the frequencies
