Exercise 4.119 on page 303 revealed an association between owning a cat as a child and developing schizophrenia later in life. Many people enjoy cats as pets, so this conclusion has profound implications and could change pet ownership habits substantially. However, because of the chance for false positives (Type I errors) and potential problems with generalizability, good scientific conclusions rarely rest on a foundation of just one study. Because of this, significant results often require replication with follow up studies before they are truly trusted. If study results can be replicated, especially in a slightly different setting, they become more trustworthy, and if results can not be replicated, suspicions of a Type I error (significant results by random chance) or a lack of generalizability from the setting of the initial study may arise. In fact, the paper ) cited in Exercise 4.119 actually provided three different datasets, all from different years (1982, 1992, and 1997) and with different choices for choosing the control group. The sample proportions for each dataset, with the sample sizes in the denominator, are given in Table 4.13.

(a) As we know, statistics vary from sample to sample naturally, so it is not surprising that the sample proportions differ slightly from year to year. However, does the relative consistency of the sample proportions affect the credibility of any single dataset?

(b) Use technology to calculate the p-value for each dataset, testing the alternative hypothesis that the proportion of cat owners is higher among schizophrenics.

(c) Do all datasets yield significant results? Should this increase or decrease potential suspicions that the significance of any single study may have been just a Type I error?

(d) Why is the p-value lowest for the 1982 data, even though this dataset yields the smallest difference in proportions? Similarly, why is the p-value highest for the 1992 data, even though this data yielded the largest difference in proportions?

Exercise 4.119:

Could owning a cat as a child be related to mental illness later in life? Toxoplasmosis is a disease transmitted primarily through contact with cat feces, and has recently been linked with schizophrenia and other mental illnesses. Also, people infected with Toxoplasmosis tend to like cats more and are 2.5 times more likely to get in a car accident, due to delayed reaction times. The CDC estimates that about 22.5% of Americans are infected with Toxoplasmosis (most have no symptoms), and this prevalence can be as high as 95% in other parts of the world. A study randomly selected 262 people registered with the National Alliance for the Mentally Ill (NAMI), almost all of whom had schizophrenia, and for each person selected, chose two people from families without mental illness who were the same age, sex, and socioeconomic status as the person selected from NAMI. Each participant was asked whether or not they owned a cat as a child. The results showed that 136 of the 262 people in the mentally ill group had owned a cat, while 220 of the 522 people in the not mentally ill group had owned a cat.

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Table 4.13 Cat Ownership and Schizophrenia Year 1982 Data (Analyzed in 2015) 1992 Data 1997 Data Proportion of schizophrenics who owned cats as children 1075/2125 = 0.506 84/165 = 0.509 136/262 = 0.519 Proportion of controls who owned cats as children 2065/4847 = 0.426 65/165 = 0.394 == 220/522 = 0.421