People are poor at making judgments about probability. One source of error in judgment of probability is the base rate fallacy in which people ignore the base rates of low probability events. In a study of the base rate fallacy by Bar-Hillel (1980), participants were exposed to a vignette about a traffic accident. In the scenario, a taxicab was observed in a hit-and-run accident. In the city where the accident occurred, 85% of cabs are blue and 15% of cabs are green. Later, a witness testified that the cab in the accident was green and the witness was shown to be 80% accurate in identifying blue and green cabs (i.e., 20% of the time, the witness confused the cabs). What do you think is the probability that a green cab was in the hit-and-run? Most participants who encounter this problem report that the probability of the cab being green is much higher than the actual probability of 41%. That is, most participants ignore the fact that green cabs are relatively rare. Suppose that a researcher replicates the Bar-Hillel experiment with a sample of n = 16 participants. The researcher observes an average rated probability of M = 60.06% with SS = 656.66. Use a two-tailed test (⍺ = . 05) of the hypothesis that participants showed a base rate fallacy. Assume that μ = 41 if there is no base rate fallacy. Compute two different measurements of effect size.
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
People are poor at making judgments about
- Use a two-tailed test (⍺ = . 05) of the hypothesis that participants showed a base rate fallacy. Assume that μ = 41 if there is no base rate fallacy.
- Compute two different measurements of effect size.
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