than the critical t corresponding to the smallest possible df, the result is significant. If the separate-variances t is smaller than the critical t corresponding to the largest possible df, the result is not significant. If neither of these situations applies, a more exact determination of the df (one les be associated ater may 7. Two-group experiments are usually based on random assignment from one sample of convenience, rather than two separately drawn random samples. Random assignment can lead to an inflated Type I error rate when the samples differ in both size and variance and the larger sample is required (see Advanced Material after the Exercises). has the smaller variance. In that case, the separate variances t recommended, in order to conservatively control Type I errors 8. In certain experimental situations, differences in variance may be more dramatic or interesting than the difference in the means. For such situations, the homogeneity of variance test may have more important practical or theoretical implications. EXERCISES *1. Seven acute schizophrenics and 10 chronic schizophrenics have been measured on a clarity of thinking scale. The mean for the acute sample was 52, with s = mean for the chronic sample was 44, with 11. Perform a pooled-variance t test with alpha = .05 (two-tailed), and state your statistical conclusion. 2. A group of 30 participants is divided in h based on their self-rating of the vividnes of their visual imagery. Each particp is tested on how many colors of objecs 12, and the S =
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.
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