1. A researcher was interested in investigating the effectiveness of four different drugs and a placebo (sugar pill) on cholesterol levels. Twenty-five participants were randomly assigned to one of five conditions, where they received either a placebo (control) or one of the four cholesterol drugs. Two of the drugs had been on the market for several years (Drug A and Drug B) while the other two drugs were recently released (Drug C and Drug D). Conduct the appropriate test to assess whether there is an overall difference between the 5 drugs (that is, conduct the appropriate procedure that assesses, in a single test, whether there is a difference anywhere between the groups). (Testing exactly where the differences are for this problem is not required; what I want you to do is perform the appropriate overall test to assess if differences exist in general in the data). Higher scores indicate worse cholesterol Type of pill Drug B- old 145, 159, 171, 170, 168 Drug D 132, 142, 135 156, 142 Drug A-old 163, 161, 153, 166, 174 Drug C-new 116, 117, 132 127, 134 Placebo -new 188, 179, 158 173, 150 A. State the null and alternative hypotheses for the test below. B. Report the results of the hypothesis test in (a) below. Be sure to express the results in terms of the context of the study and use APA format as appropriate. (Post hoc tests are not required here -just the overall APA formatted results of the test of the null hypothesis provided in (a) above.) C. What is the effect size for the study? Calculate and report the effect size below. Interpret the effect size according to Cohen's standards 2. Using the data provided in # 1 , conduct the following contrasts in SPSS. The researcher was interested in examining whether there was a significant difference between (a) the placebo vs. the drug conditions (include all drugs here), (b) the old drugs vs. the new drugs, and (c) the new drugs (Drug C vs. Drug D). Use a .05 for the set of 3 contrasts. a. State the null and alternative hypotheses for each of the contrasts below. Label the hypotheses as appropriate, so that I know which hypotheses go with which contrasts. (For example, write 'contrast 1,' and then provide the hypotheses for the first contrast, etc.) b. Provide the weights for each of the contrasts below. (For example, write 'contrast 1' and then provide the weights for that contrast, etc.). c. What value of alpha should each contrast be conducted at? Report the value of alpha below (show how you obtained this value -ie., show your work) d. Write the results of each of the contrast tests in APA format below.
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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