PYC3704 - Psychological Research (2021 - Semester 1 and Semester 2 - Assignment 2 Answers)

PYC3704 - Psychological Research (2021 - Semester 1 and Semester 2 - Assignment 2 Answers) Question 1 Why do we calculate a test statistic? 1. To determine whether or not we can accept that the null hypothesis is true 2. To determine how far the observed measurements deviate from what we may expect by chance 3. To get a measurement by which we can calculate the level of significance 4. To determine whether or not we can reject the alternative hypothesis Answer: Option 2 is correct. Calculating the test statistic is the first step in a process of comparing the observed data with what may be expected by chance (that is, if in fact the null hypothesis is true and any effects observed in the sample of data are due to random errors). Option 1 is not really appropriate because the emphasis is wrong here. The test statistic is calculated to determine whether the effect is large enough to reject the null hypothesis and not to try to accept it. For the same reason, Option 4 is not really correct (rejecting the alternative hypothesis would follow only as a consequence of the null hypothesis not being rejected). The level of significance is not calculated but chosen, so Option 3 is false. Question 2 When applying a statistical test, the probability of a Type I error is equal to the probability of - - - - -. 1. rejecting H0 in error 2. rejecting H1 in error 3. accepting H0 in error 4. not accepting H1 when in fact you should Answer: Option 1 is correct. Option 1 is basically a definition of a Type I error. Such an error occurs when a researcher rejects the null hypothesis when it is actually true, and should not have been rejected. The p-value is a direct reflection of the probabily of making this error. (See pp. 84 – 85 in the PYC3704 Guide). Question 3 A researcher wants to test the hypothesis that the mean depression score on a depression scale for patients diagnosed with clinical depression is greater than 120. The statistical hypothesis to be tested is: PYC3704/202 3 H0: = 120 H1: > 120 She uses a random sample of n=64 drawn from the population of diagnosed patients and finds that ¯x = 127 and s = 24. Which of the values below is the closest to the correct value of s¯x? 1. 0.37 2. 3.0 3. 0.61 4. s¯x cannot be calculated from the information that was provided Answer: Option 2 gives the correct answer. This question refers to the standard error of the mean, which is a measurement of how well a sample mean approximates a population mean (see p. 61 in the PYC3704 Guide). This can be calculated from the data which is provided by substituting the (unknown) population parameters with measurements from the sample (see p. 105 in the Guide where a similar substitution is done), as follows: Question 4 Suppose the alternative hypothesis states that µ > 60. The researcher should test H0 against H1 if the - - - - -. 1. sample mean is larger than 60 2. sample mean is smaller than 60 3. sample mean differs from 60, irrespective of the direction of the difference 4. p-value is smaller than the level of significance Answer: Option 1 is correct. This is a one-tailed test (see p. 81 in the PYC3704 Guide) where only sample means of larger than 60 are relevant. If the sample mean is calculated and a value of ¯x ≤ 60 is found, the null hypothesis can obviously not be rejected, since there in zero probability that a value of 60 or smaller is also larger than 60. (See p. 77 of the Guide for the discussion of a situation where the observed value of a sample statistic lies in the wrong direction). Question 5 When applying a t-test for the difference between the means of two independent samples, the probability of obtaining the calculated t-statistic under the null hypothesis is compared to the - - - - - to reach a decision. 1. level of significance 2. degrees of freedom 3. two-tailed probability 4. effect size Answer: The correct answer is Option 1. 4 The probability of obtaining the calculated t-statistic under the null hypothesis' refers to the p-value, and this calculated p-value is to be compared to α, the level of significance chosen as a cut-off point by the researcher. If the p-value < α, it implies that there is a low probability that any difference between the means which is observed in the sample data is due only to random factors. If this is the case, the null hypothesis can be rejected in favour of the alternative hypothesis. Question 6 A social psychologist wants to test how long people will wait before responding to cries of help from an unknown person. The psychologist wants to confirm his suspicion that people will take less time to react when they hear a female voice than when they hear a male voice. He tests this on a sample of n=15 people who are told (one at a time) to sit in a waiting room to be called for an interview. While they wait, each participant hears a call for help from a male or female voice, which is actually a recording. The dependent variable is the number of seconds that each participant waits until they go to investigate or tried to find help. The sample following sample statistics are calculated from the results: Male voice: ¯x1= 11.9 seconds; s1 = 3.5 Female voice: ¯x2 = 15.3 seconds; s2 = 4.1 Given these findings, what type of statistical test will the psychologist have to do to confirm the relevant statistical hypothesis? 1. A one-tailed statistical test 2. A two-tailed statistical test 3. A test for independent samples 4. No statistical test is necessary Answer: Option 4 is correct. The hypothesis that it will take less time to react when people hear a female voice than when they hear a male voice can be stated as follows: H0: ¯x1 = ¯x2 and H1: ¯x2 < ¯x1 The sample results however show that people take less time when the voice is male than when it is female; i.e. ¯x2 = 15.3 > ¯x1= 11.9. There is no probability that this finding can confirm the alternative hypothesis, so no further statistical testing is really necessary. (See p. 77 of the PYC3704 Guide as well as the feedback on Question 3, above). Question 7 A researcher wants to test the following hypotheses: H0: µ1 = µ2 H1: µ1 µ2 On the basis of data provided, the output from a computer program indicates that a t-value of t = 1.72 was found, with the p-value for a two-tailed test given as p = 0.056. What should the researcher do to evaluate this result at a level of significance of = 0.05? 1. Divide the p-value by 2 before comparing it with 2. Multiply the p-value by 2 before comparing it with 3. Divide by 2 before comparing p to PYC3704/202 5 4. Compare the p-value as given with Answer: The correct answer is given by Option 4. The test is non-directional or two-tailed, so the two-tailed p-value should be used without any adjustment. It is only if the test was one-tailed that an adjustment to the given (two-tailed) p-value should be made (see p. 81 in the PYC3704 Guide). Question 8 A matched-pair t test should be used when you are - - - - -. 1. testing a two-tailed hypothesis 2. comparing means on a measurement from before and after a specific event 3. comparing two variables which come from the same group 4. comparing two means on a variable where the data were drawn from the same population Answer: Option 2 is correct. A measurement from before and after a specific event (for example a therapeutic intervention) is an example of matched-pairs test for dependent variables (see pp. 117 – 118 in the PYC3704 Guide). The type of hypothesis being tested (one- or two-tailed) is not relevant to the used of matched pairs, so Option 1 is false. The reference to 'two variables which come from the same group' is not very clear, but this could imply measurements on totally different ranges of values in which case a matched-pair t test could not be used, so Option 3 is not applicable. Two means from samples from the same population) need not be dependent or matched, which eliminates Option 4.