Indep-Ss t WS1- Violent Crime - WORKSHEET new format (1) (1)

WORKSHEET : Independent-Samples t Test – Example 1 (Violent Crime) A psychologist conducted an experiment examining the effect of weapons used during violent crimes on juror sentencing. One group of participants read a scenario in which an adult male criminal used a gun as a weapon. The second group of participants read a scenario in which an adult male criminal used a knife as a weapon. The sentence term, in years, is listed in the table. Do these data indicate that using a gun in a violent crime results in a different sentence length than using a knife? Step 1. State your hypotheses. a. Is it a one-tailed or two-tailed test? Two-tailed When the prediction is that scores on the dependent variable (in this case, the duration of the prison sentence chosen by the participants) will be different in the different conditions, this indicates that you are going to conduct a two-tailed test . b. Research hypotheses H A : The length of the sentence for committing a violent crime using a gun _is different__ from length of the sentence for committing a violent crime using knife. H 0 : The length of the sentence for committing a violent crime using a gun __is___ __not___ ___different___ from length of the sentence for committing a violent crime using knife. Hypotheses should be written in the future tense because, at the time they are written, the researcher does not yet know what the result will be. c. Statistical hypotheses Replace the blank with the correct comparator (i.e., =, ≠, >, ≤, <, or ≥). Remember to choose the comparator based on the study using a two-tailed test. H A : µ gun - µ knife _ ≠, __ 0 H 0 : µ gun - µ knife _=__ 0 Whatever comparator(s) are included in the alternative hypothesis, the null hypothesis must address all the other possibilities. When the hypothesis is two-tailed, the alternative includes two comparators (out of the three that exist: <, =, and >). The other one must be included in the null hypothesis. The comparator ≠ is equivalent to saying either < or >. In other words, if something is not equal to something else, it must be either more or less than that other thing. Step 2. Set the significance level (  = .05). Determine the critical value of t. t crit = +/- 2.086

Because this is a two-tailed test, you must be sure to look at the column in the t Tables in which the Proportion in Two Tails Combined shows 0.05, which is the fourth of the six columns of p values. The degrees of freedom for this study equal (n 1 -1) + (n 2 -1); you can find the sample sizes in the tables below (n = the # of scores in each group). You can confirm your result by adding df1 + df2 from the tables below. Because this is a two-tailed test, you will indicate that the critical values are both negative and positive, which you can write in two ways. You can use the symbol ± or type +/- before the number representing the critical value. If you want to use the symbol but don’t know how to use Insert/Symbols, you can copy it from here: ± and paste it wherever it’s needed. Step 3. Compute the appropriate statistical test using the data provided in the two tables below. Note the sum of squares for each group (copied from above): SS 1 = ¿ 58.833 SS 2 = ¿ 17.500 Gun Group (X 1 ) ¯ X X − X ( X − X ) 2 5 6.833 -1.833 3.361 5 6.833 -1.833 3.361 3 6.833 -3.833 14.694 12 6.833 5.167 26.694 10 6.833 3.167 10.028 6 6.833 -0.833 0.694 ΣX = 41 SS 1 = ∑ ( X − X ) 2 = 58.833 n 1 = 6 df 1 = 5 X = 6.833 Knife Group (X 2 ) ¯ X X − X ( X − X ) 2 2 3.500 -1.500 2.250 3 3.500 -0.500 0.250 1 3.500 -2.500 6.250 6 3.500 2.500 6.250 4 3.500 0.500 0.250 5 3.500 1.500 2.250 ΣX 2 = 21 SS 2 = ∑ ( X − X ) 2 = 17.500 n 2 = 6 df 2 = 5 X = 3.500

t crit = -2.086 t obt = 2.090 t crit = 2..086 Is t obt in the critical region? no Should you reject or retain the H 0 ? retain Are your results significant or nonsignificant? nonsignificant Step 5. Report the statistical results. t (_10__) = 2.090 , p > 0.05 Notice that there is no space between the t and the open parenthesis, but there should be a space on both sides of the = symbol and of the > and < symbols. Round the obtained value of t to 2 decimal places even when that requires adding an ending 0. Italicize the symbols t (the name of the inferential test statistic) and p (for probability). Because the value of p can never be greater than 1.0, you should not put a 0 before the decimal point. Step 6. Write a complete APA-style conclusion. The length of the sentence for committing a violent crime using a gun ( M = 6.833) __is shorter than_ the length of the sentence for committing a violent crime using a knife ( M = 3.500), t (_10__) = 2.090, p > 0.05 . Put a comma after the substantive conclusion, write the statistical conclusion exactly as you did in Step 5, and put a period at the end. There should be a space on both sides of each = symbol. Round the group means to 2 decimal places even when that requires adding an ending 0. Italicize the symbol M (for mean). Write the conclusion in the past tense because, at the time it is written, you already know the result. Step 7. Compute the estimated d if it’s appropriate. If it’s not appropriate, please explain why. You don’t compute the effect size when the results are nonsignificant.

Step 8. Compute r 2 and write a conclusion for this measure of effect size if it’s appropriate. If it’s not appropriate, please explain why. You don’t compute the effect size when the results are nonsignificant.