What does it mean to say that the results of an experiment are (or are not) statistically significant? The significance level,  (conventionally set to .05) The test statistic, Z The critical value of Z The decision to reject, or not reject, the null hypothesis

Numerical and Graphical Summary of Data from the 68 Girls: Mean: 8.60 sec. 6.40 sec. Variance: 27.78 19.78 S.D.: 5.27 sec. 4.45 sec. Experimental group (N=34) Control group (N=34) Violent Nonviolent 10 8 6 4 2 Mean seconds on “hurt” button

Calculating Z from the given data: Group 1: N1 = 34 M1 = 8.6 S12 = 27.78 Group 2: N2 = 34 M2 = 6.4 S22 = 19.78

Two possibilities about the populations: HO or H1: Null hypothesis HO: 1 = 2 (Exp. Condition does not increase aggression.) Alternate Hypothesis H1: 1 > 2 (Exp. Condition does increase aggression.) Experiment to decide which of these is true: 1. Obtain data from two random samples of N = 34. 2. From the data, calculate the test statistic, Z. The larger Z is, the less likely the data arose by chance from two populations that have the same mean (HO).

The parallel example of coin tossing: Null hypothesis: Coin is “fair.” p = .5 Alternate hypothesis: Coin is “loaded.” p > .5 Experiment to decide which is true: 1. Toss the coin 20 times. 2. Record X, the number of heads. [The larger X is, the less likely the data arose by chance from tossing a fair coin.] Example: Suppose X=15. The probability of getting at least 15 heads in 20 tosses of a fair coin can be theoretically calculated to be equal to only about .02. This result is therefore “statistically significant.” We conclude that the coin is indeed “loaded.”

Underlying inferential model, assuming Ho: Assume that 1 = 2 Experimental Population (1) 1 Control Population (2) 2 Populations 1 and 2 (assumed): N1 = 34 N2 = 34 Hypothetical experiment 1: Compute M1 and S12 Compute M2and S22 Calculate Z N1 = 34 N2 = 34 Compute M1 and S12 Compute M2 and S22 Calculate Z Hypothetical experiment 2: Repeat indefinitely and keep track of the values of Z.

Normal distribution of Z: Mean of Z = 0 S.D. of Z = 1 ( = .05) .05 1.86 +1.65 (critical value of Z) Mean Z

 is called the significance level. If  is set to .05... then, on the normal distribution of Z, the critical value of Z is 1.65.

Four different ways to express the statistical conclusion: 1. The obtained Z, 1.86, exceeds the critical value of 1.65. Therefore we reject HO. 2. “The results are statistically significant at the .05 level.”

3. The data indicate that the. experimental condition produces 3. The data indicate that the experimental condition produces more aggression than does the control condition (Z = 1.86, p <.05). 4. Given HO, the probability of obtaining a difference between two randomly selected groups by chance as great as was obtained (yielding Z = 1.86) is very small, i.e. is less than .05.