Practice 10.15 Did the type of signal effect response time?

t crit (15) = +/- 2.447 t obs = -2.24 Fail to reject Ho The type of signal does not have a significant effect on response time.

New Step Should add a new page Determine if One-sample t-test Two-sample t-test If it is a dependent samples design If it is a independent samples with equal N If it is a independent samples with unequal N

Thus, there are 4 different kinds of designs Each design uses slightly different formulas You should probably make up ONE cook book page (with all 7 steps) for each type of design Will help keep you from getting confused on a test

Practice Does drinking milkshakes affect (alpha = .05) your weight? To see if milkshakes affect a persons weight you collected data from 5 sets of twins. You randomly had one twin drink water and the other twin drank milkshakes. After 3 months you weighed them.

Results Water Twin A 186 Twin B 200 Twin C 190 Twin D 162 Twin E 175 Milkshakes 195 202 196 165 183

Hypothesis Two-tailed Alternative hypothesis H1: water = milkshake Null hypothesis H0: water = milkshake

Step 2: Calculate the Critical t N = Number of pairs df = N - 1 5 - 1 = 4  = .05 t critical = 2.776

Step 3: Draw Critical Region tcrit = -2.776 tcrit = 2.776

Step 4: Calculate t observed tobs = (X - Y) / SD

(D) -9 -2 -6 -3 -8 D = -28 D2 =194 N = 6 -28 3.04 = 194 5 5 - 1

Step 4: Calculate t observed tobs = (X - Y) / SD 1.36=3.04 / 5 N = number of pairs

Step 4: Calculate t observed -4.11 = (182.6 – 188.2) / 1.36 X = 182.6 Y = 188.2 SD = 1.36

Step 5: See if tobs falls in the critical region tcrit = -2.776 tcrit = 2.776 tobs = -4.11

Step 6: Decision If tobs falls in the critical region: Reject H0, and accept H1 If tobs does not fall in the critical region: Fail to reject H0

Step 7: Put answer into words Reject H0, and accept H1 Milkshakes significantly ( = .05) affect a persons weight.

What if. . . You were asked to determine if psychology and sociology majors have significantly different class attendance (i.e., the number of days a person misses class) You would simply do a two-sample t-test two-tailed Easy!

But, what if. . . You were asked to determine if psychology, sociology, and biology majors have significantly different class attendance You can’t do a two-sample t-test You have three samples No such thing as a three sample t-test!

One-Way ANOVA ANOVA = Analysis of Variance This is a technique used to analyze the results of an experiment when you have more than two groups

Example You measure the number of days 7 psychology majors, 7 sociology majors, and 7 biology majors are absent from class You wonder if the average number of days each of these three groups was absent is significantly different from one another

Hypothesis Alternative hypothesis (H1) H1: The three population means are not all equal

Hypothesis Alternative hypothesis (H1) socio = bio

Hypothesis Alternative hypothesis (H1) socio = psych

Hypothesis Alternative hypothesis (H1) psych = bio

Hypothesis Alternative hypothesis (H1) psych = bio =  soc

Hypothesis Alternative hypothesis (H1) Notice: It does not say where this difference is at!!

Hypothesis Null hypothesis (H0) psych = socio = bio In other words, all three means are equal to one another (i.e., no difference between the means)

Results X = 3.00 X = 2.00 X = 1.00

Logic Is the same as t-tests 1) calculate a variance ratio (called an F; like t-observed) 2) Find a critical value 3) See if the the F value falls in the critical area

Between and Within Group Variability Two types of variability Between the differences between the mean scores of the three groups The more different these means are, the more variability!

Results X = 3.00 X = 2.00 X = 1.00

Between Variability S2 = .66 X = 3.00 X = 2.00 X = 1.00

Between Variability + 5 X = 3.00 X = 2.00 X = 1.00

Between Variability X = 8.00 X = 2.00 X = 1.00

Between Variability S2 = 9.55 X = 8.00 X = 2.00 X = 1.00

Between Group Variability What causes this variability to increase? 1) Effect of the variable (college major) 2) Sampling error

Between and Within Group Variability Two types of variability Within the variability of the scores within each group

Results X = 3.00 X = 2.00 X = 1.00

Within Variability S2 =.57 X = 3.00 X = 2.00 X = 1.00

Within Variability S2 =.57 S2 =1.43 S2 =.57 X = 3.00 X = 2.00 X = 1.00

Within Group Variability What causes this variability to increase? 1) Sampling error

Between and Within Group Variability Between-group variability Within-group variability

Between and Within Group Variability sampling error + effect of variable sampling error

Between and Within Group Variability sampling error + effect of variable sampling error Thus, if null hypothesis was true this would result in a value of 1.00

Between and Within Group Variability sampling error + effect of variable sampling error Thus, if null hypothesis was not true this value would be greater than 1.00