PSYC207 Class Notes Exam 2 Chapter 14 Data Set 1 2 2 2 2 2 4 4 5 6 o Sum 30 o Sample Size N 10 o Mean 30 10 3 o Median 2 Average of 2 2 o Mode 2 Variance assume population o o o o o o sum x mean 2 n in a SAMPLE it would be n 1 instead of just n variance for this set 2 4 practice calculating variance Standard Deviation square root 2 4 1 55 Standard Error o Standard deviation Square root of sample size o 1 55 10 0 49 Normal distribution mean Z score o o 68 95 99 7 rule falling within 1 2 and 3 standard deviations of the scores transformed from their raw values to a standardized metric that has a means of zero and a standard deviation of 1 allows you to interpret scores by how far they are from the mean raw score mean SD 6 3 1 55 1 94 6 as a number in the data set is above the mean the Z score is positive 1 94 reflects distance from the mean unstandardized difference between means the difference between two means in the natural units Cohen s D the difference between two means in standard deviation units M1 M2 SD pooled or of control group Cohen s D is one of the many effect size indicators strength of a relationship or difference between means correlation coefficient index indicating strength and direction of linear relationship between 2 quantitative variables 1 to 1 o negative variables moving in opposite direction o positive same direction o Pearson sum of the cross product of the z scores N o graph it o time spent studying 2 4 6 8 10 score 50 73 86 86 98 Pearson corr coef calculate it 0 943 z score raw score mean SD Pearson Sum Zx Zy n assumes linearity not a curvilinear relationship otherwise a curvilinear regression Chapter 15 Inferential Statistics sampling distribution theoretical probability distribution of the values of a statistic that would result if you selected all possible examples of a particular size from a population sampling distribution of the mean theoretical probability distribution of the means of all possible samples of a particular size from a population example finger size avg 7 cm population class of 40 sample size 10 what is the mean Repeat infinite times and plot distribution standard error the standard deviation of the sampling distribution test statistic a statistic that follows a known sampling distribution and is used for significance testing estimation branch of inf stats focus on obtaining estimates of population parameters point value estimation use of the value of a sample statistic as one s estimate of the value of a population ETC alpha level the point at which one would reject the null hypothesis and accept the alternative typically 0 05 in this case you will only incorrectly reject the null 5 of the time in other words you will only conclude 5 of the time that there is a relationship in the population when there really is not a relationship in other words 5 chance of type 1 error Independent Samples T test the significance test of the difference between 2 means that uses the t probability dsitribution critical region the area on the null hypothesis sampling distribution where the observed value of the statistic would be considered a rare event probability value p value the likelihood of an observed value of a statistic if the null hypothesis were true statistically significant conclusion that the observed finding would be very unlikely of the null were true o P value less than alpha o note you make a probability claim not an absolute claim ANOVA test o o one way analysis of variance statistical test used when you have one Analysis of Variance quantitative DV and one categorical IV two way ANOVA two independent categorical variables F variance between groups variance within groups EXAMPLE ANOVA ON SAKAI NOT IN BOOK two way ANOVA main effects interaction effects two IVs nondirectional alternative hypothesis not equal to directional alternative hypothesis or statistical power probability of rejecting the null hypothesis when it s false degrees of freedom the number of values that are free to vary used in calculating some inferential statistics hypothesis testing o o o o o o o o o o o o o if p values is less than alpha then reject the null and you have statistically significant differences if p value greater than 05 alpha fail to reject the null and there is not a statistically significant difference type 1 error null is true but you reject null claiming a difference WORST error type 2 error fail to reject the null but null is false there is a true difference