Choosing The Right Statistic SPSS Survival Manual Julie Pallant by Ali Erfanian for academic class presentation Dr. Azadeh Asgari

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To Decide Which Approach is Appropriate for Your Research Question!

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Hint: See which approach has already been used by previous researchers on your topic. Exploring Differences

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Correlation: It is used when you want to measure the strength and direction (+/-) of the relationship between two continuous variables . Exploring Differences

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A correlation has two variables involving a relationship, as if they are bend together to have conversation. A letter C is formed which is the beginning of C orrelation.

Pearson Product-moment ( r ) When? 1- two continuous variables 2- one continuous (e.g. scores) and one dichotomous (e.g. sex: M/F) variable Example: is there a relationship between age and being a smoker ? Exploring Differences

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Pearson Product-moment ( r ) -1 ≤ r ≤ +1 Positive correlation: if VAR1 ↑then VAR2 ↑ if VAR1 ↓then VAR2 ↓ Negative correlation: if VAR1 ↑then VAR2 ↓ if VAR1 ↓ then VAR2 ↑ Exploring Differences

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Coefficient of determination (r 2 ): Suppose two tests have been administered and the correlation between them turned out to be 0.736. So we can say that if a person gets a high mark on test A, it is 73% probable that he would get a high score in test B, too. If you square (r), you would get (r 2 =0.54). So you can say that 54% of the reasons for getting high scores in test A and B are the same. Exploring Differences

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Spearman rank order correlation (rho) When? 1- At times the variables are ordinal or ranked 2- At times your data does not meet the criteria for (r) Example: is there a relationship between age and optimism scores ? Exploring Differences

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One-tailed Vs Two-tailed Exploring Differences

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One-tailed Vs Two-tailed Exploring Differences

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Partial Correlation : It is like (r) except that it allows you to control (remove) for an additional (unwanted) variable. Exploring Differences

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Partial Correlation : Example: Explore the relationship between motivation and final exam scores, while controlling for the low temperature of the exam site . Exploring Differences

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Multiple Regression: It is used when you want to explore the predictive ability of a set of continuous independent variables on one continuous dependent measure Exploring Differences

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Multiple Regression: a set of continuous independent variables on one continuous dependant measure . Exploring Differences

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A Multiple Regression has many variables involving a relationship, as if they are bend together to have conversation. A letter M is formed which is the beginning of M ultiple regression.

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Multiple Regression: How well a set of variables are able to predict a particular outcome Which variable in a set of variables is the best predictor of an outcome After controlling an effective variable, are the others able to predict the outcome Exploring Differences

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Multiple Regression: STANDARD multiple regression : All predictors all entered simultaneously. HIERARCHICAL multiple regression: a predictor is entered and its effect is assessed. Then it will be controlled and the next is entered. STEPWISE multiple regression : SPSS chooses the order of entering the predictors into the equation. ( its use is NOT common) Exploring Differences

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Multiple Regression: Example: How much the variance in life satisfaction scores can be explained by self-esteem, perceived control and optimism? Which of these variables is the best predictor? Exploring Differences

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Factor Analysis : It is only a data reduction technique not for testing hypotheses. It takes a large set of variables and summarizes them by making few groups and assigning a set of variables into each group Exploring Differences

Positive feelings Negative feelings Instead of 20 items with 150 participants, we will have 2 items with 150 participants.:

Positive feelings Negative feelings Instead of 20 items with 150 participants, we will have 2 items with 150 participants.

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Factor Analysis : It is not suitable for small sample size (at least 15 participants) The strength of the relationship among the variables must be greater than 0.3. It means that the items should be similar enough to be assigned to a group. Exploring Differences

Look for numbers greater than 0.3 If you cannot find many, reconsider the use of factor analysis:

Factor Analysis: Two statistical measures generated by SPSS to assess factorability : Bartlett’s test of sphericity (=roundness) [should be significant p<0.05] Kaiser-Meyer- Olkin (KMO) measure of sampling adequacy[should be more than 0.6] Exploring Differences

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KMO and Bartlett's Test Kaiser-Meyer- Olkin Measure of Sampling Adequacy. .874 Bartlett's Test of Sphericity Approx . Chi-Square 3966.539 df 190 Sig . .000

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Factor Analysis: Kaiser’s Criterion (eigenvalue rule) It is used to decide on the number of factors to retain. [only those with the value of 1.0 or more will be retained] Exploring Differences

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Total Variance Explained Component Initial Eigenvalues Extraction Sums of Squared Loadings Total % of Variance Cumulative % Total % of Variance Cumulative % 1 6.250 31.249 31.249 6.250 31.249 31.249 2 3.396 16.979 48.228 3.396 16.979 48.228 3 1.223 6.113 54.341 1.223 6.113 54.341 4 1.158 5.788 60.130 1.158 5.788 60.130 5 .898 4.490 64.619 6 .785 3.926 68.546 7 .731 3.655 72.201 8 .655 3.275 75.476 9 .650 3.248 78.724 10 .601 3.004 81.728 11 .586 2.928 84.656 12 .499 2.495 87.151 13 .491 2.456 89.607 14 .393 1.964 91.571 15 .375 1.875 93.446 16 .331 1.653 95.100 17 .299 1.496 96.595 18 .283 1.414 98.010 19 .223 1.117 99.126 20 .175 .874 100.000 4 components are showing eigenvalue of 1 or more. But in this case only 2 components are considered by researcher to be more relevant.

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Factor Analysis: Scree test It is used to decide on the number of factors to retain. It plots eigenvalues and retains factors just before the elbow . Exploring Differences

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T-Test: It is used to compare the mean score of two tests, given either to: two different groups of participants (e.g. males/females): independent one group of participants at two different points of time (i.e. before & after treatment): paired Exploring Differences

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A T-Test has two mean scores intersecting with one an other to test group differences. So cross one finger over the other to make a T for T-Test

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T-Test: Example: Do Persian-speaking learners of English who receive pronunciation training on a computer improve their performance on intonation in comparison with controls? Exploring Differences

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Chi-square for goodness of fit: It is used to compare the proportion of cases from a sample with : hypothesized values, or those obtained previously from a comparison population. Example: Is the number of smokers in our research equivalent to 20% which is reported in a nationwide research? Exploring Differences

Choosing The Right Statistic:

Choosing The Right Statistic Ali Erfanian Exploring Differences

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Chi-square for independence: It is used to compare CATEGORIAL VARIABLES. Example: CAT 1: male/female CAT 2: smoker/non-smoker Is there an association between gender and smoking behavior? Exploring Differences

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One Way ANOVA: It is similar to t-test but with two or more groups for comparison of mean scores. It is called one-way because you are looking at the impact of only one independent categorical VAR (factor) on your dependent VAR (continuous). Exploring Differences

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A one-way ANOVA has at least three mean scores intersecting with one an other to test group differences. So cross one finger over the others to make an A for ANOVA .

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One Way ANOVA: ANOVA just tells you whether the difference exists or not. It doesn’t specify where the difference is, between group 1&2, 1&3or 2&3. Exploring Differences

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One Way ANOVA: Two types of one-way ANOVA: Repeated measures (same people) Between groups (independent samples) JUST LIKE T-TEST Exploring Differences

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One Way ANOVA: Example: Repeated measure: The effectiveness of three different teaching styles on students’ scores. Factor : teaching style Exploring Differences

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One Way ANOVA: Example: Independent measure: Is there a difference in optimism scores for young, middle aged and old participants?. Factor : age Exploring Differences

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Two Way ANOVA: It is similar to one-way ANOVA but with two independent VAR (factor) and one dependent VAR (continuous). Example: What is the effect of age and gender on optimism? Exploring Differences

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Two Way ANOVA: Two types of two-way ANOVA: Repeated measures (same people) Between groups (independent samples) JUST LIKE T-TEST & ONE-WAY ANOVA Exploring Differences

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MANCOVA: It is similar to ANOVA but with one, two or more independent VAR (factor) and a number of different but related dependent VAR (continuous). Example : Evaluation of the impact of an intervention on a variety of outcome measures. Exploring Differences

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MANCOVA: Example : do males and females differ in terms of overall well-being ? Are males better adjusted than females in terms of their positive and negative mood states and levels of perceived stress? Independent VAR: one categorical (sex) Dependent VAR: two or more continuous (negative affect, positive affect, perceived stress) Exploring Differences

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analysis of covariance (ANCOVA ): It is used in 1-way, 2-way or multivariate design when you want to statistically control for the possible effects of an additional confounding continuous variable (covariate). Exploring Differences

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analysis of covariance (ANCOVA ): Example : Are there differences between groups with different language backgrounds (3 groups) and different gender (2 groups) in how accurately they recognize the affect in someone’s voice with the participants’ age is statistically controlled for? Exploring Differences

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McNEMAR’S test: When you have matched or repeated measures designs with CATEGORICAL VARIABLES (e.g. pre-test/post-test) you cannot use the usual chi-square test. Instead you need to use McNEMAR’S test . VAR 1: recorded at time 1 (pre-test) VAR 2: recorded at time 2 (post-test) Exploring Differences

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McNEMAR’S test: Example: VAR 1: presence/absence (1/0) of a phenomenon in time 1 VAR 2: presence/absence (1/0) of a phenomenon in time 2 Example: VAR 1: People’s desire to vote or not to vote (1/0) in time 1 VAR 2: People’s desire to vote or not to vote (1/0) in time 2 Exploring Differences

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COCHRAN’S Q test: The McNEMAR’S test is suitable if you have only 2 time points. If you have 3 or more points, you will need to use Cochran’s Q test. Example : Time 1: pre-test Time 2: post-test Time 3: three months later Exploring Differences

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KAPPA Measure of Agreement: This is commonly used to assess inter-rater agreement or consistency of two different tests. ( e.g. newly developed test VS established test). Exploring Differences

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MANN-WHITNEY U test: It is used to test for differences between two independent groups (e.g. male/female) on a continuous measure. Example : Do males and females differ in terms of their levels of self-esteem? Do males have higher levels of self-esteem than females ? Exploring Differences

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WILCOXON SIGNED RANK test : It is used with repeated measures , e.g. when the participants are measured on two times or under two different conditions. Its difference with t-test is that in t-test the means are compared but in Wilcoxon the scores are converted into ranks and then compared at times 1 & 2. Exploring Differences

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KRUSKAL-WALLIS test: It is like Mann-Whitney U test but the groups are three or more. Example : Is there a difference in optimism levels across three age levels of (18-29, 30-44, 45+)? Exploring Differences

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FRIEDMAN test: It is used when you take the same sample of participants or cases and you measure them at three or more points in time or under three different conditions. Difference with COCHRAN’S Q test: COCHRAN’S Q test has categorical variables. Exploring Differences

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FRIEDMAN test: Example : Is there a change in Fear of Statistics Test scores across three time periods? Exploring Differences

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