Ass. Prof. Dr. Mogeeb Mosleh RESEARCH METHODOLOGY Ass. Prof. Dr. Mogeeb Mosleh

Qualitative Data Analysis: Hypothesis Testing Ass. Prof. Dr. Mogeeb Mosleh

What is a Statistic???? Population Sample Sample Sample Population Sample Parameter: value that describes a population Statistic: a value that describes a sample PSYCH  always using samples!!!

Descriptive & Inferential Statistics Descriptive Statistics Organize Summarize Simplify Presentation of data Inferential Statistics Generalize from samples to pops Hypothesis testing Relationships among variables Describing data Make predictions

3 Types Descriptive Statistics 1. Frequency Distributions 3. Summary Stats # of Ss that fall in a particular category Describe data in just one number 2. Graphical Representations Graphs & Tables

Analyzing Quantitative Data (for brief review only) Parametric Statistics: -appropriate for interval/ratio data -generalizable to a population -assumes normal distributions Non-Parametric Statistics: -used with nominal/ordinal data -not generalizable to a population -does not assume normal distributions

Are our inferences valid?…Best we can do is to calculate probability data Are our inferences valid?…Best we can do is to calculate probability about inferences

Inferential Statistics When making comparisons btw 2 sample means there are 2 possibilities Null hypothesis is false Null hypothesis is true Reject the Null hypothesis Not reject the Null Hypothesis

Type I Error: Rejecting a True Hypothesis Type II Error: Accepting a False Hypothesis

Type I Errors, Type II Errors and Statistical Power Type I error (): the probability of rejecting the null hypothesis when it is actually true. Type II error (): the probability of failing to reject the null hypothesis given that the alternative hypothesis is actually true. Statistical power (1 - ): the probability of correctly rejecting the null hypothesis.

ALPHA the probability of making a type I error  depends on the criterion you use to accept or reject the null hypothesis = significance level (smaller you make alpha, the less likely you are to commit error) 0.05 (5 chances in 100 that the difference observed was really due to sampling error – 5% of the time a type I error will occur) Alpha (a) Difference observed is really just sampling error The prob. of type one error

When we do statistical analysis… if alpha (p value- significance level) greater than 0.05 WE ACCEPT THE NULL HYPOTHESIS is equal to or less that 0.05 we REJECT THE NULL (difference btw means)

BETA Probability of making type II error  occurs when we fail to reject the Null when we should have Beta (b) Difference observed is real Failed to reject the Null POWER: ability to reduce type II error

Effect Size: measure of the size of the difference POWER: ability to reduce type II error (1-Beta) – Power Analysis The power to find an effect if an effect is present Increase our n 2. Decrease variability 3. More precise measurements Effect Size: measure of the size of the difference between means attributed to the treatment

Choosing the Appropriate Statistical Technique

Testing Hypotheses on a Single Mean One sample t-test: statistical technique that is used to test the hypothesis that the mean of the population from which a sample is drawn is equal to a comparison standard.

Testing Hypotheses about Two Related Means Paired samples t-test: examines differences in same group before and after a treatment. The Wilcoxon signed-rank test: a non-parametric test for examining significant differences between two related samples or repeated measurements on a single sample. Used as an alternative for a paired samples t-test when the population cannot be assumed to be normally distributed.

Testing Hypotheses about Two Related Means - 2 McNemar's test: non-parametric method used on nominal data. It assesses the significance of the difference between two dependent samples when the variable of interest is dichotomous. It is used primarily in before-after studies to test for an experimental effect.

Testing Hypotheses about Two Unrelated Means Independent samples t-test: is done to see if there are any significant differences in the means for two groups in the variable of interest.

Testing Hypotheses about Several Means ANalysis Of VAriance (ANOVA) helps to examine the significant mean differences among more than two groups on an interval or ratio-scaled dependent variable. Analysis of Variance, or ANOVA, is testing the difference in the means among 3 or more different samples. One-way ANOVA Assumptions: One independent variable -- categorical with two+ levels Dependent variable -- interval or ratio ANOVA is testing the ratio (F) of the mean squares between groups and within groups. Depending on the degrees of freedom, the F score will show if there is a difference in the means among all of the groups.

Regression Analysis Simple regression analysis is used in a situation where one metric independent variable is hypothesized to affect one metric dependent variable. Important for your research

Regression Regression is used to model, calculate, and predict the pattern of a linear relationship among two or more variables. There are two types of regression -- simple & multiple a. Assumptions Note: Variables should be approximately normally distributed. If not, recode and use non-parametric measures. Dependent Variable: at least interval (can use ordinal if using summated scale) Independent Variable: should be interval. Independent variables should be independent of each other, not related in any way. You can use nominal if it is binary or 'dummy' variable (0,1)

Regression (cont.) b. Tests c. Statistics d. Limitations Overall: The null tests that the regression (estimated) line no better predicting dependent variable than the mean line Coefficients (slope "b", etc.): That the estimated coefficient equals 0 c. Statistics Overall: R-squared, F-test Coefficient: t tests d. Limitations Only addresses linear patterns Variables should be normally distributed

Correlation (parametric) Used to test the presence, strength and direction of a linear relationship among variables. Correlation is a numerical expression that signifies the relationship between two variables. Correlation allows you to explore this relationship by 'measuring the association' between the variables. Correlation is a 'measure of association' because the correlation coefficient provides the degree of the relationship between the variables. Correlation does not infer causality! Typically, you need at least interval and ratio data. However, you can run correlation with ordinal level data with 5 or more categories.

Correlation (cont.) The Correlation Coefficient : Pearson's r, the correlation coefficient, is the numeric value of the relationship between variables. The correlation coefficient is a percentage and can vary between -1 and +1. If no relationship exists, then the correlation coefficient would equal 0. Pearson's r provides an (1) estimate of the strength of the relationship and (2) an estimate of the direction of the relationship. If the correlation coefficient lies between -1 and 0, it is a negative (inverse) relationship, 0 and +1, it is a positive relationship and is 0, there is no relationship The closer the coefficient lies to -1 or +1, the stronger the relationship.    

Correlation (cont.) Coefficient of determination: provides the percentage of the variance accounted for both variables (x & y). To calculate the determination coefficient, you square the r value. In other words, if you had an r of 90, your coefficient of determination would account for just 81 percent of the variance between the variables.

Scatter plot

Simple Linear Regression Y 1 ? `0 X

Ordinary Least Squares Estimation Xi Yi ˆ ei Yi

SPSS Analyze  Regression  Linear

SPSS cont’d

Model validation Face validity: signs and magnitudes make sense Statistical validity: Model fit: R2 Model significance: F-test Parameter significance: t-test Strength of effects: beta-coefficients Discussion of multicollinearity: correlation matrix Predictive validity: how well the model predicts Out-of-sample forecast errors

SPSS

Measure of Overall Fit: R2 R2 measures the proportion of the variation in y that is explained by the variation in x. R2 = total variation – unexplained variation total variation R2 takes on any value between zero and one: R2 = 1: Perfect match between the line and the data points. R2 = 0: There is no linear relationship between x and y.

= r(Likelihood to Date, Physical Attractiveness) SPSS = r(Likelihood to Date, Physical Attractiveness)

Model Significance H1: Not H0 H0: 0 = 1 = ... = m = 0 (all parameters are zero) H1: Not H0

Model Significance H0: 0 = 1 = ... = m = 0 (all parameters are zero) H1: Not H0 Test statistic (k = # of variables excl. intercept) F = (SSReg/k) ~ Fk, n-1-k (SSe/(n – 1 – k) SSReg = explained variation by regression SSe = unexplained variation by regression

SPSS

Parameter significance Testing that a specific parameter is significant (i.e., j  0) H0: j = 0 H1: j  0 Test-statistic: t = bj/SEj ~ tn-k-1 with bj = the estimated coefficient for j SEj = the standard error of bj

SPSS cont’d

Physical Attractiveness Conceptual Model + Likelihood to Date Physical Attractiveness

Multiple Regression Analysis We use more than one (metric or non-metric) independent variable to explain variance in a (metric) dependent variable.

Conceptual Model + + Perceived Intelligence Likelihood to Date Physical Attractiveness

Conceptual Model + + + Gender Perceived Intelligence Likelihood to Date Physical Attractiveness

Moderators Moderator is qualitative (e.g., gender, race, class) or quantitative (e.g., level of reward) that affects the direction and/or strength of the relation between dependent and independent variable Analytical representation Y = ß0 + ß1X1 + ß2X2 + ß3X1X2 with Y = DV X1 = IV X2 = Moderator

interaction significant effect on dep. var.

Conceptual Model + + + + + Gender Perceived Intelligence Likelihood to Date Physical Attractiveness + + Communality of Interests Perceived Fit

Mediating/intervening variable Accounts for the relation between the independent and dependent variable Analytical representation Y = ß0 + ß1X => ß1 is significant M = ß2 + ß3X => ß3 is significant Y = ß4 + ß5X + ß6M => ß5 is not significant => ß6 is significant With Y = DV X = IV M = mediator

Step 1

significant effect on dep. var. Step 1 cont’d significant effect on dep. var.

Step 2

significant effect on mediator Step 2 cont’d significant effect on mediator

Step 3

Step 3 cont’d insignificant effect of indep. var on dep. Var. significant effect of mediator on dep. var.