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

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

3. 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!!!

4. 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

5. 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

6. 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

7. 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

9. 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

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

12. 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.

13. 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

14. 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)

17. 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

18. 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

19. Choosing the Appropriate Statistical Technique

20. 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.

21. 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.

22. 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.

23. 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.

24. 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.

25. 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

26. 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)

27. 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

28. 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.

29. 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.    

30. 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.

31. Scatter plot

32. Simple Linear RegressionY 1 ? `0 X

33. Ordinary Least Squares EstimationXi Yi ˆ ei Yi

34. SPSS
Analyze  Regression  Linear

35. SPSS cont’d

36. 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

37. SPSS

38. 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.

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

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

41. 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

42. SPSS

43. 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

44. SPSS cont’d

45. Physical Attractiveness
Conceptual Model +
Likelihood
to Date
Physical Attractiveness

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

47. Conceptual Model + + Perceived Intelligence Likelihood
to Date
Physical Attractiveness

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

50. 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 + ß3X1X with Y = DV X1 = IV X2 = Moderator

52. interaction significant effect on dep. var.

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

54. 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

55. Step 1

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

57. Step 2

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

59. Step 3

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