Statistics Applied in Research Studies on tests and Tests Development

Range

equal to the difference between highest and the lowest score

Range

When its value is based on extreme scores of the distribution, the resulting description of variation may be understated or overstated. Hence, solely basing the variability of data using this might be less beneficial if there are outliers.

Interquartile range

difference between Q3 and Q1

Q1 and Q3

the 25th percentile and the 75th percentile

Semi-quartile range

interquartile range divided by 2

SD

approximation of the average deviation around the mean (50%)

Variance

Measures the average squared distance of scores from the mean.

If the mean is 75 and the SD is 10, what are the possible scores of the takers if it is 1 SD below and above the mean?

65 and 85

z-score

A ______ tells you exactly how many SDs a score is from the mean. Raw distance in SD units

Score minus mean/ SD (X - Mean/SD)

Formula for Z-score

1. 34%, 13.5%, 2.35%

2. z=+2

3. 97.5

4. What is its

1. In percentile ranking, From mean to +1 SD is about how many percentage? if 2? if 3?

2. If the mean is 50 and the SD is 70, what z-score does it have?

3. What is its percentile rank?

Above (higher than 50)

A T-score of 70 indicates that the score is (above or below) average?

Statistical tools for correlation

1. Pearson R

2. Spearman Rho

3. Point Biserial

4. Biserial

5. Phi Coefficient

6. Tetrachoric

7. Kendall Tau

8. Lambada

9. Rank Biserial

1. Measures the linear relationship between two continuous variables

2. Measures the rank-order correlation between two variables (monotonic relationship, not necessarily linear).

3. Measures the relationship between a continuous variable and a true binary (dichotomous) variable.

4. Measures the relationship between a continuous variable and an artificial binary (dichotomous) variable.

5. Measures the association between two binary (dichotomous) variables. One must be true binary.

6. Measures association between two false binary (dichotomous) variables.

7. Measures the rank-order correlation between three variables (monotonic relationship, not necessarily linear).

8. A nominal measure of association showing the proportionate reduction in error (PRE) when predicting the value of one categorical variable from another.

9. When nominal data is correlated to a ranked order.

Statistical tools to know differences of data

1. Independent T-test

2. Dependent T-test

3. One-way Anova

4. Repeated Measures ANOVA

5. Two-way Anova

6. ANCOVA

7. ANOVA Mixed Design

1. two separate groups, random assignment - e.g., blood pressure of male and female grad students

2. one group, two scores - e.g., blood pressure before and after the lecture of Grad students

3. 3 or more groups, tested once - e.g., people in different socio-economic status and the differences of their salaries

4. 1 group, measured at least 3 times - e.g., measuring the focus level of board reviewers during morning, afternoon, and night sessions of review

5. 3 or more groups, tested for 2 variables - e.g., people in different socio-economic status and the differences of their salaries and their eating habits

6. used when you need to control for an additional variable which may be influencing the relationship between your independent and dependent variable

7. 2 or more groups, measured more than 3 times - e.g., Young Adults, Middle Adults, and Old Adults’ blood pressure is measured during breakfast, lunch, and dinner

Non-parametric measures

1. spearman rho

2. Mann-Whitney U

3. Wilcoxon Rank

4. Kruskal-Wallis

5. Friedman

1. Non-parametric version of pearson r (ordinal)

2. Non-parametric version of Independent samples t-test

3. Non-parametric version of Dependent samples t-test

4. Non-parametric version of one way/two way ANOVA

5. Non-parametric version of Repeated measures ANOVA

0.0 No

0.1 - 0.24 Slight

0.25 - 0.49 - Moderate

0.50 - 0.74 - Strong

0.75 - 0.99 - very strong

1.00 perfect

Recite the Correlation table