Research Methods and Statistics (20) Statistics Applied in Research Studies on tests and Tests Development Flashcards
statistics that indicates the average or midmost score between the extreme scores in a distribution
Measures of Central Tendency
Identify the most typical or representative of entire group
Measures of Central Location
Goal of Measures of Central Tendency
the average of all the raw scores
- Equal to the sum of the observations divided by the number of observations
- Interval and ratio data (when normal distribution)
- Point of least squares
- Balance point for the distribution
- susceptible to outliers
Mean
– the middle score of the distribution
- Ordinal, Interval, Ratio
- for extreme scores, use median
- Identical for sample and population
- Also used when there has an unknown or undetermined score
- Used in “open-ended” categories (e.g., 5 or more, more than 8, at least 10)
- For ordinal data
- if the distribution is skewed for ratio/interval data, use median
Median
- most frequently occurring score in the distribution
- Bimodal Distribution: if there are two scores that occur with highest frequency
- Not commonly used
- Useful in analyses of qualitative or verbal nature
- For nominal scales, discrete variables
- Value of the mode gives an indication of the shape of the distribution as well as a measure of central tendency
Mode
statistics that describe the amount of variation in a distribution
- gives idea of how well the measure of central tendency represent the data
- large spread of values means large differences between individual scores
Measures of Spread or Variability
- equal to the difference between highest and the lowest score
- Provides a quick but gross description of the spread of scores
- When its value is based on extreme scores of the distribution, the resulting description of variation may be understated or overstated
Range
difference between Q1 and Q2
Interquartile Range
interquartile range divided by 2
Semi-Quartile Range
- approximation of the average deviation around the mean
- gives detail of how much above or below a score to the mean
- equal to the square root of the average squared deviations about the mean
- Equal to the square root of the variance
- Distance from the mean
Standard Deviation
- equal to the arithmetic mean of the squares of the differences between the scores in a distribution and their mean
- average squared deviation around the mean
Variance
Measures of Location - not linearly transformable, converged at the middle and the outer ends show large interval
expressed in terms of the percentage of persons in the standardization sample who fall below a given score
- indicates the individual’s relative position in the standardization sample
Percentile or Percentile Rank
Measures of Location -dividing points between the four quarters in the distribution
Specific point
Quartile
refers to an interval
Quarter
Measures of Location - divide into 10 equal parts
- a measure of the asymmetry of the probability distribution of a real-valued random about its mean
Decile/STEN
Correlation - - interval/ratio + interval/ratio
Pearson R
Correlation ordinal + ordinal
Spearman Rho
Correlation artificial Dichotomous + interval/ratio
Biserial
Correlation artificial Dichotomous + interval/ratio
Point Biserial
Correlation - nominal (true dic) + nominal (true/artificial dic.)
Phi Coefficient
Correlation - Art. Dichotomous + Art. Dichotomos
Tetrachoric
Correlation - 3 or more ordinal/rank
Kendall’s
Correlation -nominal + ordinal
Rank Biserial
Differences - two separate groups, random assignment
- e.g., blood pressure of male and female grad students
T-test Independent
Differences - one group, two scores
- e.g., blood pressure before and after the lecture of Grad students
T-Test Dependent
Differences - 3 or more groups, tested once
- e.g., people in different socio-economic status and the differences of their salaries
One-Way ANOVA
1 group, measured at least 3 times
- e.g., measuring the focus level of board reviewers during morning, afternoon, and night sessions of review
One-Way Repeated Measures
- 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
Two-Way ANOVA
- used when you need to control for an additional variable which may be influencing the relationship between your independent and dependent variable
ANCOVA
- 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
ANOVA Mixed Design
Non-Parametric Tests - t-test independent
Mann Whitney U Test and Wilcoxon Signed Rank Test
Non-Parametric Tests - one-way/two-way ANOVA
Kruskal-Wallis H Test
Non-Parametric Tests - ANOVA repeated measures
Friedman Test
Non-Parametric Tests - for 2 groups of nominal data
Lambda
Chi-Square - - used to measure differences and involves nominal data and only one variable with 2 or more categories
Goodness of Fit
Chi-Square - used to measure correlation and involves nominal data and two variables with two or more categories
Test of Independence
used when one wants to provide framework of prediction on the basis of one factor in order to predict the probable value of another factor
Regression
- Y = a + bX
- Used to predict the unknown value of variable Y when value of variable X is known
Linear Regression of Y on X
- X = c + dY
- Used to predict the unknown value of variable X using the known variable Y
Linear Regression of X on Y
– dichotomy in which there are only fixed possible categories
True Dichotomy
dichotomy in which there are other possibilities in a certain category
Artificial Dichotomy
