chapter 3 Flashcards
What is the role of statistics in psychological testing?
Summarizes data, compares individual scores, aids in decision-making for education, employment, and clinical diagnosis.
Define the Nominal Scale.
Categorizes data without any inherent order.
Provide an example of the Nominal Scale.
- Gender (Male, Female, Non-binary)
- Eye color (Blue, Brown, Green)
Define the Ordinal Scale.
Ranks data but does not specify equal intervals between ranks.
Provide an example of the Ordinal Scale.
- Class ranking (1st, 2nd, 3rd)
- Likert scale responses (Strongly Agree to Strongly Disagree)
Define the Interval Scale.
Equal intervals between values but lacks a true zero point.
Provide an example of the Interval Scale.
IQ scores.
Define the Ratio Scale.
Equal intervals and a true zero point, allowing for meaningful ratios.
Provide an example of the Ratio Scale.
Reaction time in milliseconds.
What is a frequency distribution?
Arranges test scores to show how often each score occurs.
What does a histogram represent?
Graphical representation for continuous data.
What does a bar graph represent?
Graphical representation for categorical data.
What is the Mean?
Arithmetic average calculated as ( \bar{X} = \frac{\sum X}{n} ).
Example calculation of the Mean for scores {50, 60, 70, 80, 90}.
( \bar{X} = 70 ).
How is the Median determined?
Middle score if n is odd, average of two middle scores if n is even.
What is the Mode?
The most frequent score in a dataset.
Define Range.
( \text{Range} = X_{\max} - X_{\min} ).
What is the Interquartile Range (IQR)?
( IQR = Q3 - Q1 ).
What does Standard Deviation (SD) measure?
The spread of scores around the mean.
What is the Empirical Rule related to the Normal Curve?
- 68% of scores within ±1 SD
- 95% within ±2 SD
- 99.7% within ±3 SD
What are z-Scores used for?
Allow comparisons across different distributions.
How is a z-Score calculated?
( z = \frac{X - \bar{X}}{\sigma} ).
What is a T-Score?
Converts z-scores to a scale with a mean of 50 and SD of 10.
What does Pearson’s r measure?
The strength and direction of correlation between two variables.
What is the range of Pearson’s r?
-1 to +1.
What is Skewness?
Describes the asymmetry of a distribution.
What does Positive Skew indicate?
Few high scores, tail on the right.
What does Negative Skew indicate?
Few low scores, tail on the left.
Define Kurtosis.
Describes the peak of a distribution.
What is a Leptokurtic distribution?
Tall peak.
What is a Platykurtic distribution?
Flat peak.
What is a Mesokurtic distribution?
Normal curve.
What are the key takeaways from Chapter 3?
- Scales of measurement define how data is categorized.
- Central tendency and variability describe distributions.
- The normal curve standardizes expectations for performance.
- Standard scores and correlation coefficients allow for meaningful comparisons.
What is the definition of Mean?
The average of a set of values, calculated by adding all values and dividing by N.
N represents the total number of values
What does Median refer to in a data set?
The middle value when data is arranged in order.
If there is an even number of observations, the median is the average of the two middle numbers.
What is the Mode in statistics?
The most frequent value in a data set.
A data set may have one mode, more than one mode, or no mode at all.
How is Range defined?
The difference between the largest and smallest values in a data set.
Calculated as Xmax - Xmin.
What does Variance measure?
The average of the squared differences from the Mean.
It indicates how much the values in a data set differ from the mean.
What is Standard Deviation?
The square root of the variance.
It provides a measure of the dispersion of a set of values.
What is a z-Score?
A measure of how many standard deviations an element is from the mean.
Calculated by subtracting the mean from X and dividing by the standard deviation.
What does Correlation (r) indicate?
The strength and direction of a linear relationship between two variables.
Pearson’s r ranges from -1 to 1.
What is the formula for Pearson’s r?
Computed step by step using sum of X, Y, XY, X², and Y².
It quantifies how two variables relate to each other.
What is a t-test used for?
To compare the means of two groups.
It helps determine if there is a significant difference between the groups.
Fill in the blank: To find the mean, you must _______.
Add all values, divide by N.
N is the total number of values in the data set.
Fill in the blank: To find the median, you must _______.
Arrange data, find middle score.
This ensures you accurately identify the central value.
Fill in the blank: To identify the mode, you must _______.
Identify highest frequency score.
This means finding the value that appears most often.
Fill in the blank: To calculate variance, you must _______.
Find mean, subtract from each score, square, sum, divide.
This process quantifies the variability of data.
Fill in the blank: To calculate standard deviation, you must _______.
Take square root of variance.
This gives a more interpretable measure of dispersion.
Fill in the blank: To compute a z-Score, you must _______.
Subtract mean from X, divide by SD.
This standardizes the score relative to the mean.
