Statistics in Behavioral and Social Sciences: Measures, Distributions, and Z Scores

What are the three representative measures of a group of scores?

Mean, Median, Mode

How is the mean calculated?

Sum of the scores divided by the number of scores.

What is the formula for the mean?

M = ΣX / N, where ΣX is the sum of scores and N is the number of scores.

What is the median?

The middle score when scores are arranged from lowest to highest.

How do you find the median in an even set of scores?

Average the two middle scores.

What is the mode?

The most common single value in a distribution.

When is the median preferred over the mean?

When a few extreme scores would strongly affect the mean but not the median.

What is an outlier?

An extreme score that can make the mean unrepresentative of most scores.

What does a normal curve represent?

A distribution where the mean, median, and mode are all equal.

What is variability in statistics?

The amount of spread of the scores around the mean.

What is variance?

A measure of how spread out a set of scores are, calculated as the average of the squared differences from the mean.

What is the formula for calculating variance?

Variance = Σ(X - M)² / N, where M is the mean and N is the number of scores.

What is the difference between variance and standard deviation?

Standard deviation is the square root of the variance.

How is standard deviation calculated?

Calculate the variance and then take the square root of the variance.

What is the formula for standard deviation?

SD = √(Σ(X - M)² / (N - 1))

What is the significance of using N - 1 in variance and standard deviation calculations?

It provides an unbiased estimate of the population variance and standard deviation.

What does a positively skewed distribution indicate?

The mean is greater than the median.

What does a negatively skewed distribution indicate?

The mean is less than the median.

What is the relationship between mean, median, and mode in a perfectly symmetrical distribution?

They are all equal.

What is the mode in the following set of scores: 4, 5, 5, 6, 6, 6, 7, 8, 8, 9?

6

What is the median of the following scores: 4, 5, 5, 6, 6, 6, 7, 8, 8, 9, 9, 11?

6.5

What is the mean of the following scores: 1, 3, 3, 6, 7, 7, 8, 8, 8, 9?

6

How does the presence of outliers affect the mean?

Outliers can skew the mean, making it unrepresentative of the data.

What is the average of the two middle scores in an even set of data?

It is calculated by adding the two middle scores and dividing by 2.

What does it mean if a distribution is unimodal?

It has one peak or mode.

In a negatively skewed distribution, where is the mode located relative to the mean?

The mode is to the right of the mean.

What is the significance of the standard deviation in data analysis?

It indicates the average amount that scores differ from the mean.

What is the formula for variance?

Variance = s² = ∑(x - M)² / (N - 1)

What does standard deviation measure?

Standard deviation measures the amount of variation or dispersion of a set of values.

How is standard deviation represented mathematically?

Standard deviation is represented as SD or s.

What is the relationship between variance and standard deviation?

Standard deviation is the square root of variance.

What does a higher standard deviation indicate?

A higher standard deviation indicates more variability in the data.

What is the significance of the mean in relation to standard deviation?

The mean represents the central tendency, while standard deviation indicates how well the mean represents the data.

What does a z-score represent?

A z-score represents the number of standard deviations a score is above or below the mean.

How do you calculate a z-score?

Z-score = (X - M) / SD, where X is the raw score, M is the mean, and SD is the standard deviation.

What is the mean of the years served by mayors in the example?

The mean is 6 years.

What was the sum of the squared deviation scores in the example?

The sum of the squared deviation scores (SS) was 66.

What does it mean if the standard deviation is larger for one group compared to another?

It indicates that there is more variability in the data for that group.

What is the standard deviation for the Dean's List students?

The standard deviation for Dean's List students is 0.67.

What is the standard deviation for the Probation List students?

The standard deviation for Probation List students is 6.04.

What is the purpose of calculating variance and standard deviation in research?

To explain variability and understand differences in data sets.

What does it imply if no Probation List students watch 5 hours of TV?

It implies that the mean is less representative for Probation List students due to high variability.

What is the mean square footage of desks for governors?

The mean square footage of desks for governors is 43 square feet.

What is the mean square footage of desks for CEOs?

The mean square footage of desks for CEOs is 44 square feet.

What does a standard deviation of 12.649 for CEOs imply?

It implies a high variability in desk sizes among CEOs.

What does the term 'raw score' refer to?

A raw score is the original score before it has been converted into a z-score.

What is the minimum and maximum desk size for governors?

Minimum is 36 square feet, maximum is 52 square feet.

What is the minimum and maximum desk size for CEOs?

Minimum is 32 square feet, maximum is 60 square feet.

What does it mean if the means for two groups are similar but standard deviations differ?

It suggests that while the average is similar, the variability in one group is greater.

What is the importance of variability in behavioral and social sciences research?

It helps explain differences in behaviors and experiences among individuals.

How can z-scores be used in comparing different variables?

Z-scores allow for comparison of scores from different variables by standardizing them.

What is the formula to convert a z-score back to a raw score?

Raw Score = (Z * SD) + M.

What are the two main branches of statistics?

Descriptive statistics and Inferential statistics.

What is the purpose of descriptive statistics?

To summarize, organize, and describe data from a research study.

What does inferential statistics allow researchers to do?

Draw conclusions and make inferences based on collected data.

What is a population in the context of statistics?

The entire group of individuals or instances about whom we hope to learn.

What is a sample in statistics?

A subset of the population used to represent the whole population.

What is a variable?

A characteristic or condition that can have different values.

What is the difference between a numeric variable and a categorical variable?

Numeric variables have numerical values, while categorical variables have values that are names or categories.

What are the two types of numeric variables?

Equal-interval (e.g., GPA) and Rank-order (e.g., class standing).

What is an example of a nominal variable?

Gender or political party.

What is a frequency table?

A table displaying the pattern of frequencies over different values.

What is the first step in making a frequency table?

List each possible value from lowest to highest.

How do you calculate the percentage of scores for each value in a frequency table?

Divide the frequency of the value by the total number of scores and multiply by 100.

In the Horn-Honking Study, what was measured?

Interpersonal hostility measured as delay in seconds for cars before honking.

What is the average score for Method A in the teaching methods comparison?

76.

What is the average score for Method B in the teaching methods comparison?

71.

What is the goal of inferential statistics?

To help researchers decide between interpretations of sample data.

What does the term 'sampling error' refer to?

The possibility that the sample difference is due to chance.

What is a score in the context of statistics?

A particular person's value on a variable.

What is the significance of a 5-point difference in the teaching methods study?

It indicates a potential difference in effectiveness between the two teaching methods.

What is the definition of a value in statistics?

The possible number or category a score can have.

What is the importance of organizing data in statistics?

It helps to simplify and make sense of the data for analysis.

What does the term 'continuous variable' refer to?

A numeric variable that can take on an infinite number of values within a range.

What is the purpose of using frequency tables for categorical variables?

To analyze data in the same structured way as for numeric variables.

What is a grouped frequency table?

A frequency table that uses intervals of values to summarize data.

What is the purpose of a histogram?

To graphically represent the frequency distribution of a dataset.

What is the first step in creating a histogram?

Make a frequency table or grouped frequency table.

What does a bar graph represent?

Categorical variables with spaces between bars.

What is a unimodal distribution?

A distribution with one very high area in its frequency pattern.

What is a bimodal distribution?

A distribution with two fairly equal high points.

What is a negatively skewed distribution?

A distribution where the tail is on the left side.

What is a positively skewed distribution?

A distribution where the tail is on the right side.

What is a floor effect?

When scores pile toward the lower end of the distribution due to a lower limit.

What is a ceiling effect?

When scores pile toward the upper end of the distribution due to an upper limit.

What characterizes a normal distribution?

It is bell-shaped, unimodal, and symmetrical.

What is a heavy-tailed distribution?

A distribution with many scores in the tails, indicating more extreme values.

What is a light-tailed distribution?

A distribution with few scores in the tails, indicating fewer extreme values.

What does a histogram's bar height represent?

The frequency of each value or interval in the dataset.

What is the significance of the interval size in a histogram?

It determines the range of values grouped together in each bar.

What is the difference between extraversion and neuroticism scores in the provided exercise?

Extraversion scores are generally higher, with a concentration around the mean, while neuroticism scores are fewer and skewed towards the upper end.

What is the objective of identifying the shape of a distribution?

To understand how frequencies are spread out over various values.

What does a symmetrical distribution indicate?

An approximately equal number of scores on both sides of the distribution.