Quantitative Research Methods Chapter 3

Used to summarize data about a variable (or variables) quickly and efficiently.

Summarize or describe the distribution of a single variable.

A standardized value (always on a scale of 1.00) expressing a part of a whole.

A standardized value (always on a scale of 100) representing a part of a whole.

f / n, where f is the count within a category and n is the total count.

A table or graph that displays the frequency of different values in a dataset.

Data that can be ranked or ordered, but the difference between values isn't necessarily meaningful (e.g., categories like 'satisfied' or 'dissatisfied').

Data that can be ranked and also has meaningful differences between values (e.g., age or temperature).

The number of usable data points in a dataset, after removing missing or invalid values.

The percentage of data points that fall below or equal to a certain value in a dataset.

A ratio compares two quantities, often expressing 'for every' relationship. Ratios are expressed as a:b format or a/b. They can be scaled by multiplying both quantities by a constant value.

A rate measures the frequency or ratio of one event compared to another. It's calculated as: Rate = (actual occurrences) / (possible occurrences).

Illustrates a rate calculation using deaths and population. It represents deaths per a specific number of people, often 1000.

A ratio shows the relationship between two categories. For every 100 Canadians not angry, 532 were angry about the sponsorship scandal.

Calculated by dividing the actual number of events by the possible number of events. Commonly used to determine frequency of events like deaths in a population.

Allows direct comparisons by multiplying the ratio parts by a common factor, often to remove decimals from values.

Frequency distribution is not a measurement tool (instrument) but a summary of data category frequency by values. Instruments like rulers measure qualities.

The Index of Qualitative Variation (IQV) measures the diversity or variation within a variable. It ranges from 0.00 (no variation) to 1.00 (maximum variation). A higher IQV indicates more diversity.

The IQV reaches its maximum value of 1.00 when a variable has a perfectly even distribution, such as 50% in one category and 50% in another. This indicates the greatest possible diversity.

The IQV is 0.00 when everyone falls into the same single category or when there is no difference between categories. This indicates complete homogeneity.

The formula for calculating the IQV is: IQV = (k - 1) / (k - sum of squared percentages), where k is the number of response categories.

A higher IQV over time suggests that the distribution of a variable is becoming more diverse. This could happen due to an increase in specific categories or a more even spread across categories.

The median represents the central value in a dataset when the data is arranged in order. Exactly half of the data values fall above the median and half fall below.

If the median household income in a city is $88,000, this means that 50% of the households earn less than $88,000 and 50% earn more than $88,000.

To find the median, the data must be ordered from lowest to highest (or highest to lowest). If the number of data points is odd, the median is the middle value. If the number of data points is even, the median is the average of the two middle values.

The formula for range is R = H - L, where H is the highest score and L is the lowest score.

The range is limited because it is only based on the highest and lowest scores, and can be misleading if there are outliers.

The IQR is the range of the middle 50% of data and is calculated as Q3 - Q1, where Q3 is the third quartile and Q1 is the first quartile.

Quartiles divide a dataset into four equal parts, each representing 25% of the data.

The first quartile represents the point below which 25% of the cases fall, and above which 75% of the cases fall.

The third quartile represents the point below which 75% of the cases fall, and above which 25% of the cases fall.

The IQR is resistant to outliers because it only considers the middle 50% of the data, excluding extreme values.

The formula for calculating the mean (or average) is = / , where is the sample mean, is the sum of the scores, and is the number of cases in the sample.

The population mean represents the average of all values in a population.

The sample mean represents the average of values in a sample, which is a smaller subset of the population.

The mean, or average, is a measure of central tendency that represents the central value of a set of data.

The sum of scores refers to adding all the values in a dataset together.

The notation for the population mean is , where represents the population mean, represents the sum of scores, and represents the number of cases in the population.

The notation for the sample mean is , where represents the sample mean, represents the sum of scores, and represents the number of cases in the sample.

The sum of differences between each score in a dataset and the mean will always equal zero.

The mean is the point in a distribution where the sum of squared differences between scores and the mean is minimized.

The mean is the point that is closest to all other scores in the distribution.

The sum of the negative differences between scores and the mean will always be equal to the sum of the positive differences.

The mean is useful for summarizing the center of data and provides a point of reference for understanding variations in scores.

Add all scores in a dataset together and then divide by the number of scores.

It shows that the mean is a useful measure of central tendency, as it minimizes variability around itself.