Introduction to Quantitative Research Concepts

What is research?

A systematic investigation into and study of materials and sources to establish facts and reach new conclusions.

How is research compared to cooking?

Research is like cooking; it involves obtaining information and uncovering the truth, similar to how baking is a science.

What is knowledge translation (KT)?

Bridging the gap between research and clinical practice.

What are the components of the research trinity?

Design, Measurement, and Analysis.

What does research design establish?

The integrity of the research, including internal and external validity.

What does validity mean in research?

Validity refers to the truthfulness of the research findings.

What is the purpose of measurement in research?

To determine constructs and establish operational definitions for what is being measured.

What is reliability in the context of measurements?

The consistency of measurements across different instances.

What does analysis establish in research?

Conclusion validity, which reflects the truthfulness of the research findings.

What is the difference between correlation and causation?

Correlation indicates a relationship between variables, while causation implies that one variable directly affects another.

What are discrete variables?

Measured in whole units that cannot be subdivided, containing gaps, such as dichotomous and categorical variables.

What are continuous variables?

Measured in units that can be subdivided infinitely, taking on values along a continuum without gaps.

What is the role of the dependent variable in research?

It measures the outcome of interest, such as blood alcohol content or infection rates.

What is the role of the independent variable in research?

A factor that influences the outcome being measured.

What are the two general statistical approaches?

Descriptive statistics and inferential statistics.

What does descriptive statistics do?

Summarizes basic characteristics of a person or group and describes relationships between variables.

What is inferential statistics used for?

To infer results from a sample to a larger population and establish cause-and-effect relationships.

What is the significance of empirical information?

It is obtained via observation and measurement, producing data.

Why is understanding statistics important?

It helps in understanding information, ensuring accuracy and validity, and separating fact from fiction.

What is the 'holy grail' of research?

Causation, which seeks to establish definitive cause-and-effect relationships.

What is an example of a dichotomous variable?

A variable with only two possible outcomes, such as yes/no or agree/disagree.

What is an example of a continuous variable?

A variable like age, which can take on an infinite number of fractional values.

What is the dependent variable?

The value that depends on the independent variable.

Provide an example of an independent variable and its dependent variable.

Number of alcoholic drinks (IV) affects blood alcohol level (DV).

What does a sample size 'n' represent?

The sample drawn from within a group.

What does 'N' represent in statistics?

The overall sample size.

What is exploratory research?

Research that examines relationships between variables without establishing cause and effect.

What does correlation indicate in research?

It indicates a predictive relationship between two variables.

What is the Pearson r value range?

From -1.0 to 1.0, indicating direct or inverse relationships.

What is regression analysis used for?

To predict the outcomes of variable Y given variable X.

What is the formula for a simple linear regression?

Y = a⋅x + b, where 'a' is the slope and 'b' is the y-intercept.

What does 'error' mean in the context of regression analysis?

Variability in predictions; it does not imply a mistake.

What is descriptive statistics?

Statistics that describe characteristics of a sample.

What is inferential statistics?

Statistics that relate data from a sample to a larger population.

What is central tendency?

A measure that summarizes the location of a distribution on a variable.

What are the three measures of central tendency?

Mode (most frequent score), Median (middle score), Mean (average score).

What characterizes a normal distribution?

It is symmetrical and represents the ideal distribution of scores.

What is kurtosis in statistics?

It refers to the distribution of scores relative to the mean, indicating how narrow or flat the distribution is.

What does a leptokurtic distribution indicate?

A positive kurtosis value, meaning scores are closer to the mean and the graph is more narrow.

What does a platykurtic distribution indicate?

A negative kurtosis value, meaning scores are further from the mean and the graph is more flat.

What does a positively skewed distribution indicate?

A distribution with a relatively low number of extremely high scores.

What is a bimodal distribution?

A distribution with two modes, or most frequently occurring scores.

What is the median?

The score at the 50th percentile, where 50% of scores are at or below it.

What is the significance of outliers in relation to the median?

The median is not affected by extreme outliers.

What is probability in statistics?

The likelihood that any one event will occur, given all possible outcomes.

What does 'p' represent in probability?

The probability value, expressed as a ratio or decimal.

What is a sample space in probability?

A sample space is the set of all possible outcomes of an experiment.

How many total events are in the given sample space?

There are 11 total events, including 5 vets, 3 bakeries, and 3 ice cream shops.

What is the formula for calculating the probability of an event A?

P(A) = # of examples of A / total # of sample points.

What is the probability of rolling a 3 on a single die?

P(A) = 1/6, since there is only one 3 on the die out of 6 possible outcomes.

What is the probability of rolling an even number on a single die?

P(B) = 3/6 = 1/2, since the even numbers are 2, 4, and 6.

What does the Goldilocks rule refer to in probability?

The Goldilocks rule states that a probability of 95% feels just right, as it is close to 100% but allows room for error.

What is the importance of defining the sample space completely?

To determine probability accurately, the sample space must be defined completely.

What is an example of a sample space for the English alphabet?

The sample space consists of 26 letters, from A to Z inclusive.

How does case sensitivity affect the sample space of a password?

In a case-sensitive password, the sample space includes both uppercase and lowercase letters, increasing the total number of possible outcomes.

What is the probability of event A if event A is rolling a 3?

P(A) = 1/6.

What are the possible outcomes when rolling a single die?

The possible outcomes are 1, 2, 3, 4, 5, and 6.

What is the probability of rolling an even number on a single die?

P(B) = 3/6 = 0.5.

What is the definition of probability in relation to sample points?

The probability of event A is the ratio of the number of sample points that are examples of A to the total number of sample points in the sample space.

What does the term 'standard deviation' refer to?

Standard deviation is a measure of the amount of variation or dispersion in a set of values.

What is the significance of the number of sample points in calculating probability?

The total number of sample points is crucial as it serves as the denominator in the probability calculation.

What is the probability of rolling an even number on a single die?

P(B) = 3/6 = 0.5, since the even numbers are 2, 4, and 6.

What is the formula to calculate the deviation of each event from the average?

Event number - average = deviation (in units)

What problem arises when adding together deviations from the average?

It creates the zero sum problem, where the total deviation equals 0.0, suggesting little variation from the average.

How do you calculate variance from the deviations?

Square each deviation, sum all squared deviations, then divide by the number of events (N for population, N-1 for sample).

What is the relationship between variance and standard deviation?

Standard deviation is the square root of the variance.

What does a Z-score represent?

A Z-score indicates how many standard deviations an element is from the mean.

How is a Z-score calculated?

Z-score = (X - X̄) / S, where X is the value, X̄ is the mean, and S is the standard deviation.

What does a positive Z-score indicate?

It indicates that the value is above average.

What does a negative Z-score indicate?

It indicates that the value is below average.

What is the range of a data set?

The range is the difference between the highest and lowest scores.

What is the blunder range?

The blunder range is the difference between the highest erroneous value and the lowest value, which may not make sense.

What is the purpose of the 'data analysis' tool in Excel?

It provides descriptive statistics, including standard deviation and sample variance.

What does a grouped frequency distribution show?

It displays how data is distributed across different intervals or categories.

What does it mean if a distribution is skewed in the positive direction?

It indicates that most data points are on the lower end, with a few high values skewing the mean upward.

What is the median's sensitivity to outliers?

The median is not sensitive to outliers and remains the same despite extreme values.

What is the significance of +/- 1.96 standard deviations in a normal distribution?

It captures approximately 95% of the population.

What is sampling error?

It is the difference between the sample mean and the population mean.

What happens to variability as sample size increases?

As sample size increases, variability from the mean is reduced.

What is the null hypothesis (H0)?

The null hypothesis is a statement that there is no effect or no difference, which we test against.

What is a Type 1 error?

A Type 1 error occurs when the null hypothesis is rejected when it should be accepted.

What is a Type 2 error?

A Type 2 error occurs when the null hypothesis is accepted when it should be rejected.

What is statistical power?

Statistical power is the probability that a test will correctly reject the null hypothesis.

How can statistical power be increased?

By increasing sample size, using a one-tailed test, or selecting a higher significance level.

What is the standard value for Type 1 error in this course?

5% is the standard Type 1 error rate.

What does the term 'platykurtic' refer to in statistics?

It describes a distribution that is flatter than a normal distribution, indicating less variability.

What is the significance of the area under the curve in a normal distribution?

It represents the total population, with specific areas corresponding to probabilities of scores.

What does the term 'frequency' refer to in a distribution graph?

Frequency refers to the number of occurrences of each score within the data set.

What is the formula for calculating deviation from the average for each event?

Event number - average = deviation (in units)

What is the result of adding all deviations together?

It creates the 0 sum problem, resulting in an answer that equals 0.0 something, indicating little to no variation from the average.

How do you calculate variance?

Square the deviation from each event, sum all squared deviations, and divide by the number of events (N for population, N-1 for sample).

What is the relationship between variance and standard deviation?

Standard deviation is the square root of variance.

What does a Z-score represent?

A Z-score indicates how many standard deviations an event is from the average.

How is the Z-score calculated?

Z-score = (X - X̄) / S, where X is the value, X̄ is the mean, and S is the standard deviation.

What does a positive Z-score indicate?

It indicates that the score is above average.

What does a negative Z-score indicate?

It indicates that the score is below average.

What is the blunder range?

The blunder range is calculated by subtracting the lowest score from an erroneous high score.

What does the term 'grouped frequency distribution' refer to?

It refers to a way of organizing data into groups or intervals to show frequency.

What does a positively skewed distribution indicate?

It indicates that most data points are on the low end, with a few high outliers skewing the graph.

What is the median's sensitivity to outliers?

The median is not sensitive to outliers; it remains the same regardless of extreme values.