Stats exam 1

What is a hypothesis?

A proposed explanation for a phenomenon.

What should hypotheses be based on?

Prior research findings, established theoretical frameworks, widely-held ideas and beliefs, and new, thoroughly reasoned ideas.

What is a research hypothesis (Ha)?

A relational hypothesis that makes testable claims about relationships between variables.

What is a null hypothesis (H0)?

The hypothesis that states our claim does not exist.

What is the default assumption in NHST?

To retain the null hypothesis (H0).

What is preferred, a type I error or a type II error?

It is better to make a type II error (false negative) than a type I error (false positive).

What is the typical α-value (type I error rate) used in hypothesis testing?

Usually .05 (5%), .01 (1%), or .001 (0.1%).

What does a p-value represent?

The smallest type I error rate (α) that would allow us to reject the null hypothesis.

If a p-value is less than 0.05, what action should be taken?

Reject the null hypothesis.

What does an effect size indicate?

The strength of the relationship observed in the hypothesis test.

How does sample size affect the type II error rate (β)?

A larger sample size results in a smaller β-value.

What is the relationship between the null hypothesis and research hypothesis?

Every research hypothesis (Ha) creates a corresponding null hypothesis (H0) that claims the relationship does not exist.

What is the importance of effect size in hypothesis testing?

It helps to understand how large the difference is between the observed data and the null hypothesis.

What is the significance of setting an appropriate α-value?

It helps to minimize the likelihood of making a type I error.

What is the implication of retaining the null hypothesis?

It suggests that there is not enough evidence to support the research hypothesis.

What is the relationship between statistical power and sample size?

A larger sample size increases statistical power, making it easier to detect true relationships.

What is the first step in the research process?

Conceptualize: We figure out what we are researching.

What does operationalizing a concept involve?

Deciding how to measure our concepts.

What is meant by analyzing data in research?

Applying statistics to quantitative data and coding qualitative data.

What does interpreting data involve?

Determining what our analysis tells us about the concepts we chose to research.

What is the final step in the research process?

Reporting: We tell others what we have found.

What is a variable?

A logical grouping of different attributes that research subjects can have.

What is a constant in research?

A characteristic that every research subject has in common.

What distinguishes discrete variables from continuous variables?

Discrete variables have categorical attributes that cannot be subdivided, while continuous variables can take any value on a number line.

What are binary variables?

Variables that have only two attributes, commonly used for basic questions.

What defines nominal variables?

Variables that have more than two attributes and are used for qualitative demographics.

What are ordinal variables?

Variables that can be rank-ordered and have more than two attributes.

What characterizes interval variables?

Variables that can be rank-ordered with consistent spacing between attributes.

What is a ratio variable?

Variables that are rank-ordered, evenly spaced, and have a true zero.

What is a unit of analysis?

The element we collect data from; the 'stuff' that makes up our sample.

What do rows in an Excel spreadsheet represent?

Rows hold research subjects; each row is a different person, place, or thing.

What do columns in an Excel spreadsheet represent?

Columns hold variables; each column is a different variable.

What is the purpose of cells in an Excel spreadsheet?

Cells hold values, representing the attribute/value a subject has for that variable.

What does the function SUM() do in Excel?

It adds a range of cells together.

What is the significance of the sample size in research?

It indicates how many subjects are included in the study, excluding header rows.

What is the purpose of sampling in statistics?

Sampling helps connect probability theory to real-world data by allowing us to infer truths about a population based on sample statistics.

What is a population in the context of statistics?

A population refers to the entire group of individuals or observations that we want to study.

What is a sample in statistics?

A sample is a subset of observations drawn from a population, used to summarize and analyze data.

What does the law of large numbers state?

The law of large numbers states that as sample size increases, sample statistics converge towards population parameters, reducing sampling error.

What happens to sampling error as sample size increases?

As sample size increases, sampling error decreases.

What is the relationship between sample size and accuracy of estimates?

Larger sample sizes lead to more accurate estimates of population parameters and narrower confidence intervals.

What is the Central Limit Theorem?

The Central Limit Theorem states that as the number of samples increases, the sampling distribution of the sample means approaches a normal distribution, regardless of the population's distribution.

What does the Central Limit Theorem imply about sample means?

The mean of the sampling distribution approaches the true population mean as the number of samples increases.

How does sample size affect the standard deviation of the sampling distribution?

The standard deviation of the sampling distribution approaches 0 as the sample size increases.

What is a confidence interval (CI)?

a range of values that is estimated to contain the true population mean.

How can the margin of error be expressed?

as a confidence interval (CI).

What is the effect of larger sample sizes on confidence intervals?

Larger sample sizes lead to narrower confidence intervals and smaller standard error of the mean.

What is an unbiased estimator in statistics?

An unbiased estimator is a statistic that, on average, equals the parameter it estimates, such as the sample mean estimating the population mean.

What is the sample standard deviation used for?

The sample standard deviation (s) is used as an estimate of the population standard deviation (σ).

What is the significance of the empirical rule in statistics?

The empirical rule helps calculate confidence intervals by stating that for a normal distribution, approximately 95% of data falls within two standard deviations of the mean.

What is the relationship between sample size and standard error of the mean (SEM)?

The standard error of the mean (SEM) decreases as sample size (n) increases, calculated as SEM = s / √n.

What is the importance of random sampling?

helps ensure that the sample is representative of the population, reducing bias in estimates.

What is the role of descriptive statistics in sampling?

Descriptive statistics summarize and describe the main features of a dataset, providing a basis for further analysis.

What are descriptive statistics?

Descriptive statistics summarize observational data.

Why are descriptive statistics important?

They provide a clear overview of a sample, answer basic descriptive questions, and inform the choice of inferential statistics.

What are the three main types of descriptive statistics?

Measures of central tendency, measures of variability, and shape of the distribution.

What do measures of central tendency describe?

They describe the central or typical value for a variable.

What is the mean?

The average value for a variable, calculated by summing all observed values and dividing by the sample size.

What is the median?

The middle observed value for a variable, calculated by sorting values and finding the middle value.

What is the mode?

The most frequently observed value for a variable, determined by inspection.

What do measures of variability describe?

They describe how spread out a variable is, also known as measures of dispersion.

What is the range?

The difference between the maximum and minimum values of a variable.

What is the interquartile range (IQR)?

The range of the middle 50% of observed values, calculated as Q3 - Q1.

What are outliers?

Values that are much higher or lower than most other observed values.

What is the standard deviation?

The typical distance of values from the mean, calculated as the square root of the variance.

What is a frequency distribution?

A table that shows how many elements in a sample have each value for a variable.

What types of variables can measures of variability be used for?

They can only be used for interval and ratio variables.

What is the limitation of the range as a measure of variability?

It can be easily biased by extreme values or outliers.

What is the usefulness of standard deviation compared to range?

Standard deviation is less vulnerable to outliers and provides a better understanding of data spread.

What is the importance of describing the shape of a distribution?

It helps answer basic descriptive questions and can be used to infer things about the population.

What is the normal distribution?

An important distribution that is always symmetric and resembles real-world random variables.

What are the parameters of a standard normal distribution?

Mean = 0, Standard deviation = 1.

What do measures of central tendency indicate?

They tell us the middle of the distribution.

What do measures of variability indicate?

They tell us the spread of the distribution.

What does skewness measure?

How symmetrical the distribution of observed values is for a variable in a sample.

What does kurtosis measure?

How tall or flat the distribution of observed values is for a variable in a sample.

What is the skewness of a normal distribution?

Skew = 0 (perfectly symmetric).

What characterizes positively skewed data?

It has a long right tail (skew > 0).

What characterizes negatively skewed data?

It has a long left tail (skew < 0).

What is the kurtosis of a normal distribution?

Kurtosis = 0.

What are leptokurtic data?

Data with kurtosis > 0, which are taller than the normal distribution.

What are platykurtic data?

Data with kurtosis < 0, which are flatter than the normal distribution.

What is a histogram?

A graph that shows the distribution of observations for a variable by dividing possible values into bins.

What does the x-axis represent in a histogram?

The value of the variable.

What does the y-axis represent in a histogram?

The frequency of observations for the value (i.e., density).

What is a boxplot?

A graph that shows the distribution of observations for a variable, serving as an alternative to the histogram.

What is a bar graph?

A graph that shows the frequency distribution of a nominal or ordinal variable.

What is the main takeaway from the summary of descriptive visualizations?

Different visualizations serve to represent data distributions effectively.

What are inferential statistics?

Inferential statistics estimate the true parameters of an entire research population based on sample statistics.

How does probability theory relate to inferential statistics?

provides the mathematical foundation for making inferences about a population from a sample.

What is the law of total probability?

The law states that the sum of the probabilities of all possible events equals 1: P(X1) + P(X2) + ... + P(XN) = 1.

What is a uniform distribution?

when all outcomes are equally likely, such as in a fair coin flip.

What is a binomial distribution?

A binomial distribution describes the number of successes in a fixed number of independent Bernoulli trials.

What does 'n' represent in a binomial distribution?

'n' represents the number of trials or observations in the experiment.

What does 'p' represent in a binomial distribution?

'p' represents the probability of success on a single trial.

What is the standard normal distribution?

The standard normal distribution has a mean (μ) of 0 and a standard deviation (σ) of 1.

What does the empirical rule state about the normal distribution?

68.3% of observations fall within ±1 standard deviation, 95.4% within ±2, and 99.7% within ±3 standard deviations from the mean.

What is the purpose of integral calculus in probability?

Integral calculus is used to calculate the area under the curve (AUC) to determine probabilities for interval or ratio variables.

What is the T-distribution?

The T-distribution is similar to the normal distribution but has heavier tails, useful for small sample sizes.

What is the chi-squared (χ²) distribution?

The χ² distribution arises from the sum of squares of normally distributed variables.