Chapter 7: Summarizing and Interpreting Data

What are the two main types of statistics?

Descriptive statistics (describing your data set) and Inferential statistics (generalizing your data set to describe a population)

What is a distribution?

A set of scores

What are the three main categories of descriptive statistics?

Central tendency, Variability, and Graphs or tables showing these

What are the three basic measures of central tendency?

Mean (average of the distribution), Median (middle number), and Mode (most common value)

How is the mean calculated?

By adding together all the values in the distribution and dividing by the number of values

What is the median and how is it found?

The median is the middle number of the distribution. Half of the numbers are above it and half are below. If there's an even number of values, take the average of the middle two values

What is the mode?

The most common value in the distribution—the value that occurs most often

When should you use mean, median, or mode?

Mean is most commonly reported but can be affected by extreme scores. Median is reported when distribution has several outliers. Mode is reported when distribution includes frequencies of responses

What is variability in statistics?

How different values in a distribution are from one another. Low variability means most values cluster together; high variability means values are spread out

What are the four measures of variability?

Range (highest score minus lowest score), Standard deviation (average difference between scores and the mean), Variance (standard deviation squared), and Z score (number of standard deviations a raw score is from the mean)

What are degrees of freedom?

How many random numbers can be selected in a sample before there is a number that must be selected to meet a mean value. Calculated as n - 1

What are the steps to calculate standard deviation?

1. Find the mean,

2. Calculate difference between each value and mean,

3. Square the differences,

4. Sum the squared differences,

5. Divide by (n-1) for sample or (n) for population to get variance,

6. Take the square root

What are the main types of graphs used in descriptive statistics?

Frequency distribution/histogram (binned data showing how often each score appears), Bar graph (categorical variables with means), Line graph (numerical predictor with continuous mean scores), and Scatterplot (relationship between two variables using dots)

What is the distribution of sample means?

The distribution of all possible sample means for all possible samples from a population

What are the two types of hypotheses and how are they represented?

Scientific/alternative hypothesis (H1) states that a relationship between IV and DV does exist. Null hypothesis (H0) states that a relationship does not exist

What is the difference between one-tailed and two-tailed hypotheses?

Two-tailed hypothesis considers both directions of a difference. One-tailed (directional) hypothesis considers which direction a hypothesis goes (Does the DV increase or decrease)

What is a confidence interval?

A range of values that the population mean will fall into for a certain percentage of samples. It is converted to a z score (e.g., 95% CI corresponds to a Z score of 1.96)

What is the formula for calculating a confidence interval?

CI = X̄ ± (Z × (s/√n)), where X̄ is sample mean, Z is the z score for the confidence level, s is standard deviation, and n is sample size

What is the alpha level and what is it typically set to?

The alpha level (α) is the threshold for statistical significance, usually set to 0.05 or 5%

What is the critical region?

The most extreme portion of a distribution of statistical values for the null hypothesis determined by the alpha level (typically 5%)

What is a p value and when is a result statistically significant?

The p value is the probability of obtaining that statistic in a distribution corresponding to the null hypothesis (probability of getting the observed result by random chance). A result is statistically significant when p value is less than the alpha level

When should you fail to reject the null hypothesis?

Fail to reject the null hypothesis when the p value is greater than the alpha level, indicating the result is not statistically significant

What is a Type I error?

A false positive—rejecting the null hypothesis when it is actually true. The chance is determined when the alpha level is chosen (typically 5%)

What is a Type II error?

A false negative—failing to reject the null hypothesis when it is actually false. Can be influenced by alpha level and sample size. Researchers can lower chance of error by using optimal sample sizes

What is statistical power and what factors impact it?

Power is the ability to detect effects if they are present; the probability of not making a Type II error. Impacted by: sample size, effect size, alpha significance level, type of statistical test, and data variability

What is effect size?

How big the relationship is between variables