##### Psych 311 Unit 3

Descriptive statistics

Methods that ehlp researchers organize, summarize, and simplify the results obtained from research studies

- Organizing a set of scores into a graph or a table, calculating average score

Inferential statistics

Use information from samples to answer general questions about populations, help researchers determine when it is appropriate to generalize from a sample to a populations

Statistic

A summary value that describes a sample such as the average score of a sample

- Describe the entire set of scores in the sample

- Provide information about the corresponding summary values for the entire population

Parameter

A summary value that describes a population such as the average score for a population

Descriptive statistics techniques

- Organize the entire set of scores into a table or a graph that allows researchers to see the whole set of scores

- Compute one or two summary values (such as the average) that describe the entire group

Frequency distribution

Consists of a tabulation of the number of individuals in each category on the scale of measurement

- Shows the set of categories that make up the scale of measurement and the number of individuals with scores in each of the categories

Histogram

Shows a bar above each score and the height of the bar indicates the frequency, the bars for adjacent scores touch each other.

- Used for interval or ratio scale of measurement

Polygon

Shows a point above each score so that the height of the point indicates the frequency, straight lines connect the points and additional straight lines are drawn down to the horizontal axis at each end to complete the figure

- Used for interval or ratio scale of measurement

Bar graph

Like a histogram except that a space is left between adjacent bars

- Used for nominal or ordinal scales

Central tendency

A statistical measure that identifies a single score that defines the center of distribution, goal is to identify a value that is most typical

Mean

Arithmetic average of the data, usually obtained from an interval or ratio scale of measurement

Median

The score that divides the distribution in half, works well for nominal scales

Mode

The score with the greatest frequency

- bimodal: two distinct modes

- multimodal: more than two modes

Variability

Describes the spread of scores in a distribution, small when the scores are all clustered together

Variance

Measure variability by computing the average squared distance from the mean.

- Measure the distance from the mean for each score

- Square the distances

- Find the sum of the squared distances and divide by n-1 (degrees of freedom)

Standard deviation

The square root of the variance and provides a measure of variability by describing the average distance from the mean

- 70% within one SD

- 95% within two SD

Factorial research studies

Include two ore more independent variables

Correlation

Measures and describes the relationship between two variables

- Indicates direction of relationship

- Form of the relationship is determined by the type of correlation

- Pearson correlation (r): evaluates linear relationships

- Spearman correlation (r_{s}):
applied to ordinal data (ranks) and measures the degree to which the
relationship is consistently one-directional

- Strength of relationship is described by the numerical value of the correlation

Regression

The process of finding the linear equation (regression equation) for the straight line that provides the best fit for the data points

Linear equation

Y = bX + a

- b: slope constant

- a: y-intercept (point at which the line intersects the Y axis

- Standardized version (X and Y transformed into z-scores): z_{y}=βz_{x4}

- Average amount of error directly correlated to the value of Pearson correlation (+/-1.00 = average error is small)

- Squared value of correlation (r^{2}): describes overall
accuracy of prediction

Multiple regression

The process of finding the most accurate prediction equations with multiple predictors

Multiple regression equation

Y = b_{1}X_{1} + b_{2}X_{2 }+ a

- R^{2}: describes the proportion of the total variance of
the Y scores that is accounted for by the regression equation

Sampling error

The naturally occurring difference between a sample statistic and the corresponding population parameter

Hypothesis test

A statistical procedure that uses sample data to evaluate the credibility of a hypothesis about a population, attempts to rule out chance as a plausible explanation for the results

Null hypothesis

A statement about a population and always says that there is no relationship, specifies what the population parameter should be if nothing happened

Sample statistic

Data from the research study are used to compute the sample statistic corresponding to the parameter specified in the null hypothesis

Standard error

A measure of the average, or standard, distance between a sample statistic and the corresponding population parameter

Test statistic

A mathematical technique for comparing the sample statistic with the null hypothesis, using standard error as a baseline.

Test statistic = (sample statistic - parameter from null)/ standard error = actual difference between data and hypothesis/difference expected by chance

- 1.00 = null hypothesis true

- >1.00 = null hypothesis rejected

Alpha level (level of significance)

The maximum probability that the research result was obtained simply by chance, a smaller level means you have more confidence

- Alpha level of .01 means the test demands that there is .01 probability that the results are caused only by chance

- Can be expressed as p<.05

Statistically significant result

It is extremely unlikely that the research result was obtained simply by chance, always accompanied by an alpha level that defines the maximum probability that the result is caused only by chance.

Type I Error

Occurs when the sample data appear to show a significant effect but there is no effect in the population, occurs when an extreme sample is selected

Type II Error

Occurs when sample data do not show evidence of a significant effect when a real effect does exist in the population