COM 408 Exam 1

Population

(represented by Greek symbols like σ) ¤The collection of units (be they people, plankton, plants, cities, suicidal authors, etc.) to which we want to generalize a set of findings or a statistical model.

Central Tendency:

-Attempts to answer the following questions: 1) how are most people responding? 2) What is the typical or 'average' response? -There are three major ways of measuring central tendency: the mode, the median, and the mean.

Measurement Validity

Face Validity Criterion Validity Construct Validity

Homogeneity of variance

Homoscedasticity ( homogeneity of variance) *amount of error · Variance should be the same throughout the variables. That is, the variance to be analyzed should not be concentrated on one or two levels of the independent variable.

Conceptualization

The first phase of research, which involves forming an idea about what needs to be studied

Leptokurtic

a curve that is peaked. This indicates that a large majority of responses are in a relatively small section of the x-axis. Put another way, people's responses vary less in a peaked distribution than a normal distribution. There are a large number of people at or near the typical score on the variable. A leptokurtic distribution is an indication of a homogeneous sample. That is, there are a lot of people at and around the most frequent score, and there are relatively few scores away from the 'peak.'

Continuous variable

a variable measured on an interval or ratio measurement scale

Categorical variable

a variable that can be differentiated only on the basis of type

Semantic Differential Scales

an interval measurement scale, developed by Osgood, Suci, and Tannennaum (1957), that measures the meanings people create in responses to a specific stimulus by presenting the stimulus item at the top of a list of (usually) 7-point scale representing polar opposites and asking people to choose a single point on each scale that expresses their perception of the stimulus object

Platykurtic

distributions that is flat . A flat distribution is an indication of a good deal of variation in people's responses. That is, a flat distribution is an indication of a heterogeneous sample. There is the greatest number of people at the 'peak' (such as it is), however, there are many people at either or both extremes.

Kurtosis

is the extent to which a distribution is peaked or flat.

Skew (Positive & Negative)

represents the extent to which a distribution has its 'peak' on one side or another (rather than in the middle). You determine the skew of the curve by which way the 'tail' points. Positive skew: occurs when a majority of the scores are on the lower (or negative) end of the distribution and there are relatively few scores on the upper (or positive) end. I know this seems backwards, but a positively skewed distribution has a majority of scores on the negative side. Negative skew: most of the scores are on the positive end and the tail points in the negative direction.

Operationalization

the process of determining the observable characteristics associated with a concept or variable

Type II error

¤occurs when we believe that there is no effect in the population when, in reality, there is. ¤The probability is the β-level (often .2)

Test Statistic

¨A Statistic for which the frequency of particular values is known. ¨Observed values can be used to test hypotheses. *Formula on Study guide

Deviation

¨A deviation is the difference between the mean and an actual data point. ¨Deviations can be calculated by taking each score and subtracting the mean from it: Deviation = x i - x_

Effect size (Pearson's r and #s)

¨An effect size is a standardized measure of the size of an effect: ¤Standardized = comparable across studies ¤Not (as) reliant on the sample size ¤Allows people to objectively evaluate the size of observed effect.

Null Hypothesis

¨Definition: a statement that statistical differences or relationships have occurred for no reason other than chance. ¨We use statistics to determine whether or not to accept or reject the null: NOT prove or disprove H's. ¨We focus on estimating the probability that H's are true/not true. Hence our language regarding findings is qualified and tentative.

Confidence Interval

¨Domjan et al. (1998) ¤'Conditioned' sperm release in Japanese Quail. ¨True Mean ¤15 Million sperm ¨Sample Mean ¤ 17 Million sperm ¨Interval estimate ¤12 to 22 million (contains true value) ¤16 to 18 million (misses true value) ¤CIs constructed such that 95% contain the true value.

Hypothesis Testing

¨Examines how likely differences between groups and relationships between variables occur by chance ¨When you statistically test H's, you are looking for significant findings--not necessary big or important!! ¨What is statistical significance? ¤Alpha (α) is the preset probability (p) of finding the same result in the population merely by chance. ¨Do we really test research hypotheses? ¤NO! We test the Null Hypothesis. (H0)

Remember:

¨The Sum of Squares, Variance, and Standard Deviation represent the same thing: ¤The 'Fit' of the mean to the data ¤The variability in the data ¤How well the mean represents the observed data ¤Error

Statistical Significance

¨The importance of an effect? ¤No, significance depends on probability (and is affected greatly by our sample size). ¨That the null hypothesis is false? ¤No, it is always false. ¨That the null hypothesis is true? ¤No, it is never true.

Power

¨The probability of rejecting a null hypothesis that is, in fact, false. ¨Can be used to estimate the effect size we might find that way we can guarantee we have enough power in the study to reject the null. ¨Can be used to calculate how large of a sample size we need to reject the null. Enhancing Power ¨Sampling Techniques ¤Random ¤Larger sample - Central Limits Theorem ¨Measurement ¤Interval (most powerful measurement, stats runs best on interval data) ¤Reliability and validity - measures ¨Hs ¤One-tailed H

Sum of Squared Errors

¨We could add the deviations to find out the total error. ¨Deviations cancel out because some are positive and others negative. ¨Therefore, we square each deviation. ¨If we add these squared deviations we get the Sum of Squared Errors (SS).

Normally distributed data

· Sampling Distribution · Residuals The distribution of scores being examined is fairly close to being normal. Normal distributions are mesokurtic, not skewed, and have identical mean, median, and mode.

Levene's test

· Tests if variances in different groups are the same. · Significant = Variances not equal · Non-Significant = Variances are equal Levene is the only time we want p > .05 no diiff = same amount of errors Not significant is good.

Independence

· The behavior of one participant is not influencing the behavior of any other participant. This assumption can be violated in repeated-measures designs.

Variance

•The sum of squares is a good measure of overall variability, but is dependent on the number of scores. •We calculate the average variability by dividing by the number of scores minus 1 (N-1). •This value is called the variance (s2).

Standard Deviation

•The variance has one problem: it is measured in units squared. •This isn't a very meaningful metric so we take the square root value. •This is the Standard Deviation (s).

Sample (represented by letters like s)

A smaller (but hopefully representative) collection of units from a population used to determine truths about that population

Levels of Measurement

Nominal Ordinal Interval Ratio

Type I error

Occurs when we believe that there is a genuine effect in our population, when in fact there isn't. ¤The probability is the α-level (usually .05)

The Only Equation Ever Needed

Outcome i = (Model) + error i