Lecture quiz 1 Janowsky
Sign if below
.05->or Lowe (.000)
the mean of distribution of z score is always
0 This is so because when you change each raw score to a Z score, you take the raw score minus the mean. So the mean is subtracted out of all the raw scores, making the overall mean come out to 0 Which is why when you add all z scores they come out to 0.
strength of correlation: trivial
0.1 and below (also negatives)
strength of correlation: large/strong
0.5 and above (also negatives)
the standard deviation of z score is always
1 This is because when you change each raw score to a Z score, you divide the score by one standard deviation.
Split-half reliability
A measure of reliability in which a test is split into two parts and an individual's scores on both halves are compared.
population
ENTIRE group of people to which a researcher intends the results applies to
Postive correlation
If you multiply a high Z score by a high Z score, you will always get a positive cross-product. —if you multiply a low Z score by a low Z score, you also always get a positive cross-product. This is because no matter what the variable, scores below the mean are negative Z scores, and a nega-tive multiplied by a negative gives a positive. If highs on one variable go with highs on the other, and lows on the one go with lows on the other, the cross-products of Z scores always will be positive.
Test-restest Reliability
Is determined by comparing scores earned by the same person on the same test taken at different times.
Mean
Most commonly used measure of central tendency Usually the best measure of central tendency is the ordinary average, the sum of all the scores divided by the number of scores. Used with Equal interval variables.
negative correlation
On the other hand, with a negative correlation, highs go with lows and lows with highs. In terms of Z scores, this would mean positives with negatives and negatives with positives. Multiplied out, that gives all negative cross-products. If you add all these negative cross-products together, you get a large negative number.
descriptive statistics
Psychologists use descriptive statistics to summarize and describe a group of numbers from a research study. ( What we've been learning so far) Describes the sample you collected
inferential statistics
Psychologists use inferential statistics to draw conclu-sions and to make inferences that are based on the numbers from a research study but that go beyond the numbers. For example, inferential statistics allow researchers to make inferences about a large group of individuals based on a research study in which a much smaller number of individuals took part Makes inferences about the population based on your sample
Correlation in Research Articles
Scatter diagrams are occasionally included in research articles, most commonly when there are relatively small numbers of individuals involved, such as in many perception and neuroscience studies. But sometimes they are included in larger studies, Correlation coefficients are very commonly reported in research articles. positive correlation (r=.51). (r(n-2)=.92, p<.05 Tables of correlations are common when several variables are involved.
validity
The ability of a test to measure what it is intended to measure
standard deviation
The most widely used number to describe the spread of a group of scores. how much the data varies from the mean (square root of the variance) Approx the average amount that scores in a distribution vary from the mean.
central tendency
Three measures: mean, median, mode of a group of scores (a distribution) refers to the middle of the group of scores. Typical or most representative value of a group of scores.
standard error of estimate
What you use to calculate confidence intervals
Logic of Figuring the Linear Correlation
Z scores are so useful when figuring the exact correlation. if you multiply a score on one variable by a score on the other variable, which is called a cross-product
bimodal dis-tribution.
a distribution has two fairly equal high points,
equal-interval variable (level) ( numeric variable) {table 1-2}
a variable in which the numbers stand for approximately equal amounts of what is being measured. For example, grade point average (GPA) is a roughly equal-interval variable , since the difference b e t w e e n a GPA of 2.5 and 2.8 means about as much as the difference between a GPA of 3.0 and 3.3 (each is a difference of 0.3 of a GPA).
criterion variable
a variable that is predicted in formulas the predictor variable is usually labeled X, and the criterion variable is usually labeled Y.
Discriminant Validity
an empirical test of the extent to which a measure does not associate strongly with measures of other, theoretically different constructs ( loneliness and weight)
Convergent validity
an empirical test of the extent to which a measure is associated with other measures of a theoretically similar construct (Both test for loneliness, related)
ratio scale ( equal-interval variable) {table 1-2}
an equal-interval variable is measured on a ratio scale if it has an absolute zero point, meaning that the value of zero on the variable indicates a complete absence of the variable. For example, the number of siblings a person has is measured on a ratio scale, because a zero value means having no siblings. we can say that a person with four siblings has twice as many siblings as a person with two siblings.
why are normal curves natural?
because everything is random and the results spread each other out
strength of correlation: small/weak
between 0.1 and 0.3 (also negatives)
strength of correlation: moderate
between 0.3 and 0.5 (also negatives)
standard deviation and variance are _____ estimators
biased
statistics
branch of mathematics that focuses on the organization, analysis, and interpretation of a group of numbers.
ruling out possible directions of causality
by conducting a true expierement true experiment, participants are randomly assigned to a particular level of a variable and then mea-sured on another variable. ex: example of this is the study in which participants were randomly assigned (say, by flipping a coin) to different numbers of exposures to a list of words, and then the number of words they could remember was measured. There was a .82 correlation between number of exposures and number of words recalled. In this situation, any causality has to be from the variable that was manipu-lated (number of exposures) to the variable that is measured (words recalled).
variable
characteristic that can have different values ex: level of stress, Height is a variable, social class is a variable,
haphazard sampling
choosing whoever is available or happens to be first on the list
correlation matrix
common way of reporting the correlation coefficients among several variables in a research article; table in which the variables are named on the top and along the side and the correlations among them are all shown
strongest way to to rule out possible directions of causality
conduct true experiments
correlation APA
correlation APA r= correlation (r(n-2)= ._ _ , p < .05 or n.s. - (italicize r, p, and n.s.)
Interpreting the Correlation Coefficient
correlation coefficient describes the linear relationship between two variables. result of dividing the sum of the products of Z scores by the number of people in the study is called the correlation coefficient. (+or -) of a correlation coefficient tells you the direction of the lin-ear correlation between two variables (a positive correlation or a negative correla-tion). correlation coefficient (r) measure of degree of linear correlation between two variables ranging from -1 (a perfect negative linear correlation) through 0 (no correlation) to +1 (a perfect positive correlation) correlation coefficient is a descriptive statistic,
reliability
degree of consistency or stability of measure across repeated measures Ability of a test to yield very similar scores for the same individual over repeated testings
2 branches of statistics
descriptive and inferential
sample statistics.
descriptive statistics, such as the mean or standard deviation, figured from the scores in a group of people studied the mean, variance & SD of the scores in a sample use ROMAN letters
APA
descriptives (M=, SD=) in ITALICS "p" and "r" are ALSO italicized NO 0 before decimals for correlation or significance
skewed distribution
distribution in which the scores pile up on one side of the middle and are spread out on the other side; distribution that is not symmetrical. Has a tail. The side with the fewer scores (the side that looks like a tail) is considered the direction of the skew. If tail is to left it is left skew
multimodal distribution
distribution with two or more high points
The Normal Curve and the Percentage of Scores Between the Mean and 1 and 2 Standard Deviations from the Mean
exactly 50% of the scores in a normal curve are below the mean, because in any symmetrical distribution half the scores are below the mean approxi-mately 34% of the scores are always between the mean and 1 standard deviation from the mean. MORE SCORES HERE Normal curve with approximate percentages of scores between the mean and 1 and 2 standard deviations above and below the mean
linear prediction rule
formula for making predictions; that is, formula for predicting a person's score on a criterion variable based on the person's score on one or more predictor variables. ex: predicting someones gpa based on SAT
symmetrical distribution
frequency distribution in which all values have approximately the same frequency. (if you fold the graph of a symmetrical distribution in half, the two halves look the same)
Theory
is a general principle or set of principles about a class of events used to explain an important psychological process. Used to explain phenomena, predict new information, allow scientist to use logical deductive reasoning to formulate testable hypothesis
hypoth-esis
is a prediction intended to be tested in a research study.
rank-order variable aka ordinal (level) ( numeric variable) {table 1-2}
is a variable in which the numbers stand only for relative ranking. A student's standing in his or her graduating class is an example. The amount of difference in underlying GPA between being second and third in class standing could be very unlike the amount of difference between being eighth and ninth. doesn't tell you the exact difference in amount of what is being measured
z score
is the number of standard deviations the actual score is above or below the mean. If the actual score is above the mean, the Z score is positive. If the actual score is below the mean, the Z score is negative. Used mean and SD to find z score. example, Jerome has a score of 5, which is 1.60 units above the mean of 3.40. One standard deviation is 1.47 units; so Jerome's score is a little more than 1 sd above the mean
inductive reasoning
look for a trend or pattern then generalize it (specific->general)
types of causality and three directions of causality
means: what is causing what x causes y, y causes x, and 3rd possibility causing both ex: activités and martial satisfaction 1. doing activities together can make the couple more satisfied 2. People who are more satisfied choose more exciting activities 3. Or some other variable like having less stress at work makes more people happy in their marriage and gives them more time and energy to do activities
random selec-tion (sampling)
method for select-ing a sample that uses truly random procedures (usually meaning that each person in the population has an equal chance of being selected);
Median
middle score when all the scores in the distribution are in order. Sometimes median is better than the mean when there are extreme numbers that affect the mean but not the median.
central tendency in research articles
mode, median and variance are rarely reported in articles Mean and SD are common in articles tables and text. Page 56
Mode
most common single value in a distribution. In a perfectly symmetrical unimodal distribution, the mode is the same as the mean. When mean and mode are not the same the mode is not a good a good way to describe central tendency, bc does not reflect many aspects of distribution. Usual way for describing central tendency for a nominal variable: like how is part of the most religions.Used in nominal variables. Used when distribution has one or more outlier, rank-order.
left skew
negatively skewed
zero correlation
no association
n.s
non significant
variance
one kind of number that tells you how spread out the scores are, around the mean. the variance is the average of each score squared difference from the mean. The more spread out a distribution is the larger the variance bc being being spread out makes the deviation scores bigger.
raw score
ordinary score (or any number in a distribution before it has been made into a Z score or otherwise transformed). z=x-m/SD the x is the raw score
Unreliability of Measurement
our measures are not perfectly accurate or or reliable. eX: Asking someone hours of sleep on a day three weeks ago and their mood the next day, It just wouldn't be accurate. There answer is prob not close to how many hours they slept. the true correlation between sleep and mood could be high, but the correlation in the particular study might be quite low, just because there is lots of "random noise" (random inaccuracy) in the scores Consider another example. Height and social power have been found in many studies to have a moderate degree of correlation. However, if someone were to do this study and measure each person's height using an elastic measur-ing tape, the correlation would be much lower.
score
particular person's value on a variable. in any variable, each person studied has a particular number or score that is his or her value on the variable. ex: your score on the stress variable might have a value of 6. Another student's score might have a value of 8.
illusory correlation
perceptions of relationships that do not really exist ex: level of happiness and amount of red lights on the way to school
right skew
positively skewed
values
possible number or category that a score can have. ex: level of stress values from 0 to 10, just a number, such as 4, -81, or 367.12. A value can also be a cat-egory, such as male or female, or a psychiatric diagnosis—major depression, post-traumatic stress disorder.
Psychology is empirical ( unbiased observations)
public (published), replicable (repeatable, you can get same findings), and creates theories.
numeric variable. { table 1-2}
quantitative variables. 2 levels of measurement stress ratings example: the scores are numbers that tell you how much there is of what is being measured. In the stress ratings example, the higher the number is, the more stress there is.
two types of sampling
random sampling and haphazard sampling
Prediction in Research Articles
rare for bivariate linear prediction rules to be reported in psychology research articles; usually, simple correlations are reported. Sometimes, however, you will see regression lines from bivariate predictions. This is usually done when there is more than one group and the researcher wants to illustrate the difference in the linear pre-diction rule between the two groups. Multiple regression results are common in research articles and are often reported in tables Usually, the table lays out the regression coefficient for each predictor variable, the table may also give the correlation coefficient (r) for each predictor variable with the criterion variable.
attenu-ation.
reduction in a correlation due to unreliability of measures. ex: sleep study, height and social power the correlations reported in that study usually underestimate the true correlation between the variables (the correlation that would be found if there was perfect measurement)
normal distribution
requency distri-bution that follows a normal curve.
sample
scores of a PARTICULAR group being studied. Use this group to generalize for population.
unimodal distribution.
shape has only one main high point: one high "tower" in the histogram. in the stress ratings study, the most frequent value is 7, giving a graph only one very high area.
regression line
shows the relation between values of the predictor variable and the predicted values of the criterion variable. visualize a linear prediction rule as a line on a graph in which the horizontal axis is for values of the predictor variable (X) and the vertical axis is for predicted scores for the criterion variable 1Yn
Scatter diagram
shows the relationship between two variables Values of one variable are on the horizontal and other variable on the vertical axis. Postive linear correlation:dots go up to the right negative linear correlation: dots go down to the right.
restriction in range
situation in which you figure a correlation but only a limited range of possible values on one of the variables is included ;don't have full data ex: testing an entire range of grade levels on geography knowledge ( larger positive correlation ) vs only first three grades than u would see a much smaller correlation and researcher would be making a mistake by concluding that grade level is only slightly related to knowledge of geography in overall grades. = LIMITED RANGE OF GRADE LEVELS
no linear correlation.
some people highs on one variable would go with highs on the other variable (and some lows would go with lows), making positive cross-products. highs on one variable would go with lows on the other variable (and some lows would go with highs), making negative cross-products. Adding up these cross-products for all the people in the study would result in the positive cross-products and the negative cross-products cancelling each other out, giving a result of 0
normal curve
specifically and mathematically defined bell shaped frequency. distribution that is symmetrical and unimodal, approximate a precise and important mathematical distribution called the normal distribution ( normal curve). Researchers compare the actual distributions of the variables they are studying to the normal curve to check if it at least follows a normal curve.
slope
steepness of the angle of a regression line in a graph of the relation of scores on a predictor variable and predicted scores on a criterion variable; number of units the line goes up for every unit it goes across.
deductive reasoning
taking general facts and eliminating false facts (general->specific)
correlation
the association between scores
error
the difference between a person's predicted score on the criterion variable and the persons ACTUAL score on the criterion variable ( the weaker the correlation the further apart the scores will be)
population parameters.
the mean, variance, & SD of a population use GREEK letters
intercept
the point where the regression line crosses the vertical axis the intercept is the predicted score on the criterion variable (Y) when the score on the predictor variable (X) is 0.
attenuation
the reduction in a correlation due to unreliability of measures (bad research/experimental procedures)
false consensus effect
the tendency to overestimate the extent to which others share our beliefs and behaviors ( movie theatre example)
sample mean is an _______ estimator
unbiased
negative correlation
up, down or down, up
positive correlation
up, up or down, down
diving by n vs n-1
use n-1 ( ss/n-1)(SPSS will divide by n-1) when you have scores from a particular group of people ( sample) and want to estimate what the variance is for the larger group of people who these individuals represent. Infrential stats ss/n using descriptive statistics when describing the variation in a particular group.
continuous variable
variable for which, in theory, there are an infinite number of values between any two values. ex: weight, temp etc
discrete variable
variable that has specific values and that cannot have values between these specific values. ex: siblings
predictor variable
variable that is USED to predict scores on another variable in formulas the predictor variable is usually labeled X, and the criterion variable is usually labeled Y.
nominal variable aka categorical variables (level){table 1-2} ( discrete variables)
variable with values that are categories (that is, they are names rather than numbers). Also called categorical variable. nominal variable gender, the values are female and male.
