Psychology’s Statistics Statistical Methods

Statistics  The overall purpose of statistics is to make to organize and make data more meaningful.  Ex. If a friend tells you that they earned a 27 out of 30 on a history test – great…if they tell you that they earned a 27 out of 100…well that is a different story.

Two central ways of using numbers  Inferential Statistics: Are used to determine if two or more groups are essentially the same or different.  Descriptive Statistics: simple quantitative description or summary. –Batting average in baseball –Grade-point average

Describing data  We characterize the general trend or character of data using two key statistics:  1. Central tendency or general “drift” of the scores. –Mode most common score –Median middle of the distribution –Mean average score

Describing data continues  2. Variance: how diverse the scores are (how much they vary from each other).

Measures of Variation  Range: describes the spread between the high score and the low score.  Range provides a limited amount of information. Uses the two most extreme scores  Standard Deviation (SD): is a statistical measure that tells us how much scores vary around a mean score.  If scores are packed tightly around the mean, the standard deviation will be small. If scores are spread out widely on either side of the mean, the SD will be larger.

What are the important characteristics of a normal distribution?  Scores fall near the mean and very few scores fall at the extremes.  Normal distributions are not skewed  The mean, median, and mode all fall at the high point of the graph.

What are the important characteristics of a normal distribution? Continue..  In a normal distribution, 68% of the population fall within one SD of the average, and 95% fall within two SDs of the mean.  More than 99.7% fall within three SD

Frequency distribution  A list of scores placed in order from highest to lowest (or vise versa).  Info can be presented as a bar graph, bell curve, etc.  Put the scores/numerical data in order this creates a frequency distribution and that makes the raw data much more meaningful.

Benefits of using a Frequency Distribution  Shows how often each possible score actually occurred.  You can compare different groups

Graphing the Data  Graph: A drawing that depicts numerical relationships. Routinely used by psychologists.

Different types of graphs  Histogram/bar graph Draw rectangles (bars) above each score, indicating the # of times it occurred by the rectangle’s height.  Frequency Polygon/line graph Frequency of each score is indicated by a dot placed directly over the score on the horizontal axis

Measures of Central Tendency  Three primary methods of finding the center of a distribution of scores: 1.mode 2.mean 3.median  Each one has its own strengths and weaknesses.

Determining Which “average” to use/site  I want to limit the # of hours students work per week.  Mean= 9 hours per week  Mode= 6 hours per week  Median= 5 hours per week.  Official report I would say that the average number of hours worked to be 9 since this was the highest number and it would support my case.

Steps for calculating the SD  1.calculate the mean  2.determine how far each score deviates from the average.  3.square the deviation scores and add them together.  4.Take the square root of the average of the squared deviation scores.

Steps for calculating the SD continues  Remember SD tells us how clustered or spread out the individual scores are around the mean; the more spread out the less “typical” the mean is.

The difference b/w percentage and percentile rank? Comparative Statistics  Percentage: compares a score to an imaginary set of one hundred.  Ex. Student scores 83% on a test---that student would have had 83 right on a test with 100 questions.  Percentile rank: compares one score with other scores in an imaginary group of 100 individuals.  Tells you where a particular score stands in that group and how many people had equal or lower scores.

Example of percentile rank  Student scores at the 83 rd percentile, it means that score would have equaled or exceeded 83 of every 100 people who took the test.

Correlations  A relationship b/w 2 variables, in which changes in one variable are reflected in changes in the other variable.  Correlation Coefficient: a number between -1.0 and +1.0 expressing the degree of relationship b/w two variables.

Correlations continue  Positive correlation: both variables increase or decrease together. Ex. The more a person trains, the stronger he/she will become.

Correlations  Negative correlation: involves two variables that change in opposite directions. Ex. Floss more, have fewer cavities.

Correlation coefficient  Let r stand for “correlation coefficient”  r = -1, we have a perfect negative correlation. Every time one variable increases by a certain amount, the other variable would decrease by an equally certain amount.  r = +1, we have a perfect positive correlation. Every time one variable increases by a certain amount, the other variable will also increase by an equally certain amount. Similarly—decrease.

THERE IS NO CORRELATION WHATSOEVER BETWEEN TWO VARIABLES IF r =0.

Statements: +, -, no  1. Increased milk drinking occurs with increased cancer rate.  2.increased smoking produces increased lung cancer  3. Increased absences occur with decreased grades in school.  4. increased studying occurs with increased grades

Examples  5.increased listening to loud music sometimes increases and sometimes decreases hearing ability  6.city dwellers have greater cancer rates.  7. increasing education occurs with decreasing unemployment.  8. eyesight decreases as age increases.

Making Inferences with inferential statistics  Inferential statistics are used to assess whether the results of a study are reliable or whether they might be simply the result of chance

Inferential statistics  Are used to determine if two or more groups are essentially the same or different.  Gives us guidelines for deciding whether, for example, data supports our hypotheses.

Statistical significance  Example of an Inferential statistics ; A statistical statement of how likely it is that a result occurred by chance alone.  most psychologists are willing to accept up to a 5% a.k.a=P<0.05 likelihood that experiment’s results are due to chance, “luck of the draw”  95% is a result of the manipulation of the independent variable.

Three most important factors involved in inferential statistics.  1.the difference between the two groups’ means. If the means are far apart, the result is more likely to be significant.  2.the # of participants. If each group has only a few people, the results are not as likely to be significant as they would be if each group has a large # of randomly selected people in it.  3.the standard deviation of the two groups.

Review questions  Which of the following coefficients of correlation indicates the strongest relationship? a b c d. -.75

Review question  The mean and standard deviation are ________ statistics. a. Inferential b. Descriptive c. Correlational d. Case study

Review question  Significance tests tell the researcher how likely it is that the results of the study are due to________, and the results are said to be significant if this likelihood is very________. a. chance; low b. The independent variable; low c. Change; high d. The independent variable; high

Review  hypothesis: An investigator’s testable prediction about the outcome of research.  Theory: A testable explanation for a set of facts or observations. A theory is not just speculation or a guess.

Review  Operational Definition: A statement of the procedures (operations) used to define research variables. A specification of the exact procedures used to make a variable specific and measurable for research purposes.  Describes the actions or operations that will be used to measure or control a variable. ++allows anyone to replicate their observations.  If researchers re-create a study with different participants and materials and get similar results, then our confidence in the finding’s reliability grows.