<p>BHS Name______AP PSYCH</p><p>AIM: We will not fear statistics!</p><p>There are different ways that psychologists can show data and describe it for the specific group studied. This is known as descriptive statistics.</p><p>A. One way to describe data is to show someone as being in a certain percentile. If a person is in the 74th percentile, this means 74% of students performed lower. Describe the percentiles of the following students. a. Mary i. 20th percentile Math______</p><p> ii. 58th percentile English______</p><p> iii. Which subject can we infer that Mary is better in?______Why?</p><p> b. Joe i. 85th percentile Math______</p><p> ii. 45th percentile English______</p><p> iii. Which subject can we infer that Joe is better in? ______Why?</p><p>B. MEASURES OF CENTRAL TENDANCY (a single number that represents a whole set of scores) a. 3 Ms i. MEAN</p><p> ii. MEDIAN</p><p> iii. MODE</p><p>C. Skewed distributions a. The MEAN is the ______; however, it is the MOST ______to outliers or extreme scores.</p><p>In a normal distribution, the measures of central tendency tend to fall in the middle</p><p> b. In a POSITIVE or RIGHT SKEW… the MEAN is pulled ______because the outliers or extreme scores are on the upper data points of x- axis. Yet, the bulk of the scores are on the lower data points of x-axis. If this were test data, we could conclude that, the majority did ______, and a few outliers ______</p><p> c. In a NEGATIVE or LEFT SKEW… the MEAN is pulled </p><p>______because the outliers or extreme scores are on the lower data points of x-axis. Yet, the bulk of the scores are on the upper data points of x-axis. If this were test data, we could conclude that, the majority did ______and a few outliers ______</p><p>**MEMORY TIP! The “tail” of the skewed distribution graph points to the type of skew (tail pointing the left=negative skew; tail pointing to the right=positive skew). This will help you remember what happens to the mean in skewed distributions… Typically, in these cases, the MEDIAN is more accurate reflection of group than the mean.</p><p>D. Dispersion or spread of scores (define) a. Range</p><p> b. Variance</p><p> c. Standard Deviation</p><p>1. Two classes took the same psychology test. The scores for the first period class were: 81, 85, 94, 88, 80, 77, and 90. The scores for the second period class were: 55, 105, 92, 73, 95, 95, and 80. Which group has the greater standard deviation? (I do not expect you to do any calculations)</p><p>2. IQ (intelligence quotient) scores are normally distributed with a mean of 100 and a standard deviation of 16. What percentage of people have scores above 116?</p><p>3. What statistical technique would be appropriate for a researchers to use in trying to determine how consistent intelligent scores are over time? a. coefficient; b. mean; c. median; d. range; e. standard deviation</p><p>4. When a distribution of scores is skewed, the best representation of the central tendency is the: a. Standard deviation; b. mean; c. median; d. coefficient Using the bell curve provided... 1. Examine the Weschler Adult Intelligence (top) scale scores. What is the standard deviation?______points 2. Examine the SAT Math scale scores (below). What is the standard deviation?______points 3. Which has a higher standard deviation: SAT or IQ test? What does this mean?</p><p>4. If your SCORE is 800 on the SAT Math Scale, how many standard deviations (z-scores) are you from the mean?______5. What is the SCORE one standard deviation above the mean on the Wechsler Adult Intelligence Scale?______the Z score is:______6. What is the SCORE one standard deviation below the mean on the SAT Math Scale? _____ The Z score is:___ E. The Empirical Rule or “68-95-99 Rule”</p><p>Pretend the mean is a 75% on an AP test. The standard deviation is 5. Draw what the curve might look like. Draw at least two standard deviations away from the mean.</p><p>What does a Z score of +1 equal?______What about -2______? (tells us how far away score is from the mean) What does that say about the scores of 68% of the class? They scored between _____ and ______. What about 95% of class? They scored between ______and ______What % of class scores were above 85%?______II. Inferential statistics : The researcher can INFER about the POPULATION based on what is known about the sample.</p><p>Statistics is a measure for a sample (n).</p><p>Parameter is a measure for the population (N).</p><p>Is the data for sample (n) descriptive of the population (N)? We will never know, but we make an inference. The larger the sample, the more representative, the more reliable.</p><p>F. Statistical significance  The results were not due to CHANCE  If p is LOW, .05 or .04 or .03 or .02 or .01  WE CAN REJECT NULL! The null hypothesis is what the researcher tries to disprove, reject, or nullify. **You can never 100% fully prove anything in science; you can only reject the null hypothesis, which is the opposite of the hypothesis (you can only disprove, not prove). You can’t prove anything is 100% true because you can never know if it was 100% not due to chance (never a 0% p-value) BUT if the p-value is less that .05%, you can be confident enough (statistically significant)</p><p>NULL: (H0) A new vaccine does not change the proportion of people with a fever ALTERNATIVE: (H1) A new vaccine has a LOWER proportion of people with a fever p value = .0139 -What can we conclude?</p><p>H0: The new treatment does not improve mental health H1: The new treatment does improve mental health p value = .06 What can we conclude?</p><p>5. Basketball team data is as follows – calculate the measures of central tendency and draw a frequency histogram. Does it have a positive or negative SKEW?</p><p>Jake 14 points Scott 4 points Josh 22 points Bobby 6 points Christian 19 points Grant 8 points Billy 3 points Thomas 6 points </p>