GOVT 201: Statistics for Political Science Prof. Brian Conley Levin and Fox Elementary Statistics In Social Research Chapter 1

The Function of Statistics The Function of Statistics: When researchers use numbers -- they quantify their data at the nominal, ordinal and interval level of measurement -- they are likely to employ them as a tool of: 1) Description: Descriptive Statistics 2) Decision-Making: Inferential Statistics

The Function of Statistics: The Function of Statistics: Description When studying a topic, researchers will often analyze a large number of cases or individuals and must figure out some way of describing or summarizing the data they gather.

The Function of Statistics Exam Grades for 80 students: Raw Data (N = 80) 72 49 81 72 49 81 32 56 38 81 58 54 77 23 44 79 43 56 45 77 82 90 47 87 81 60 52 78 92 84 58 73 79 83 63 82 76 78 90 77 71 89 73 83 89 77 88 34 65 60 69 91 86 83 54 51 59 83 75 79 66 69 52 22 90 89 91 76 71 60 35 68 83 60 49 67 56 31 77 89 What can you tell me about this population?

The Function of Statistics Exam Grades for 80 students: Frequency Distribution Grades f 90-99 3 80-89 7 70-79 16 60-69 17 50-59 15 40-49 11 30-39 9 20-29 2 Totals: N = 80

The Function of Statistics Exam Grades for 80 students: Bar Graph: y axis: frequencies x axis: grades

The Function of Statistics The Function of Statistics: Description We can also find the average or mean test score by adding up the scores and dividing this sum by the number of students. Average Exam Score = 60.5

The Function of Statistics The Function of Statistics: Description Thus, so, far, statistical analysis has enabled us to: Turn raw data in group frequencies Create a bar graph of the frequencies Find the average or mean exam score In the process we able to begin to detect and describe patterns or tendencies in the distribution of exam scores.

The Function of Statistics Decision-making: Inferential Statistics We can also begin to think about going beyond mere description and to think about what inferences we can draw from the data, specifically data drawn from a sample of the population, rather than the entire population. M-W defines Inference as : “the act of passing from one proposition, statement, or judgment considered as true to another whose truth is believed to follow from that of the former.”

The Function of Statistics Decision-making: Inferential Statistics Every time a researcher tests hypotheses on a sample, they must decide whether it is accurate to generalize the findings to the population from which it was drawn. Error always results from sampling. Statistics and Generalizations: What statistics does is allow you generalize with a high degree of confidence from a sample to a population.

The Function of Statistics Decision-making: Inferential Statistics Statistics and Generalizations: Example Hypothesis: Male (cause) college students are more likely than female college students to have tried marijuana (effect). Study: Urban University with 20,000 students (50%: Male, 50%: Female) Sample: 100 Randomly Selected Students (50%: Male, 50%: Female) Each student was asked whether they had ever tried marijuana.

The Function of Statistics Decision-making: Inferential Statistics: Marijuana Study Table 1.7 Marijuana Use Male Female Have Tried It Have Not 35 65 15 85 Total: (N) 100 100 Can we generalize these findings to the entire student population?

The Function of Statistics Decision-making: Inferential Statistics: Marijuana Study How about these results? Table 1.8 Marijuana Use Male Female Have Tried It Have Not 30 70 20 80 Total: (N) 100 100 Or these? Table 1.9 Marijuana Use Male Female Have Tried It Have Not 26 74 24 76 Total: (N) 100 100

The Function of Statistics Decision-making: Inferential Statistics Statistical analysis can help us make decisions about the relationship between samples and populations. Significance: At what point does sample difference become large enough to be regarded as significant? Using various statistical tests would demonstrate that only Table 1.7 can be generalized to the population. The variation observed in Table 1.8 and 1.9 is not statistically significant. Thus, what statistics is a set of decision-making techniques that aid researchers in drawing inferences from samples to populations and, hence in testing hypotheses regarding the social world.

Marijuana Use Male Marijuana Use Male Marijuana Use Male Decision-making: Inferential Statistics: Marijuana Study Table 1.8 Difference Table 1.7 Marijuana Use Male Female Have Tried It Have Not 35 65 15 85 Total: (N) 100 100 20 Marijuana Use Male Female Have Tried It Have Not 30 70 20 80 Total: (N) 100 100 10 Table 1.8 Marijuana Use Male Female Have Tried It Have Not 26 74 24 76 Total: (N) 100 100 2