Chapter 7 Summarizing and Interpreting Data Using Statistics

Chapter 7 Summarizing and Interpreting Data: Using Statistics Dawn M. Mc. Bride The Process of Research in Psychology Second Edition

Steps in the Research Process 2 Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

Statistics: Descriptive vs. Inferential l Descriptive Statistics § l Inferential Statistics § 3 techniques for summarizing and understanding data without examining every score techniques that use descriptive statistics to test hypotheses about the population (make inferences) Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

Measures of Central Tendency l Values that represents typical score in a distribution § Mean-average of the scores in a distribution. § Median-middle score in a distribution, half of the scores are above and half are below the median § 4 Mode-most common score in a distribution. .

Central Tendency 5 Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

Outliers 6 Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

Normal Distribution 7 l The distributions of many natural phenomena are at least approximately normally distributed l Quetelet: Flemish scientist, 1800’s human characteristics such as height, weight, and strength are normally distributed Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

Normal Distribution of Scores 8 Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

Variability l 9 How much scores differ from each other across the response scale (options) § In a 1 to 5 rating scale, if most participants respond with 2 to 4 -- low variability § If participants use all values 1 to 5– higher variability Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

Variability: Range l 10 The difference between the highest and lowest scores in a distribution Ø Highest score = 75 Ø Lowest Score = 25 Ø Range = ? Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

Variability: Standard Deviation (SD) l l Standard deviation (SD) § How different scores are from the sample’s Mean § The higher the SD value, the higher the variability of the scores around the mean Variance § 11 The SD 2 ---- SD squared Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

12 Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

Variability: Standard Deviation (SD) l Average difference between the scores and the mean of the distribution. Ø The sum of the differences between each score and the distribution mean = 0, therefore Ø the standard deviation= square root of M-Sc 1 2 + M-Sc 2 2 + M-Sc 32 = SD N-1 § N-1= Degrees of Freedom- number of scores that can vary in the calculation of a statistic 13 Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

Variability: Variance l The standard deviation squared Variance = SD 2 Standard deviation and variance measures are important for inferential statistical tests. 14 Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

Descriptive Statistics l. Lab 15 #20 Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

Graphs/Tables l Display frequency distribution of scores for a data set Ø how often each score or category appears in a distribution. Ø x-axis (the horizontal axis) – Response Options y-axis (the vertical axis) --frequency of each response in the distribution is Ø 16 Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

Frequency Distribution 17 Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

Graphs – Experimental Study l Bar Graph § l Line Graph § 18 Height of bar shows value of the mean for different conditions in a study Mean for each condition is graphed as a point and the points are connected in a line Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

Bar Graph 19 Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

Line Graph 20 Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

Displays of Data: Graphs l. Lab 21 #21 Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

Percentage of men and women who sought counseling for anxiety and depression (Lab 21 – Bar graph) 60 50 40 Men 30 Women 20 10 0 Anxiety 22 Depression Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

Percentage of men and women who sought counseling for anxiety and depression (Line Graph Lab 21) 60 50 40 Men 30 Women 20 10 0 Anxiety 23 Depression Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

Inferential Statistics 24 l Hypotheses l Significance Testing l Errors Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

Hypotheses l Null hypothesis § l Scientific/Alternative hypothesis § 25 predicts no effect or relationship in the population or effect in the opposite direction as the scientific hypotheses predicts an effect (cause) or relationship in the population (with or without specific direction) Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

Types of Research Questions: Correlation l Is there a relation between two constructs? § Pearson Correlation coefficient r Ø Ranges form 0 to 1 -- (r =1 identical distributions) Ø Value of r can be or positive 26 negative Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

Hypotheses: No direction specified Variables Direction • Depression and self esteem • GPA and Hours Watching TV • Math-self efficacy and math test score • Marital stress and relationship satisfaction • Size of students’ ears and IQ 27 Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

Correlations: Hypothesis Variables Direction • Depression and self esteem • GPA and Hours Watching TV • Math-self efficacy and math test score • Marital stress and relationship satisfaction • Size of students’ ears and IQ 28 Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc. + + ?

Scatter Plot: Correlations 29 Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

Types of Research Questions: Means (1/2) l Is there a difference in the mean of a construct between two or more groups l Quasi-independent variable – age § In a memory test, Mean scores were: Ø Test #1 Adults = 90 ----- Children = 62 When is a difference in means large enough to be meaningful? 30 Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

Line Graph 31 Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

Types of Research Questions: Means (2/2) l True Independent Variable § Is there a difference in the Mean # of aggressive behaviors in children who played Violent versus Non Violent Videogames? Study 1 Study 2 Mean Aggressive Play Behs. Violent VG Non-Violent VG 32 4. 3 2. 5 significant? 2. 9 2. 7 significant? Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

Bar Graph- 33 Group Means Study #1 & #2 Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

When is a difference between groups large enough to be “significant” ? l Inferential Statistics § Used to determine what can be learned about the population of interest based on the data obtained from the sample. § 34 Based on probability theory: what are the chances that we are correct to reject the null hypothesis (and by default accept the alternative hypothesis)? Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

DELETE Scientific/Alternative hypothesis l One-tailed Hypothesis – In the population, Ø l Two-Tailed Hypothesis – In the population, Ø 35 Children who watch aggressive VG will differ in the number of aggressive play behaviors than children who play non-aggressive VG Children who watch aggressive VG will display a higher number of aggressive play behaviors than children who play nonaggressive VG Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

Scientific/Alternative hypothesis l Two-Tailed § Predicts a hypothesis in either direction (a difference; a correlation) Ø 36 Hypothesis Children who watch aggressive Vs will differ in the number of aggressive play behaviors compared to children who watch non-aggressive Vs Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

Null Hypotheses (two-tailed hypotheses) l Null hypothesis § Predicts no effect: Ø 37 Children who watch aggressive Vs will not differ in the number of aggressive play behaviors than children who watch non-aggressive Vs Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

How likely it is that we will obtain the observed mean when the null hypotheses is true 38

Scientific/Alternative hypothesis l One-tailed § Predicts an effect in one direction (higher vs. lower; + vs. -) Ø 39 Hypothesis Children who watch aggressive Vs will display a higher number of aggressive play behaviors than children who watch non-aggressive Vs Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

Null Hypotheses (one-tailed hypotheses) l Null hypothesis § Predicts an effect in the opposite direction or no effect: Ø 40 children who watch aggressive Vs will display a lower number or similar number of aggressive behaviors than children who watch non- aggressive Vs. Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

Significance Testing 41 Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

Significance Testing 42 l Is there enough evidence in the data to reject the null hypothesis and accept the alternative (or scientific) hypotheses? l What are the chances of obtaining the means observed in the sample when the null hypothesis is correct (or true)? 90%, 50% 10% 5% ? ? Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

Assumptions We assume that • If we took a large number of samples (subgroups) from the population of interest • Calculated the mean for each sample (e. g. in the memory test) • Made a plot of these values, • The distribution of means would be normal. 43

Distribution of Sample Means 44 l Distribution of all possible sample means of all possible samples from a population will resemble a normal distribution l Most sample means will be close to the mean of the population Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

45 Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

Significance Testing l Alpha level § l P Value § 46 highest probably value acceptable as evidence that sample value is too extreme for null hypothesis to be true (level of risk willing to take) Actual probability given by the inferential test (Pearson correlation; T-Test) of obtaining the correlation/mean observed in study sample, when the null hypothesis is true Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

Significance Testing l Alpha Level § § l P Value § § § 47 Chosen by researcher: . 10; . 05; . 01; 001 p<. 05 -- null hypothesis is rejected Actual probability with one’s sample Obtained from inferential test Compared to Alpha level Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

Significance Testing l Critical region § 48 portion of distribution of sample means in the normal curve containing extreme (high and low) scores Ø Size is equal to alpha level Ø Location- in one tail; or both tails Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

Errors 49 Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

Errors l Type I error: reject the null hypothesis when it is true (an effect is claimed, but it does not really exist) § l 50 Alpha =. 05 --- 5% of making a Type I error Type II error: retain the null hypothesis when it is false (an effect is not claimed, but it does really exist) Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

Type I and Type II Error 51 Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

Power l l Ability of a significance test to detect and effect (difference in means, significant correlation) when one exists (optimal--80%) The following increase power § § 52 Larger alpha level Larger sample size Larger size of the effect Higher internal reliability of measurements Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

Confidence Interval l Gives an estimated range of values that will include the mean of a population (or %, correlations) with specific probability level 99% or 95%) § 53 Estimate of the mean ± Margin of Error Ø Opinion poll 82% agree smoking is harmful ± 3% ® Confidence interval 79% - 85% Ø Mean Beck Depression score women 14 ± 5 ® Confidence interval 9 --- 19 Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

Predicting Null Hypotheses 54 l Significant statistical tests provide evidence against he null hypotheses but not for it l Not possible to draw strong conclusions in the absence of a significant result l A series of studies with high levels of power (80%) that consistently support null hypotheses, would provide support for the lack of the hypothesized effect. Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.

Common Pitfalls l l l 55 Problem: Supporting the null hypothesis—students often make the error of stating that the null hypothesis is supported with a nonsignificant result. Problem: Stating that results “prove” the hypothesis is true—students sometimes make the mistake of stating that statistical results prove that an effect exists. Problem: Ignoring the power of the test—researchers sometimes do not consider the power of their tests carefully enough, concluding that a nonsignificant result can be relied on with the same certainty as a significant result. Dawn M. Mc. Bride - The Process of Research in Psychology, 2 nd Edition © 2013 SAGE Publications, Inc.