Inferential Statistics: Interpreting data

What are inferential statistics? They are a tool used to determine whether or not there is a true relationship between variables or difference between groups They are grounded in probability theory.

Probability Theory procedures/rules used to predict events Probability of = # of specific outcomes of x event X # of all possible outcomes

Inferential Statistics True score + random error Random error will be responsible for some difference between groups/scores Inferential statistics determine if what we observe we could have observed by chance alone: random error explains any differences or relationship OR there is a difference/relationship that is unlikely due to chance

Samples and Populations Samples are a subset of a population that we hope represents the population Inferential statistics help determine how likely it is we would obtain the same result using numerous samples

What is a confidence interval? “The president’s approval rating is at 31%, + or – 3 percentage points, with a 95% confidence interval.” takes sample size into account (the bigger the sample, the more representative of the population) we are confident that if we took this poll 100 more times, 95 of those times we would obtain the same result within 3 percentage points

Null and Research Hypotheses Null hypothesis Ho: there is no difference between groups Ho: there is no relationship between variables Research hypothesis H1: there is a difference between groups H1: there is a relationship between variables

Null and Research Hypotheses Goal of research is to reject the null hypothesis and accept the research hypothesis Null hypothesis is rejected when there is a low probability that the results could be due to random error = statistical significance if we don’t find a statistically significant difference, we ‘fail to reject the null hypothesis’

Probability and Sampling Distributions What is the probability of obtaining the observed results if ONLY random error is operating? Probability required for significance is called the alpha level (e.g. .05, .01, .001) If probability is low (.05 or less), reject the null hypothesis If probability is high (over .05), fail to reject the null hypothesis

Type I and Type II Errors Type I: Made when the null hypothesis is rejected but the null hypothesis is actually true Type II: Made when the null hypothesis is accepted although in the population the research hypothesis is true

What does it mean if results are nonsignificant? could mean that there is no relationship could be a Type II error weak manipulation dependent measure not adequate other noise interfered low alpha level small sample size

Correlation Coefficient Numerical index that reflects the relationship between 2 variables Ranges from –1 to +1 Pearson product-moment correlation or Pearson’s r

Understanding a correlation Eyeballing your data .8 to 1.0 Very Strong .6 to .8 Strong .4 to .6 Moderate .2 to .4 Weak .0 to .2 Very weak

Scatterplot Illustrates the relationship between variables X on the horizontal axis Y on the vertical axis Positive correlation Data from lower left to upper right Negative correlation Data from upper right to lower left

Scatterplot for + correlation

Scatterplot for - correlation

Significance of Pearson r Correlation Coefficient Is the relationship statistically significant? Ho: r = 0 and H1: r 0

Importance of Replications Scientists attach little importance to results of a single study Detailed understanding requires numerous studies examining same variables