INFERENTIAL STATISTICSINFERENTIAL STATISTICS

Inferential Statistics

statistics that permit inferences on whether relationships observed in a sample are likely to occur in a larger population (Polit and Beck, 2004)

based on the laws of probability based on the assumption that the sample

was randomly selected

2 Purposes of Inferential Statistics

1. Estimating population parameter from sample data

2. Testing hypothesis about a population

Estimating Population Parameters From Sample Data

Sample Error – occurs when the sample does not accurately reflect the population

Sample Distribution – a theoretical frequency distribution that is based on an infinite number of samples

--based on mathematical formulas and logic

Statistical Inference

• The process of inferring attributes about the population based on information from a sample, using laws of probability

• 2 Types of Error in Statistical Inference A. Type I or Alpha Error - the researchers’ rejection of the null

hypothesis when it is actually true B. Type II or Beta Error - the researchers’ acceptance of a null

hypothesis that is actually false

Level of Significance

also referred as alpha level (α) is the probability of making a type I

error, or the probability of rejecting a true null hypothesis

two most frequently used significance levels are: .05 and .01

Six Steps in Tests of Significance (Gillis, 2002)

1. State the research and the null hypothesis2. Determine where the outcome will fall in the

sampling distribution if the null hypothesis is to be rejected

3. Indicate the chosen significance level to be used in the test ( usually 0.05)

4. Compute the test statistics5. Note whether the test indicates if you should accept

or reject the null hypothesis 6. Interpret the findings

Statistical Tests

an analytic tool that estimates the probability that obtained results from a sample reflect true population values

2 Broad Classes of Statistical Tests

A. Parametric Tests

B. Nonparametric Tests

Parametric Tests

characterized by three attributes: 1. they involve the estimation of a

parameter 2. they require measurements on at

least an interval scale 3. they involve several assumptions,

such as the assumption that the variables are normally distributed in the population

t - Test

• sometimes referred to as Student’s t• for testing differences in group means• used when there are 2 independent

groups (ex. male versus female), and when the sample is paired or dependent (ex. when pretreatment and post-treatment scores are compared for a single group

Analysis of Variance (ANOVA)

for testing differences between means where there are 3 or more groups, or of 2 or more independent variables

the statistics computed is the F – ratio statistics

Nonparametric Tests are used when the data are nominal or ordinal or when a normal distribution cannot be

assumed

Chi-Square Test ( X2 )• most commonly used statistics with nominal data• primarily used in cross-table analysis and is used when: 1. the dependent variable is a nominal one 2. you wish to determine if frequencies vary across categories 3. the expected frequencies are above 5 in most cells of the table 4. the variables are normally distributed 5. the measures of the variables are independent of one another

Chi-Square Test ( X2 )most commonly used statistics with nominal dataprimarily used in cross-table analysis and is used

when: 1. the dependent variable is a nominal one 2. you wish to determine if frequencies vary

across categories 3. the expected frequencies are above 5 in

most cells of the table 4. the variables are normally distributed 5. the measures of the variables are

independent of one another

Other Nonparametric Tests

Fisher’s Exact Test - when the total sample size is small or when there are cells with o frequencies

McNemar Test - when proportions being compared are from two paired groups

Pearson’s r - calculated when two variables are measured on at least the interval scale, is both descriptive and inferential

Spearman rho - used when the assumptions of Pearson’s analysis cannot be met

Kendall’s Tau - used when both variables have been measured at the ordinal level

Guidelines for Critiquing Inferential Statistics

1. Are inferential statistics presented in the research report?

2. If inferential statistics are present, is enough information presented for the reader to determine whether the appropriate tests were used?

3. Is the reader provided with the calculated value of the inferential statistic, the degree of freedom, and the level of significance that was obtained?

4. Were the parametric or nonparametric tests used when the other type would have been more appropriate?

Guidelines for Critiquing Inferential Statistics contd.

5. Are the chosen tests appropriate considering the level of measurement of the variables, the number of groups that were tested, the size of the sample, etc?

6. Are inferential statistics presented for each hypothesis stated in the study?

7. Are the results of the inferential tests clearly and thoroughly discussed?

8. Are the results presented both in the text and in tables?