L7 - Introduction to inferential statistics

Question 1

Measure of central tendency (location)

Answer 1

Mean: average value
Median: exact middle value
Mode: most frequently value

Question 2

Measure of dispersion (variability / spread)

Answer 2

Range and standard deviation

Question 3

Range

Answer 3

• The spread of data - distance between the min and max values of the variable.
• Can use to describe the variability of open-ended questions (Respondents define range by their answers).

Question 4

Standard deviation

Answer 4

Describes the average distance of the distribution values from the mean.
> indicate the usefulness of the mean as typical value.

Question 5

Role of Descriptive analysis

Answer 5

+ Provide summary measures of typical or average values
+ Present data in a digestible format
+ Provide preliminary insights about the distribution of values for each variable
+ Help detect errors in the coding process

Question 6

Population (Malhora, 2010)

Answer 6

the complete set of individuals or objects of interest

Question 7

Sample (Malhora, 2010)

Answer 7

a subset of population from which information is gathered

Question 8

Parameter (Malhora, 2010)

Answer 8

• true value of a variable
• fixed values referring to the population and are unknown
  > It is the same from sample to sample

Question 9

Sample statistic (Malhora, 2010)

Answer 9

• value of a variable that is estimated from a sample.

- it is hoped to be close to parameter of the population of which the sample is a subset.

Question 10

Point estimate (Malhora, 2010)

Answer 10

a single value that is obtained from sample data and is used as the best guess of the corresponding population parameter
> It differs from sample to sample

Question 11

Confidence interval

Answer 11

a range into which the true population parameter will fall, assuming a given level of confidence.
CI = sample statistic +- k * standard error

Question 12

Standard error parameter (k)

Answer 12

value of desired standard errors for the estimate (ex: k = 1.96 for a 95% CI)

Question 13

Hypothesis (Hair, 2017)

Answer 13

an unproven supposition that tentatively explains certain facts or phenomena. It is developed prior to data collection.
> Test are designed to disprove null hypothesis.

Question 14

Null hypothesis

Answer 14

If null hypothesis is accepted, we do not have to change the status quo. If cannot rejecting, conclude that it may be true.

Question 15

Steps in hypothesis testing (slide)

Answer 15

1) Formulate the hypothesis
2) Decide on test, test statistic
3) Select a significance level
4) Statistical decision (reject or not reject)
5) Conclusion

Question 16

Test the hypothesis based on 4 factors:

Answer 16

• Type of hypothesis
• Number of variables
• Scale of measurement
• Distribution assumptions

Question 17

Three types of hypothesis

Answer 17

• Specific population characteristics
• Contrasts / Comparisons
• Associations / Relationships

Question 18

2 types of Distribution assumptions

Answer 18

Parametric (interval scale, normal bell-shaped distribution) and Nonparametric (nominal and ordinal scale) types of statistic.

Question 19

Type of scale use what Appropriate statistic: measure of location, spread and statistics technique

Answer 19

• Nominal: mode, none, Chi-square
• Ordinal: median, percentile, Chi-square
• Interval: mean, standard deviation, t-test and ANOVA

Question 20

Comparing means with Independent vs. Related samples

Answer 20

• Means are from independent samples: (ex: coffee drink of female and male)
• Means are from related samples: (ex: coffee drink and milk tea drink of female) Since the sample is the same, it is called a paired sample.

Question 21

Test statistic

Answer 21

• serves as a decision maker, since the decision to accept or reject Ho depends on its magnitude (how close the sample comes to the Ho)
• an univariate hypothesis test using the t distribution, which is used when the standard deviation is unknown and the sample size is small.

Question 22

Frequency distribution (Malhora, 2013; Hair, 2017)

Answer 22

• a mathematical distribution whose objective is to obtain a count of the number of responses associated with different values of one variable and to express these counts in percentage terms.
• descriptive statistics are used to accomplish this task.

Question 23

Role of frequency distribution (Malhotra, 2013)

Answer 23

• Determine the extent of item nonresponse.
• Indicate the extent of illegitimate responses.
• Detect outlier cases with extreme value.
• Indicate the shape of empirical distribution of the variable. By constructing a histogram, we can examine whether the observed distribution is consistent with the assumed distribution.

Question 24

One-tailed and two-tailed test differences

Answer 24

• It is a one-tailed test because the alternative hypothesis is expressed directionally (<= or >).
• It is a two-tailed test where the alternative hypothesis is not expressed directionally.

Question 25

Type I error

Answer 25

sample result as rejecting null hypothesis when in fact it is true. > Significance level: the probability of making Type I error. ( α = 0.05 )

Question 26

Type II error

Answer 26

sample result as non-rejecting null hypothesis when in fact it is false.

Question 27

Power of a test ( 1 - β )

Answer 27

the probability of rejecting null hypothesis when it is in fact false and should be rejected.

Question 28

p value

Answer 28

the probability of observing a value of the t-test as extreme as the value actually observed, assuming that the null hypothesis is true. ( = α )

Question 29

Reject Ho when:

Answer 29

- l t-test l > l critical value l | - or Probability of t-test < significance level ( α )

Question 30

Coefficient of variation (CV)

Answer 30

- The ratio of the standard deviation to the mean (%). | - It shows the variability in relation to mean of the population.

Question 31

Statistics associated with frequency distribution

Answer 31

Measures of location, Measures of dispersion, Measures of shape

Question 32

Measures of shape

Answer 32

The shape is assessed by examining skewness and kurtosis.

Question 33

Skewness (Malhotra, 2013)

Answer 33

- Assess the distribution’s symmetry about the mean (mode = mean = median). => Skewness - the tendency of the deviations from the mean to be larger in one direction than in the other.

Question 34

Kurtosis (Malhotra, 2013)

Answer 34

- A measure of the relative peakedness or flatness of the curve defined by the frequency distribution. - Normal distribution = 0. More peaked >0. Flatter <0.

Question 35

Calculate t-test

Answer 35

= (sample statistic - hypothesized parameter value) / standard error of the statistic

Question 36

When to use F-test (Malhora, 2010)

Answer 36

In two independent samples test: Using F test as the statistical test of the equality of the variances of two populations.

Question 37

t-distribution

Answer 37

- It is similar to the normal distribution in appearance, but it has more area in the tails and less in the center. - An increase in number of df > 2 similar distributions.