Thanks Alex, I will expand this a bit:

if I need to calculate a score for every case (row in SPSS) should I than use "total" or "mean" (or median) score?

For example, if scale has 4 items (questions) and I have values for first respondent:

3, 4, 4, 5. What is best way to calculate scores.

3+4+4+5= sum of items

(3+4+4+5) / 4 = mean

4 = median

The idea is to get scores to calculate correlation between factors. I use likert scale to measure factors, and I need to investigate relations between factors (effect of one factor to another), like for example "use of e-marketing" (F1) on "marketing effectiveness" (F2) where I use likert scales to measure F1 and F2.

Thank you for your time.

Thanks Alex,

yes, I am aware of everything about validity and reliability of scales, and I know whole process I need to do, before I start any inferential statistics data analyze.

I use scales that are already used by others (already tested),  except one scale I developed for measuring "e-marketing use". However, I will test everything with my data. I have 7 scales (for latent variables) and one more variable "e.marketing budget",as percent of total marketing budget.

Question I asked here is part of my broader question: how should I analyze relationships between constructs. As my constructs are measured with likert scales, that's why I asked about scores, "total items score",  "mean" and "median".

Thank you very much for your time.

Kenan

For some variables (qualitative with orientation) the mean doesn't have any signification. in such a case we use Median as a central tendancy indicator. for the case the scale doesn't have an orientation, the estimation of the central tendancy doesn't have also any signification. in this case we can use the Mode (the more frequent value in the observation series)

This may shed some light 

http://stats.stackexchange.com/questions/31139/likert-scale-question-divided-into-different-group-how-to-calculate-mean-of-dif

I would use mean if you have a normal distribution and potentially median if you have a skewed distribution of your Likert findings. When I was doing analyses on SPSS it only allowed to do analyses on the mean anyhow - so I think you may be limited by what SPSS can offer. I maybe outdated though.... 

The advantage of the mean is that it can be located on the original scale. The median of a five-point scale is likely to span a wide range of actual percentile values, so is going to be very inefficient at showing differences between groups.

And as for testing, the t-test has been shown in simulation studies to work well on 5-point scales, so there's another argument for doing t-tests/regressions and reporting the means. 

See 

1. de Winter, J. C., & Dodou, D. (2010). Five-point Likert items: t test versus Mann-Whitney-Wilcoxon. Practical Assessment, Research & Evaluation, 15(11), 1–12.

2. Fagerland, M. W., Sandvik, L., & Mowinckel, P. (2011). Parametric methods outperformed non-parametric methods in comparisons of discrete numerical variables. BMC Medical Research Methodology, 11(1), 44. doi:10.1186/1471-2288-11-44

Dear colleagues, thank you very much for your inputs.

OK, so it seems that "mean score" for all scale items is a way to go. If I understand, after calculating mean scores, I will have to test if distribution is normal? If data is normally distributed, then I can do correlation analysis (Pearson's correlation), otherwise I have to use non-parametric tests. Is this OK?

To connect this to my research model, in simplest situation:

I have 4 constructs C1, C2, C3, C4.

C1, C2, C3 are measured with likert scales. C4 is budget expressed as percentage (ratio data).

What I want to know is:

H1:Higher C1 leads to higher C2? (both variables are scale mean scores)

H2:Higher C4 (ratio data) leads to higher C3 (scale mean score)?

In my other question on researchgate someone proposed me to use gamma statistic for H1, is that acceptable? And what about H2, which statistics to use in this case?

Thank you very much for your time.

I think one could find arguments for mean and also for median.

Additional to the strict mathematical argumentation,  Median could also be appropiate for practical issues, for example if you have some clear outlier  which you do not want to value equal/elliminate.

For ordinal data, the best measure of central tendency should be the mean. This mean is a weighted mean score which combines the scale points with the # of responses for each using a simple formula: mean score = 

For example, if respondents in a survey are asked to score the attributes of several similar products on a 5-point Likert scale: 1-very weak, 2-weak, 3-average, 4-strong and 5-very strong, the mean score of  a product for a particular attribute is given as

MS =   (5n5 + 4n4  +3n3 +2n2 + 1n1)/ (n5 + n4 +n3 + n2 + n1)

 where   n1 = number of respondents who answered  “Very weak”

   n2 = number of respondents who answered  “Weak”

   n3 = number of respondents who answered  “Average”

   n4 = number of respondents who answered  “Strong”

   n5 = number of respondents who answered  “Very strong”

MS can be obtained directly from data entered into SPSS, for example

The mean of the responses to a particular question can be compared to the hypothesised mean of the Likert scale used. For a 5-point Likert scale, for example, the hypothesised mean is the mid-point value of 3. The significant agreement or otherwise with the notion being tested is determined by comparing the mean score with 3 ( see Coakes and Steed, 2001). This implies that any result significantly different from this uncommitted or unsure value of 3 is assumed to be either positive or negative to the notion being tested (Pullin and Haidar, 2003).

References

Coakes, S.J. and Steed, L.G. (2001): SPSS: analysis without anguish. John Wiley & Sons, Milton

Pullin, L. and Haidar, A. (2003): Managerial values in local government – Victoria,

Australia, The International Journal of Public Sector Management, 16(4), 286-302

 thanks, i also need to know if mean is possible with likert scale

With a 1-5 scale, it is hard to make a confident call whether the distribution is 'smmetric'. With a symmetric distribution, the mean and median will be the same. When in doubt, using median would appears to be a more appropriate measure. 

what about if the scale is set with strongly disagree, disagree, undecided, agree and strongly agree? Is it possible to use  mean ?

mean is more appropriate but for a 4 point scale. The Undecided should be remove.

If distribution is not normal, use median. Consider answers: 1,2,2,5,5. Mean=3, median=2. How to report 3. As neutral? However, if you check frequencies, we have 2 x 5 (totally agree), and 3 x not agree. So 40%agree, and 60 % not agree. Its not neutral. Its obviuos that median is more suitable in this case.

if the median is used for Likert scale variable with 5 - points (strongly disagree .... strongly agree), how can you interpret the median? what does 3.75 median mean?

@Amani Alsaqqaf it means that 50% of respondents have scale average higher than 3.75, and 50% below 3.75. 3 is neutral, so it means that more respondents agree than dissagree. If you analyse likert item (not scale) I preffer to sum 1 and 2, and 4 and 5, and than report %, and make conclusion.

Thanks for reply. Iam analysing likert scale variable with more than one items. I found adifferent way of analysing median regarding likert scale, if you could look at it ?

https://community.tableau.com/s/question/0D54T00000C5dwE/calculating-the-median-of-likert-scale-data-that-assumes-that-the-5-point-scale-represents-a-continuous-random-variable

Amani Alsaqqaf Please use some stats package to calculate, like R (open source) or IBM SPSS (commercial), or even sheets calc like excel of google sheets (they all have built-in functions). Honestly, I never do the math manually, if the software is available. How you will use median value (are you trying to calculate median per respondent, or for the whole sample). Many things depend on your research question and on the method you chose to analyze the hypothesis.

We can not use mean for Likert Scale because it does not have any meaning. E.g. how can one calculate mean of Strongly agree and Strongly Disagree? For Likert Scale, the most appropriate method as measure of central tendency is Median or most frequent response.

But somehow, it also depends on how you have asked questions for response.

Hey there Kenan Mahmutovic

why don't you use the Skewness? Negative or Positive one ;)

https://en.wikipedia.org/wiki/Skewness#:~:text=In%20probability%20theory%20and%20statistics,zero%2C%20negative%2C%20or%20undefined.

Ioannis C. Drivas – I've never seen skewness used for anything in real life. Can you link to an actual example where someone interpreted skewness in the course of presenting their results? I'd be really curious.

Median